Exploring Cosmic Origins with CORE: Cosmological Parameters

Exploring Cosmic Origins with CORE: Cosmological Parameters

Abstract

We forecast the main cosmological parameter constraints achievable with the CORE space mission which is dedicated to mapping the polarisation of the Cosmic Microwave Background (CMB). CORE was recently submitted in response to ESA’s fifth call for medium-sized mission proposals (M5). Here we report the results from our pre-submission study of the impact of various instrumental options, in particular the telescope size and sensitivity level, and review the great, transformative potential of the mission as proposed. Specifically, we assess the impact on a broad range of fundamental parameters of our Universe as a function of the expected CMB characteristics, with other papers in the series focusing on controlling astrophysical and instrumental residual systematics. In this paper, we assume that only a few central CORE frequency channels are usable for our purpose, all others being devoted to the cleaning of astrophysical contaminants. On the theoretical side, we assume as our general framework and quantify the improvement provided by CORE over the current constraints from the Planck 2015 release. We also study the joint sensitivity of CORE and of future Baryon Acoustic Oscillation and Large Scale Structure experiments like DESI and Euclid. Specific constraints on the physics of inflation are presented in another paper of the series. In addition to the six parameters of the base , which describe the matter content of a spatially flat universe with adiabatic and scalar primordial fluctuations from inflation, we derive the precision achievable on parameters like those describing curvature, neutrino physics, extra light relics, primordial helium abundance, dark matter annihilation, recombination physics, variation of fundamental constants, dark energy, modified gravity, reionization and cosmic birefringence. In addition to assessing the improvement on the precision of individual parameters, we also forecast the post-CORE overall reduction of the allowed parameter space with figures of merit for various models increasing by as much as as compared to Planck 2015, and with respect to Planck 2015 + future BAO measurements.

1,2]Eleonora Di Valentino, 3]Thejs Brinckmann, 4]Martina Gerbino, 3,5]Vivian Poulin, 1]François R. Bouchet, 3]Julien Lesgourgues, 6]Alessandro Melchiorri, 7]Jens Chluba, 3]Sébastien Clesse, 8]Jacques Delabrouille, 9]Cora Dvorkin, 10,84]Francesco Forastieri, 1]Silvia Galli, 3]Deanna C. Hooper, 10,84]Massimiliano Lattanzi, 11]Carlos J. A. P. Martins, 6]Laura Salvati, 6]Giovanni Cabass, 6]Andrea Caputo, 29]Elena Giusarma, 1]Eric Hivon, 10,84]Paolo Natoli, 12]Luca Pagano, 6]Simone Paradiso, 27,28]Jose Alberto Rubiño-Martin, 13,14]Ana Achúcarro, 44]Peter Ade, 21]Rupert Allison, 50]Frederico Arroja, 35]Marc Ashdown, 15,16,17]Mario Ballardini, 51,52]A. J. Banday, 8]Ranajoy Banerji, 18,19,20]Nicola Bartolo, 8]James G. Bartlett, 82,83]Soumen Basak, 53,54]Jochem Baselmans, 21,22]Daniel Baumann, 6]Paolo de Bernardis, 55]Marco Bersanelli, 7]Anna Bonaldi, 69]Matteo Bonato 56]Julian Borrill, 57]François Boulanger, 8]Martin Bucher, 16,17,10]Carlo Burigana, 48,49]Alessandro Buzzelli, 24]Zhen-Yi Cai, 58]Martino Calvo, 59]Carla Sofia Carvalho, 60]Gabriella Castellano, 21,35,61]Anthony Challinor, 58]Ivan Charles, 60]Ivan Colantoni, 6]Alessandro Coppolecchia, 62]Martin Crook, 6]Giuseppe D’Alessandro, 6]Marco De Petris 20]Gianfranco De Zotti, 25]Josè Maria Diego, 2]Josquin Errard, 33]Stephen Feeney, 25]Raul Fernandez-Cobos 26]Simone Ferraro, 16,17]Fabio Finelli, 48,49]Giancarlo de Gasperis, 27,28]Ricardo T. Génova-Santos, 30]Joaquin González-Nuevo, 31,32]Sebastian Grandis, 33]Josh Greenslade, 31,32]Steffen Hagstotz, 65]Shaul Hanany, 34,35]Will Handley, 8]Dhiraj K. Hazra, 39]Carlos Hernández-Monteagudo, 7]Carlos Hervias-Caimapo, 62]Matthew Hills, 37,38]Kimmo Kiiveri, 56]Ted Kisner, 63]Thomas Kitching, 40]Martin Kunz, 37,38]Hannu Kurki-Suonio, 6]Luca Lamagna, 34,35]Anthony Lasenby, 36]Antony Lewis, 18,19,20]Michele Liguori, 37,38]Valtteri Lindholm, 41]Marcos Lopez-Caniego, 6]Gemma Luzzi, 12]Bruno Maffei, 58]Sylvain Martin, 25]Enrique Martinez-Gonzalez, 6]Silvia Masi, 64]Darragh McCarthy, 42]Jean-Baptiste Melin, 31,32,43]Joseph J. Mohr, 10,16,84]Diego Molinari 66]Alessandro Monfardini, 44]Mattia Negrello, 67]Alessio Notari, 6]Alessandro Paiella, 16,17]Daniela Paoletti, 8]Guillaume Patanchon, 6]Francesco Piacentini, 8]Michael Piat, 44]Giampaolo Pisano, 10,84]Linda Polastri, 68,70]Gianluca Polenta, 71,72]Agnieszka Pollo, 73,81]Miguel Quartin, 7]Mathieu Remazeilles, 74]Matthieu Roman, 45]Christophe Ringeval, 8]Andrea Tartari, 55]Maurizio Tomasi, 27]Denis Tramonte, 64]Neil Trappe, 16,17,10]Tiziana Trombetti, 44]Carole Tucker, 37,38]Jussi Väliviita, 78]Rien van de Weygaert, 46]Bartjan Van Tent, 47]Vincent Vennin, 76]Gérard Vermeulen, 25]Patricio Vielva. 48,49]Nicola Vittorio, 65]Karl Young, 79,80]Mario Zannoni,

\affiliation

[1]Institut d’Astrophysique de Paris (UMR7095: CNRS & UPMC-Sorbonne Universités), F-75014, Paris, France \affiliation[2]Sorbonne Universités, Institut Lagrange de Paris (ILP), F-75014, Paris, France \affiliation[3]Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, D-52056 Aachen, Germany. \affiliation[4]The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, AlbaNova, SE-106 91 Stockholm, Sweden \affiliation[5]LAPTh, Université Savoie Mont Blanc & CNRS, BP 110, F-74941 Annecy-le-Vieux Cedex, France. \affiliation[6]Physics Department and Sezione INFN, University of Rome La Sapienza, Ple Aldo Moro 2, 00185, Rome, Italy \affiliation[7]Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester, M13 9PL, U.K. \affiliation[8]APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Observatoire de Paris Sorbonne Paris Cité, 10, rue Alice Domon et Leonie Duquet, 75205 Paris Cedex 13, France \affiliation[9]Department of Physics, Harvard University, Cambridge, MA 02138, USA \affiliation[10]Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, I-44122 Ferrara, Italy \affiliation[11]Centro de Astrofísica da Universidade do Porto and IA-Porto, Rua das Estrelas, 4150-762 Porto, Portugal \affiliation[12]Institut d’Astrophysique Spatiale, CNRS, Univ. Paris-Sud, University Paris-Saclay. 121, 91405 Orsay cedex, France \affiliation[13]Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, 2333 CA, Leiden, The Netherlands \affiliation[14]Department of Theoretical Physics, University of the Basque Country UPV/EHU, 48040 Bilbao, Spain \affiliation[15]DIFA, Dipartimento di Fisica e Astronomia, Alma Mater Studiorum Università di Bologna, Viale Berti Pichat, 6/2, I-40127 Bologna, Italy \affiliation[16]INAF/IASF Bologna, via Piero Gobetti 101, I-40129 Bologna, Italy \affiliation[17]INFN, Sezione di Bologna, Via Irnerio 46, I-40127 Bologna, Italy \affiliation[18]DFA, Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università degli Studi di Padova, Via Marzolo 8, I-131, Padova, Italy \affiliation[19]INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy \affiliation[20]INAF-Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, I-35122 Padova, Italy \affiliation[21]DAMTP, Cambridge University, Cambridge, CB3 0WA, UK \affiliation[22]Institute of Physics, University of Amsterdam, Science Park, Amsterdam, 1090 GL, The Netherlands \affiliation[23]Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California, USA \affiliation[24]CAS Key Laboratory for Research in Galaxies and > Cosmology, Department of Astronomy, University of Science and Technology of China, Hefei, Anhui 230026, China \affiliation[25]IFCA, Instituto de Física de Cantabria (UC-CSIC), Av. de Los Castros s/n, 39005 Santander, Spain \affiliation[26]Miller Institute for Basic Research in Science, University of California, Berkeley, CA, 94720, USA \affiliation[27]Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, La Laguna, Tenerife, Spain \affiliation[28]Departamento de Astrofísica, Universidad de La Laguna (ULL), La Laguna, Tenerife, 38206 Spain \affiliation[29]McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA \affiliation[30]Departamento de Física, Universidad de Oviedo, C. Calvo Sotelo s/n, 33007 Oviedo, Spain \affiliation[31]Universitäts-Sternwarte, Fakultät für Physik, Ludwig-Maximilians Universität München, Scheinerstr. 1, D-81679 München, Germany \affiliation[32]Excellence Cluster Universe, Boltzmannstr. 2, D-85748 Garching, Germany \affiliation[33]Astrophysics Group, Imperial College, Blackett Laboratory, Prince Consort Road, London SW7 2AZ, UK \affiliation[34]Astrophysics Group, Cavendish Laboratory, Cambridge, CB3 0HE, UK \affiliation[35]Kavli Institute for Cosmology, Cambridge, CB3 0HA, UK \affiliation[36]Department of Physics and Astronomy, University of Sussex, Falmer, Brighton, BN1 9QH, UK \affiliation[37]Department of Physics, Gustaf Hallstromin katu 2a, University of Helsinki, Helsinki, Finland \affiliation[38]Helsinki Institute of Physics, Gustaf Hallstromin katu 2, University of Helsinki, Helsinki, Finland \affiliation[39]Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, planta 2, E-44001, Teruel, Spain \affiliation[40]Département de Physique Théorique and Center for Astroparticle Physics, Université de Genève, 24 quai Ansermet, CH–1211 Genève 4, Switzerland \affiliation[41]European Space Agency, ESAC, Planck Science Office, Camino bajo del Castillo, s/n, Urbanización Villafranca del Castillo, Villanueva de la Cañada, Madrid, Spain \affiliation[42]CEA Saclay, DRF/Irfu/SPP, 91191 Gif-sur-Yvette Cedex, France \affiliation[43]Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 85748 Garching, Germany \affiliation[44]School of Physics and Astronomy, Cardiff University, The Parade, Cardiff CF24 3AA, UK \affiliation[45]Centre for Cosmology, Particle Physics and Phenomenology, Institute of Mathematics and Physics, Louvain University, 2 chemin du Cyclotron, 1348 Louvain-la-Neuve, Belgium \affiliation[46]Laboratoire de Physique Théorique (UMR 8627), CNRS, Université Paris-Sud, Université Paris Saclay, Bâtiment 210, 91405 Orsay Cedex, France \affiliation[47]Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth PO1 3FX, United Kingdom \affiliation[48]Dipartimento di Fisica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, I-00133, Roma, Italy \affiliation[49]INFN Roma 2, via della Ricerca Scientifica 1, I-00133, Roma, Italy \affiliation[50]Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, 10617 Taipei, Taiwan (R.O.C.) \affiliation[51]Université de Toulouse, UPS-OMP, IRAP, F-31028 Toulouse Cedex 4, France \affiliation[52]CNRS, IRAP, 9 Av. colonel Roche, BP 44346, F-31028 Toulouse Cedex 4, France \affiliation[53]SRON (Netherlands Institute for Space Research), Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands \affiliation[54]Terahertz Sensing Group, Delft University of Technology, Mekelweg 1, 2628 CD Delft, The Netherlands \affiliation[55]Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy \affiliation[56]Computational Cosmology Center, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA \affiliation[57]IAS (Institut d’Astrophysique Spatiale), Université Paris Sud, Bâtiment 121 91405 Orsay, France \affiliation[58]Univ. Grenoble Alpes, CEA INAC-SBT, 38000 Grenoble, France \affiliation[59]Institute of Astrophysics and Space Sciences, University of Lisbon, Tapada da Ajuda, 1349-018 Lisbon, Portugal \affiliation[60]Istituto di Fotonica e Nanotecnologie, CNR, Via Cineto Romano 42, 00156, Roma, Italy \affiliation[61]Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, UK \affiliation[62]STFC Rutherford Appleton Laboratory, Harwell Campus, Didcot OX11 0QX, UK \affiliation[63]Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Darking, Surrey, RH5 6NT, UK \affiliation[64]Department of Experimental Physics, Maynooth University, Maynooth, County Kildare, W23 F2H6, Ireland

\affiliation

[65]School of Physics and Astronomy, University of Minnesota, 116 Church Street SE, Minneapolis, Minnesota 55455, United States \affiliation[66]Institut Néel CNRS/UGA UPR2940 25, rue des Martyrs BP 166, 38042 Grenoble Cedex 9, France \affiliation[67]Departament de Física Quàntica i Astrofísica i Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain \affiliation[68]Agenzia Spaziale Italiana Science Data Center, via del Politecnico, 00133 Roma, Italy \affiliation[69]Department of Physics & Astronomy, Tufts University, 574 Boston Avenue, Medford, MA, USA \affiliation[70]INAF, Osservatorio Astronomico di Roma, via di Frascati 33, Monte Porzio Catone, Italy \affiliation[71]National Centre for Nuclear Research, ul. Hoza 69, 00-681 Warszawa, Poland \affiliation[72]Astronomical Observatory of the Jagiellonian University, Orla 171, 30-001 Cracow, Poland \affiliation[73]Instituto de Fisica, Universidade Federal do Rio de Janeiro, 21941-972, Rio de Janeiro, RJ, Brazil \affiliation[74]Institut Lagrange, LPNHE, place Jussieu 4, 75005 Paris, France. \affiliation[75]INAF, IASF Milano, Via E. Bassini 15, Milano, Italy \affiliation[76]Institut NEEL CNRS/UGA UPR2940, 25 rue des Martyrs BP 166 38042 Grenoble cedex 9, France \affiliation[77]Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands \affiliation[78]Kapteyn Astronomical Institute, University of Groningen, P.O. Box 800, 9700AV Groningen, The Netherlands \affiliation[79]Dipartimento di Fisica, Università di Milano Bicocca, Milano, Italy \affiliation[80]INFN, sezione di Milano Bicocca, Milano, Italy \affiliation[81]Observatório do Valongo, Universidade Federal do Rio de Janeiro, Ladeira Pedro Antonio 43, 20080-090, Rio de Janeiro, Brazil \affiliation[82]Department of Physics, Amrita School of Arts & Sciences, Amritapuri, Amrita Vishwa Vidyapeetham, Amrita University, Kerala 690525, India \affiliation[83]SISSA, Astrophysics Sector, via Bonomea 265, 34136 Trieste, Italy \affiliation[84]INFN Sezione di Ferrara, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, I-44122 Ferrara, Italy

\emailAdd

bouchet@iap.fr,lesgourg@physik.rwth-aachen.de, alessandro.melchiorri@roma1.infn.it

1 Introduction

In the quarter century since their first firm detection by the COBE satellite [1], Cosmic Microwave Background (CMB) anisotropies have revolutionized the field of cosmology with an enormous impact on several branches of astrophysics and particle physics. From observations made by ground-based experiments such as TOCO [2], DASI [3] and ACBAR [4], balloon-borne experiments like BOOMERanG [5, 6], MAXIMA [7] and Archeops [8], and satellite experiments such as COBE, WMAP [9, 10] and, more recently, Planck [11, 12], a cosmological “concordance” model has emerged, in which the need for new physics beyond the standard model of particles is blatantly evident. The impressive experimental progress in detector sensitivity and observational techniques, combined with the accuracy of linear perturbation theory, have clearly identified the CMB as the “sweet spot” from which to accurately constrain cosmological parameters and fundamental physics. Such a fact calls for new and significantly improved measurements of CMB anisotropies, to continue mining their scientific content.

In particular, observations of the CMB angular power spectrum are not only in impressive agreement with the expectations of the so-called model, based on cold dark matter (CDM hereafter), inflation and a cosmological constant, but they now also constrain several parameters with exquisite precision. For example, the cold dark matter density is now constrained to % accuracy using recent Planck measurements, naively yielding an evidence for CDM at about standard deviations (see [12]). Cosmology is indeed extremely powerful in identifying CDM, since on cosmological scales the gravitational effect of CDM are cleaner and can be precisely discriminated from those of standard baryonic matter. In this respect, no other cosmological observable aside from the CMB could show, if considered alone, the need for CDM to such a level of significance. Moreover, the cosmological signatures of CDM rely mainly on gravity, while astrophysical searches of DM annihilating or decaying into standard model particles depend on the strength of the interaction. Similarly, a possible signal in underground laboratory experiments depends on the coupling between CDM particles and ordinary matter (nuclei and electrons). It is possible to construct CDM models that could interact essentially just through gravity, and the current lack of detection of CDM in underground and astrophysics experiments is leaving this possibility open. If this is the case, structure formation on cosmological scales could result in the best observatory we have where to study the CDM properties, and a further improvement from future CMB measurements will clearly play a crucial and complementary role. The CMB even allows to put bounds on the stability and decay time of CDM through purely gravitational effects [14, 15, 16, 17].

CMB measurements also provide an extremely stringent constraint on standard baryonic matter. The recent results from Planck constrain the baryonic content with a accuracy, nearly a factor better than the present constraints derived from primordial deuterium measurements [18], obtained assuming standard Big Bang Nucleosynthesis. In this respect, the experimental uncertainties on nuclear rates like He that enter in BBN computations are starting to be relevant for accurate estimates of the baryon content from measurements of primordial nuclides. A combination of CMB and primordial deuterium measurements is starting to produce independent bounds on these quantities (see, e.g. [19, 20]). As a matter of fact, a further improvement in the determination of the baryon density is mainly expected from future CMB anisotropy measurements and could help not only in testing the BBN scenario but also in providing independent constraints on nuclear physics.

In this direction, it is also important to stress that CMB measurements are already so accurate that they are able to constrain some aspects of the physics of hydrogen recombination, such as the two photon decay channel transition rate, with a precision higher than current experimental estimates [12]. New CMB measurements can, therefore, considerably improve our knowledge of the physics of recombination. Since primordial Helium also recombines, albeit at higher redshifts, the CMB is sensitive to the primordial He abundance which lowers the free electron number density at recombination. The Planck mission already detected the presence of primordial Helium at the level of standard deviation [12]. Next-generation CMB experiments could significantly improve this measurement, reaching a precision comparable with current direct measurements from extragalactic HII regions that may, however, still be plagued by systematics [21, 22]. Constraining the physics of recombination will also bound the possible presence of extra ionizing photons that could be produced by dark matter self annihilation or decay (see e.g. [Chen & Kamionkowski(2004), Galli et al.(2009), 24, 25, 26]). The Planck 2015 data release already produced significant constraints on dark matter annihilation at recombination that are fully complementary to those derived from laboratory and astrophysical experiments [12].

The CMB is also a powerful probe of the density and properties of “light” particles, i.e. particles with masses below  eV that become non-relativistic between recombination (at redshift , when the primary CMB anisotropies are visible) and today. Such particles may affect primary and secondary CMB anisotropies, as well as structure formation. In particular, this can change the amplitude of gravitational lensing produced by the intervening matter fluctuations ([27]) and leave clear signatures in the CMB power spectra. Neutrinos are the most natural candidate to leave such an imprint (see e.g. [28, 29]). From neutrino oscillation experiments we indeed know that neutrinos are massive and that their total mass summed over the three eigenstates should be larger than  meV in the case of a normal hierarchy and of  meV in the case of an inverted hierarchy (see e.g. [30, 31, 32] for recent reviews of the current data). The most recent constraints from Planck measurements (temperature, polarization and CMB lensing) bound the total mass to  meV [33] at c.l. Clearly, an improvement of the constraint towards a sensitivity of  meV will provide a guaranteed discovery for the neutrino absolute mass scale and for the neutrino mass hierarchy (see e.g. [34, 35, 36, 37]). Neutrinos are firmly established in the standard model of particle physics and a non-detection of the neutrino mass would cast serious doubts on the model, opening the window to new physics in the dark sector, such as, for instance, interactions between neutrinos and new light particles [38]. On the other hand, several extensions of the standard model of particle physics feature light relic particles that could produce effects similar to massive neutrinos, and might be detected or strongly constrained by future CMB measurements. Thermal light axions (see e.g. [39, 40, 41]), for example, can produce very similar effects. Axions change the growth of structure formation after decoupling and increase the energy density in relativistic particles at early times1, parametrized by the quantity . Models of thermal axions will be difficult to accommodate with a value of , and a CMB experiment with a sensitivity of could significantly rule out or confirm their existence. Other possible candidates are light sterile neutrinos and asymmetric dark matter (see e.g. [42, 43, 44] and [45]). More generally, a sensitivity to could rule out the presence of any thermally-decoupled Goldstone boson that decoupled after the QCD phase transition (see e.g. [46]). The same sensitivity would also probe non-standard neutrino decoupling (see e.g. [47]) and the possibility of a low reheating temperature of the order of (MeV) [48].

In combination with galaxy clustering and type Ia luminosity distances, CMB measurements from Planck have also provided the tightest constraints on the dark energy equation of state [12]. In particular, the current tension between the Planck value and the HST value of the Hubble constant from Riess et al. 2016 [49] could be resolved by invoking an equation of state [50]. Planck alone is currently unable to constrain the equation of state and the Hubble constant independently, due to a “geometrical degeneracy” between the two parameters. An improved measurement of the CMB anisotropies could break this degeneracy, produce two independent constraints on and , and possibly resolve the current tension on the value of the Hubble constant. Moreover, modified gravity models have been proposed that could provide an explanation to the current accelerated expansion of our universe. The CMB can be sensitive to modifications of General Relativity through CMB lensing and the late Integrated Sachs-Wolfe (ISW) effect. Current Planck measurements are compatible with certain types of departures from GR (and even prefer such models, albeit at small statistical significance, see [51]). Future CMB measurements are, therefore, extremely important in addressing this issue.

In order to further improve current measurements and provide deeper insight on the nature of dark matter and dark energy, a CMB satellite mission is clearly our ultimate goal. This does, however, raise two fundamental questions. The first one is whether we really need to go to space and launch a new satellite, given that several other ground-based and balloon-borne experiments are under discussion or already under construction (see e.g. [54]). In fifteen years it is certainly reasonable to assume that these experiments will collect excellent data that could, in principle, constrain cosmological parameters to similar precision. However, there is a fundamental aspect to consider: ground-based experiments have very limited frequency coverage and sample just a portion of the CMB sky. Contaminations from unknown foregrounds can be extremely dangerous for ground-based experiments, and can easily fool us. The claimed detection of a primordial Gravitational Waves (GW) background from the BICEP2 experiment [55] was latter ruled out by Planck observations at high frequencies, showing that contaminations from thermal dust in our Galaxy are far more severe than anticipated. This shows that unprecedented control of systematics and a wide frequency coverage are required, both of which call for a space-based mission. In fact, future ground-based and satellite experiments must be seen as complementary: while ground-based experiments could provide a first hint for primordial GWs or neutrino masses, a satellite experiment could monitor the frequency dependence of the corresponding signal with the highest possible accuracy, and unambiguously confirm its primordial nature.

Moreover, most of the future galaxy and cosmic shear surveys will sample several extended regions of the sky. Cross correlations with CMB data in the same sky area will offer a unique opportunity to test for systematics and new physics. It is, therefore, clear that a full sky survey from a satellite will offer much more complete, consistent and homogeneous information than several ground based observations of sky patches. Moreover, an accurate full-sky map of CMB polarisation on large angular scales can provide extremely strong constraints on the reionization optical depth, breaking degeneracies with other parameters such as neutrino masses.

The second fundamental question related to a new CMB satellite proposal arises from the fact that after increasing sensitivity and frequency coverage, one has to deal with the intrinsic limit of cosmic variance. At a certain point, no matter how much we increase the instrumental sensitivity, we reach the cosmic variance limit and stop improving the precision of parameter estimates. This clearly opens the following issue: how close are we from cosmic variance with current CMB data? The Planck satellite measured the temperature angular spectrum up to the limit of cosmic variance in a wide range of angular scales; however, we are far from this limit when we consider polarization spectra. But how much can current constraints improve with a future CMB satellite?

This is exactly the question we want to address in this paper. Assuming that foregrounds and systematics are under control, as should be the case with a well-designed satellite mission, we study by how much current constraints can improve, and find whether these improvements are worth the effort. In this respect, we adopt the proposed baseline experimental configuration of the recent CORE satellite proposal [57], submitted in response to ESA’s call for a Medium-size mission opportunity (M5) as the successor of the Planck satellite. We refer to this experimental configuration (with a  cm mirror) as CORE-M5 in all the next sections of this paper. We compare the results from CORE-M5 with other possible experimental configurations that range from a minimal and less expensive configuration (LiteCORE-80), with a  cm mirror, aimed mainly at measuring large and mid-range angular scale polarization, up to a much more ambitious configuration (COrE+), with a  cm mirror. Given different experimental configurations, we forecast the achievable constraints assuming a large number of possible models, trying to review most of the science that could be extracted from the CORE data (with the exception of constraints on GWs and on inflation, addressed separately in a companion paper [58]). After a description of the analysis method in Section II, we start in Section III by providing the constraints achievable under the context of the concordance model. We then review the constraints that could be obtained on spatial curvature (Section IV), extra relativistic relics (Section V), primordial nucleosynthesis and Helium abundance (Section VI), neutrinos (Section VII), dark energy (Section VIII), extended parameters spaces (Section IX), recombination (Section X), Dark Matter annihilation and decay (Section XI), variation of fundamental constants (Section XII), reionization (Section XIII), modified gravity (Section XIV) and cosmic birefringence (Section XV).

This work is part of a series of papers that present the science achievable by the CORE space mission and focuses on the constraints on cosmological parameters and fundamental physics that can be derived from future measurements of CMB temperature and polarization angular power spectra and lensing. The constraints on inflationary models are discussed in detail in a companion paper [58] while the cosmological constraints from complementary galaxy clusters data provided by CORE are presented in [59]. The impact of CORE on the study of extragalactic sources is presented in [60].

2 Experimental setup and fiducial model

We run Monte Carlo Markhov Chains (MCMC) forecasts for several possible experimental configurations of the CORE CMB satellite, following the commonly used approach described for example in [61] and [62]. The method consists in generating mock data according to some fiducial model. One then postulates a Gaussian likelihood with some instrumental noise level, and fits theoretical predictions for various cosmological models to the mock data, using standard Bayesian extraction techniques. For the purpose of studying the sensitivity of the experiment to each cosmological parameter, as well as parameter degeneracies and possible parameter extraction biases, it is sufficient to set the mock data spectrum equal to the fiducial spectrum, instead of generating random realisations of the fiducial model.

Unless otherwise specified, we choose a fiducial minimal CDM model compatible with the recent Planck 2015 results [33], i.e. with baryon density , cold dark matter density , spectral index , and optical depth . This model also assumes a flat universe with a cosmological constant, neutrinos with effective number (with masses and hierarchy that change according to the case under study), and standard recombination.

We use publicly available Boltzmann codes to calculate the corresponding theoretical angular power spectra , , for temperature, cross temperature-polarization and polarization2. Depending on cases, we use either CAMB3 [63] or CLASS4 [64, 65], which are known to agree at a high degree of precision [66, 67, 68].

In the mock likelihoods, the variance of the “observed” multipoles ’s is given by the sum of the fiducial ’s and of an instrumental noise spectrum given by:

(1)

where is the FWHM of the beam assuming a Gaussian profile and where is the experimental power noise related to the detectors sensitivity by .

As we discussed in the introduction, we adopt as main dataset the one presented for the recent CORE proposal, a complete survey of polarised sky emission in 19 frequency bands, with sensitivity and angular resolution requirements summarized in Table 1.

channel beam PS ()
GHz arcmin .arcmin .arcmin .arcmin kJy/sr.arcmin .arcmin mJy

60
17.87 48 7.5 10.6 6.81 0.75 -1.5 5.0
70 15.39 48 7.1 10 6.23 0.94 -1.5 5.4
80 13.52 48 6.8 9.6 5.76 1.13 -1.5 5.7
90 12.08 78 5.1 7.3 4.19 1.04 -1.2 4.7
100 10.92 78 5.0 7.1 3.90 1.2 -1.2 4.9
115 9.56 76 5.0 7.0 3.58 1.45 -1.3 5.2
130 8.51 124 3.9 5.5 2.55 1.32 -1.2 4.2
145 7.68 144 3.6 5.1 2.16 1.39 -1.3 4.0
160 7.01 144 3.7 5.2 1.98 1.55 -1.6 4.1
175 6.45 160 3.6 5.1 1.72 1.62 -2.1 3.9
195 5.84 192 3.5 4.9 1.41 1.65 -3.8 3.6
220 5.23 192 3.8 5.4 1.24 1.85 - 3.6
255 4.57 128 5.6 7.9 1.30 2.59 3.5 4.4
295 3.99 128 7.4 10.5 1.12 3.01 2.2 4.5
340 3.49 128 11.1 15.7 1.01 3.57 2.0 4.7
390 3.06 96 22.0 31.1 1.08 5.05 2.8 5.8
450 2.65 96 45.9 64.9 1.04 6.48 4.3 6.5
520 2.29 96 116.6 164.8 1.03 8.56 8.3 7.4
600 1.98 96 358.3 506.7 1.03 11.4 20.0 8.5
Array 2100 1.2 1.7 0.41
Table 1: Proposed CORE-M5 frequency channels. The sensitivity is calculated assuming bandwidth, 60% optical efficiency, total noise of twice the expected photon noise from the sky and the optics of the instrument at 40K temperature. This configuration has 2100 detectors, about 45% of which are located in CMB channels between 130 and 220 GHz. Those six CMB channels yield an aggregated CMB sensitivity of K.arcmin (K.arcmin for the full array).

Obviously, data from low (60-115 GHz) and high frequencies (255-600 GHz) channels will be mainly used for monitoring foreground contaminations (and deliver rich related science). In our forecasts we therefore use only the six channels in the frequency range of  GHZ. As stated in the introduction we will refer to this experimental configuration as CORE-M5.

In what follows we also compare the baseline CORE-M5 configuration with other four possible versions: LiteCORE-80, LiteCORE-120, LiteCORE-150 and COrE+. Experimental specifications for these configurations are given in Table 2. We assume that beam uncertainties are small and that uncertainties due to foreground removal are smaller than statistical errors. In Figure 1, for each configuration, we show the variance compared to the fiducial model for the temperature (left) and polarisation (middle) auto-correlation spectra. The data are cosmic-variance-limited up to the multipole at which this variance departs from the fiducial model.

Figure 1: Fiducial model and variance of each data point , given the sensitivity of each CORE configuration (Planck is also shown for comparison). As long as the variance traces the fiducial model, the data is cosmic variance limited. This happens down to different angular scales for the temperature (left) and E-mode polarisation (middle). For CMB lensing extraction (right), on all scales, there is a substantial difference between the noise level of the different configurations.
Channel [GHz] FWMH [arcmin] [K arcmin] [K arcmin]
LiteCORE-80,
195
LiteCORE-120,
LiteCORE-150,
COrE+,
Table 2: Experimental specifications for LiteCORE-80, LiteCORE-120, LiteCORE-150 and COrE+: Frequency channels dedicated to cosmology, beam width, temperature and polarization sensitivities for each channel.

Together with the primary anisotropy signal, we also take into account information from CMB weak lensing, considering the power spectrum of the CMB lensing potential . In what follows we use the quadratic estimator method of Hu & Okamoto [69], that provides an algorithm for estimating the corresponding noise spectrum from the observed CMB primary anisotropy and noise power spectra. Like in [70], we use here the noise spectrum associated to the estimator of lensing, which is the most sensitive one for all CORE configurations (out of all pairs of maps). We occasionally repeated the analysis with the actual minimum variance estimator, and found very similar results. Figure 1 shows that the lensing reconstruction noise is different on all scales for the various configurations.

CORE-M5 is clearly sensitive also to the lensing polarization signal, but here we take the conservative approach to not include it in the forecasts. This leaves open the possibility to use this channel for further checks for foregrounds contamination and systematics. Note that in this work, we consider fiducial models with negligible primordial gravitational waves from inflation. Otherwise, the channel would contain primary signal on large angular scales and could not be neglected. The sensitivity of CORE-M5 to primordial gravitational waves is studied separately and with a different methodology in a companion paper [58].

We generate fiducial and noise spectra with noise properties as reported in Table 2. Once a mock dataset is produced we compare a generic theoretical model through a Gaussian likelihood defined as

(2)

where and are the fiducial and theoretical spectra plus noise respectively, , denote the determinants of the theoretical and observed data covariance matrices respectively,

(3)
(4)

is defined as

(5)

and finally is the sky fraction sampled by the experiment after foregrounds removal.

Note that for temperature and polarization, and could be defined to include the lensed or unlensed fiducial and theoretical spectra, and in both cases the above likelihood is slightly incorrect. If we use the unlensed spectra, we optimistically assume that we will be able to do a perfect de-lensing of the and map, based on the measurement of the lensing map with quadratic estimators. If we use the lensed spectra, we take the risk of double-counting the same information in two observables which are not statistically independent: the lensing spectrum, and the lensing corrections to the , and spectra. To deal with this issue, one could adopt a more advanced formalism including non-Gaussian corrections, like in [72, 73]. However, we performed dedicated forecasts to compare the two approximate Gaussian likelihoods, and even with the best sensitivity settings of COrE+ we found nearly indistinguishable results (at least for the CDM+ model). The reconstructed parameter errors change by negligible amounts between the two cases. The biggest impact is on the error on the sound horizon angular scale , which is 5% smaller when using unlensed spectra, because perfect delensing would allow to better identify the primary peak scales. When using the lensed spectra, we do not observe any statistically significant reduction of the error bars, and we conclude that over-counting the lensing information is not important for an experiment with the sensitivity of COrE+. Hence in the rest of this work we choose to always use the version of the Gaussian likelihood that includes lensed , and spectra. We will usually refer to our full CMB likelihoods with the acronym “TEP”, standing for “Temperature, E-polarisation and lensing Potential data”.

Depending on cases, we derive constraints from simulated data using a modified version of the publicly available Markov Chain Monte Carlo package CosmoMC5 [74], or with the MontePython6 [75] package. With both codes, we normally sample parameters with the Metropolis-Hastings algorithm, with a convergence diagnostic based on the Gelman and Rubin statistic performed. In exceptional cases, we switch the MontePython sampling method to MultiNest [76].

In what follows we consider temperature and polarization power spectrum data up to , due to possible unresolved foreground contamination at smaller angular scales and larger multipoles. We run CAMB+CosmoMC and CLASS+MontePython with enhanced accuracy settings7, including non-linear corrections to the lensing spectrum computed with the latest version of HaloFit [77]. We performed several consistency checks proving that the two pipelines produce identical results.

We also include a few external mock data sets in combination with CORE. For the BAO scale reconstruction, we included a mock likelihood for a high precision spectroscopic survey like DESI (Dark Energy Spectroscopic Instrument [78]). For simplicity, our DESI mock data consists in the measurement of the “angular diameter distance to sound horizon scale ratio”, , at 18 redshifts ranging from 0.15 to 1.85, with uncorrelated errors given by the second column of Table V in [79]. For the matter power spectrum reconstruction, we simulate data corresponding to the tomographic weak lensing survey of Euclid. We used the public euclid_lensing mock likelihood of MontePython, with sensitivity parameters identical to the default settings of version 2.2.2. (matched to the current recommendations of the Euclid science working group). Integrals in wavenumber space are conservatively limited to the range Mpc, to avoid propagating systematic errors from deeply non-linear scales. For simplicity we do not include extra observables from Euclid (galaxy power spectrum, cluster counts, BAO scale…) which would further decrease error bars. Hence we expect our CORE + Euclid forecasts to be very conservative.

3 CDM and derived parameters

3.1 Future constraints from CORE

Adopting the method presented in the previous section, here we forecast the achievable constraints on cosmological parameters from CORE in four configurations: LiteCORE-80, LiteCORE-120, CORE-M5 and COrE+. We work in the framework of the model, that assumes a flat universe with a cosmological constant, and is based on parameters: the baryon and cold dark matter densities, the amplitude and spectral index of primordial inflationary perturbations, the optical depth to reionization , and the angular size of the sound horizon at recombination . Assuming , constraints can be subsequently obtained on “derived” parameters (i.e. that are not varied during the MCMC process) such as the Hubble constant and the r.m.s. amplitude of matter fluctuations on spheres of ; . The CDM model has been shown to be in good agreement with current measurements of CMB anisotropies (see e.g. [12]) and is therefore mandatory to first consider the future possible improvement provided by a CMB satellite experiment such as CORE on the accuracy of its parameters.

Parameter LiteCORE-80, TEP LiteCORE-120, TEP CORE-M5, TEP COrE+, TEP
[km/s/Mpc]
Table 3: Forecasted constraints at c.l. on cosmological parameters assuming standard CDM for the CORE-M5 proposal and for three other possible CORE experimental configurations. The dataset used includes TT, EE, TE angular spectra and information from Planck CMB lensing. The numbers in parenthesis show the improvement with respect to the current constraints coming from the Planck satellite.

Our results are reported in Table 3, where we show the constraints at c.l. on the cosmological parameters from CORE-M5 and we compare the results with three other possible experimental configurations: LiteCORE-80, LiteCORE-120 and COrE+. Besides the standard parameters we also show the constraints obtained on derived parameters such as the Hubble constant and the amplitude of density fluctuations .

3.2 Improvement with respect to the Planck 2015 release

Figure 2: 2D posteriors in the vs plane (left panel) and on the vs plane (right panel) from the recent Planck 2015 data release (temperature and anisotropy) and from the simulated LiteCORE-80, CORE-M5 and COrE+ experimental configurations. CDM is assumed for the CORE simulations. The improvement of any CORE configuration in constraining parameters with respect to Planck is clearly visible.

In Table 3 we also show the improvement in the accuracy with respect to the most recent constraints coming from the TT, TE and EE angular spectra data from the Planck satellite [33] simply defined as . As we can see, even the cheapest configuration of LiteCORE-80 could improve current constraints with respect to Planck by a factor that ranges between , for the scalar spectral index , and , for the density fluctuations amplitude. The most ambitious configuration, COrE+, could lead to even more significant improvements: up to a factor in and up to a factor for , for example. Similar constraints can be achieved by the proposed CORE-M5 configuration. The improvement with respect to current Planck measurements is clearly visible in Figure 2, where we show the 2D posteriors in the vs plane (left panel) and on the vs plane (right panel) from the recent Planck 2015 data release (temperature and polarization) and from the LiteCORE-80, CORE-M5 and COrE+ experimental configurations. These numbers clearly indicate that there is still a significant amount of information that can be extracted from the CMB angular spectra even after the very precise Planck measurements. It is also important to note that the most significant improvements are on two key observables: and the Hubble constant that can be measured in several other independent ways. A precise measurement of these parameters, therefore, offers the opportunity for a powerful test of the standard cosmological model. It should indeed also be noticed that the recent determination of the Hubble constant from observations of luminosity distances of Riess et al. (2016) [49] is in conflict at above standard deviations with respect to the value obtained by Planck (see also [81, 82]). A significantly higher value of the Hubble constant has also recently been reported by the H0LiCOW collaboration [83], from a joint analysis of three multiply-imaged quasar systems with measured gravitational time delays. Furthermore, values of inferred from cosmic shear galaxy surveys such as CFHTLenS [84] and KiDS [85] are in tension above two standard deviations with Planck. While systematics can clearly play a role, new physics has been invoked to explain these tensions (see e.g. [50, 86, 87, 88, 89, 90, 91]) and future and improved CMB determinations of and are crucial in testing this possibility.

3.3 Comparison between the different CORE configurations

Figure 3: 2D posteriors for several combinations of parameters for the LiteCORE-80, CORE-M5 and COrE+ experimental configurations. CDM is assumed as the underlying fiducial model.

It is interesting to compare the results between the different experimental configurations as reported in Table 3 and as we can also visually see in Figure 3, where we show a triangular plot for the 2D posteriors from LiteCORE-80, CORE-M5 and COrE+.

We find four main conclusions from this comparison:

  • When we move from LiteCORE-80 to COrE+ we notice an improvement of a factor on the determination of the baryon density , and an improvement of a factor on the determination of the Hubble constant and the amplitude of matter fluctuations . COrE+ is clearly the best experimental configuration in terms of constraints on these cosmological parameters. However, the CORE-M5 setup provides very similar bounds on these parameters as COrE+, with a degradation in the accuracy at the level of .

  • Moderate improvements are also present for the CDM density (of about ) and the spectral index (). The constraints from CORE-M5 and COrE+ are almost identical on these parameters.

  • The constraints on the optical depth are identical for all four experimental configurations considered. This should not come as a surprise, since is mainly determined by the large angular scale polarization that is measured with almost the same accuracy with all the versions of CORE.

  • Moving from COrE+ to CORE-M5 the maximum degradation on the constraints is about (for the baryon density).

From these results, and considering also the contour plots in Figure 2 and Figure 3 that are almost identical between CORE-M5 and COrE+, we can conclude that CORE-M5, despite having a mirror of smaller size, will produce essentially the same constraints on the parameters with respect to COrE+ with, at worst, a degradation in the accuracy of just .

3.4 Constraints from CORE-M5 and future BAO datasets

Figure 4: 2D posteriors in the vs (left panel) and vs (right panel) planes from Planck (simulated), CORE-M5, and future BAO dataset from the DESI survey. CDM is assumed as the underlying fiducial model.

We have also considered the constraints achievable by a combination of the CORE-M5 data with information from Baryonic Acoustic Oscillation derived from a future galaxy survey as DESI. We found that the inclusion of this dataset will have minimal effect on the CORE-M5 constraints on CDM parameters. This can clearly be seen in Figure 4, where we plot the 2D posteriors in the vs (left panel) and vs (right panel) planes. The CORE-M5 and the CORE+DESI contours are indeed almost identical.

It is also interesting to investigate whether the Planck dataset, when combined with future BAO datasets, could reach a precision on the CDM parameters comparable with the one obtained by CORE-M5. To answer to this question we have simulated the Planck dataset with a noise consistent with the one reported in the 2015 release and combined it with our simulated DESI dataset. The 2D posteriors are reported in Figure 4: as we can see, while the inclusion of the DESI dataset with Planck will certainly help in constraining some of CDM parameters, such as and the CDM density, the final accuracy will not be competitive with the one reachable by CORE-M5. In particular, there will be no significant improvement in the determination of and the baryon density.

4 Constraints on curvature

4.1 Future constraints from CORE

Measuring the spatial curvature of the Universe is one of the most important goals of modern cosmology, since flatness is a key prediction of inflation. A precise measurement of the spatial curvature could, therefore, highly constrain some classes of inflationary models (see e.g. [92, 93, 94]). For example, inflationary models with positive curvature have been proposed in [92], while models with negative spatial curvature have been proposed in [95, 96, 97, 98, 99, 100]. Interestingly, the most recent constraint coming from the Planck 2015 angular power spectra data marginally prefers a universe with positive spatial curvature, with curvature density parameter at CL [12], suggesting a closed universe at about two standard deviations. Moreover, including curvature in the analysis strongly weakens the Planck constraints on the Hubble constant, due to the well know geometric degeneracy (see e.g. [101, 102, 103]). When is varied, the Planck 2015 dataset gives km/s/Mpc at c.l., i.e. a constraint weaker by nearly one order of magnitude with respect to the flat case ( km/s/Mpc at CL [12]).

As shown in [12], the compatibility with a flat universe is restored when the Planck data is combined with the Planck CMB lensing dataset, yielding at c.l.. However, the inclusion of the CMB lensing dataset still provides a quite weak constraint on the Hubble constant of km/s/Mpc at c.l.. It is, therefore, quite important to understand what level of precision can be reached by future CMB data alone on and, subsequently, on the Hubble constant, .

Parameter Planck + lensing LiteCORE 80, TEP LiteCORE120, TEP CORE-M5, TEP COrE+, TEP
[km/s/Mpc]
Table 4:  CL future constraints on cosmological parameters in the CDM + model for four different CORE experimental configurations. A flat universe is assumed as fiducial model. Current constraints from the Planck 2015 release (temperature, polarization and lensing) are also reported in the second column for comparison.

In Table 4 we report the results from our forecasts using CMB data only from four experimental configurations: LiteCORE-80, LiteCORE-120, CORE-M5 and COrE+. As we can see, all configurations are able to constrain curvature with similar accuracy, which is anyway always about a factor better than current constraints coming from Planck angular spectra data (about a factor when compared with Planck+CMB lensing). Future CMB data can, therefore, improve the Planck 2015 constraint on curvature by nearly one order of magnitude. The current best fit Planck value of (see e.g. [12]) can be tested (and falsified) at the level of standard deviations. Constraints on the Hubble constant are also significantly improved: a future CORE mission can provide constraints on the Hubble constant with a accuracy better than km/s/Mpc independently from the assumption of a flat universe. The 2D posteriors on the vs plane are reported in Figure 5 (left panel).

4.2 Future constraints from CORE+DESI

Parameter Planck + lensing LiteCORE 80, TEP LiteCORE120, TEP CORE-M5, TEP COrE+, TEP
+DESI +DESI +DESI +DESI +DESI
[km/s/Mpc]
Table 5:  CL future constraints on cosmological parameters in the CDM + model for four CORE experimental configurations combined with simulated data of the DESI BAO survey. In the second column, for comparison, we also report the constraints from a simulated Planck+DESI dataset. A flat universe is assumed in the simulated data.

Stronger constraints on curvature can be obtained by combining the Planck 2015 data with a combination of BAO measurements. In this case, the constraint is at c.l., and also the Hubble constant is well constrained with km/s/Mpc. The precision of these constraints is very close to the one expected by CMB data alone from CORE and reported in Table 4. It is, therefore, interesting to investigate if a future CORE mission can improve the constraints on with respect to current Planck+BAO constraints.

In Table 5 we indeed present the constraints on including future BAO simulated data assuming the experimental specification of the DESI survey. As we can see, including DESI data significantly shrinks the model space, leading to constraints that are now a factor stronger than the constraints from CORE alone and times more stringent than current Planck+BAO constraints. While, as we saw in the previous section, there is little advantage in combining CORE with future BAO survey in constraining the CDM parameters, a significant improvement is expected on extensions such as .

Figure 5: Left Panel: Constraints on the vs plane from different CORE configurations. Current constraints from Planck+CMB lensing are reported for comparison. Right Panel: Constraints on the vs plane for the following (simulated) datasets: Planck+DESI, LiteCORE80+DESI, CORE-M5+DESI, COrE++DESI. A flat universe is assumed in the simulated data.

We can also see that, once the DESI dataset is included, there is little difference in the constraints on between the CORE configurations. The constraints on the vs plane from COrE+ and DESI are reported in Figure 5 (right panel).

5 Extra relativistic relics

The minimal cosmological scenario predicts that, at least after the time of nucleosynthesis, the density of relativistic particles is given by the contribution of CMB photons plus that of active neutrino species, until they become non-relativistic due to their small mass. This assumption is summarized by the standard value of the effective neutrino number  [104] (see [105] and [106] for pioneering work and [107] for a review of the subject). A more recent calculation beased on the latest data on neutrino physics finds  [108], but at the precision level of CORE the difference is irrelevant, and we will keep 3.046 as our baseline assumption. However, there are many simple theoretical motivations for relaxing this assumption. We know that the standard model of particle physics is incomplete (e.g. because it does not explain dark matter), and many of its extensions would lead to the existence of extra light or massless particles; depending on their interactions and decoupling time the latter could also contribute to . Depending on the context, these extra particles are usually called extra relativistic relics, dark radiation or axion-like particles in more specific cases. In the particular case of particles that were in thermal equilibrium at some point, the enhancement of can be predicted as a function of the decoupling temperature [109]. Even in absence of a significant density of such relics, ordinary neutrinos could have an unexpected density due to non-standard interactions [47], non-thermal production after decoupling [154], or low-temperature reheating [48], leading to a value of larger or smaller than 3.046. There are additional motivations to consider as a free parameter (background of gravitational waves produced by a phase transition, modified gravity, extra dimensions, etc. – see [110] for a review).

Over the last years the extended CDM + has received a lot of attention within the cosmology community. Assuming has the potential to solve tensions in observational data: for instance, internal tensions in pre-Planck CMB data, which have now disappeared ( (68%CL) for Planck 2015 TT,TE,EE+lowP [12]); or tensions between CMB data and direct measurements of  [139] (however, solving this problem by increasing requires a higher value of , which brings further tensions with other datasets [12]). In any case, the community is particularly eager to measure with better sensitivity in the future, in order to: (i) test the existence of extra relics and probe extensions of the standard model of particle physics; (ii) get a window on precision neutrino physics (since the contribution of neutrinos to depends on the details of neutrino decoupling); and (iii) check whether the tensions in cosmological data are related to the relativistic density or not.

Since CMB data accurately determines the redshift of equality , the impact of on CMB observables is usually discussed at fixed  [111, 112, 28]. The time of equality can be kept fixed by simultaneously increasing and the dark matter density (or, depending on the choice of parameter basis, and ). The impact on the CMB is then minimal, which explains the well known (, ) or (, ) degeneracy: the latter is clearly visible with Planck data in Figure 6 (left plot). However, this transformation does not preserve the angular scale of the photon damping scale on the last scattering surface: hence the best probe of comes from accurate measurements of the exponential tail of the temperature and polarisation spectra at high-. Hence the accuracy with which CMB experiments can measure is directly related to their sensitivity and angular resolution, as confirmed by the following forecasts. Increasing has other effects on the CMB coming from gravitational interactions between photons and neutrinos before decoupling: a smoothing of the acoustic peaks (however, very small, and below the per-cent level for variations of the order of ), and a shift of the peaks towards larger angles caused by the “neutrino drag” effect [111, 112, 28]. This means that in order to keep a fixed CMB peak scale, one should decrease the angular size of the sound horizon while increasing : this implies an anti-correlation between and that can be observed in Figure 6 (right plot). Therefore, by accurately measuring , we could get a more robust and model-independent measurement of the sound horizon scale, which would in turn be very useful for constraining the expansion history with BAO data.

Since the parameter is closely related to neutrino properties, and since we know that neutrinos have a small mass, we forecast the sensitivity of different experimental set-ups to while varying simultaneously the summed neutrino mass . This leads to more robust predictions than if we had fixed the mass (although a posteriori we find no significant correlation between and ). We investigate the CORE sensitivity to within two distinct models:

  • The model “CDM + +” has 3 massive degenerate and thermalised neutrino species, plus extra massless relics contributing as . It is motivated by scenarios with standard active neutrinos and extra massless relics (or very light relics with  meV).

  • The model “CDM + + ” only has 3 massive degenerate neutrino species, with fixed temperature, but with a rescaled density. During radiation domination they contribute to the effective neutrino number as , which could be greater or smaller than 3.046. This model provides a rough first-order approximation to specific scenarios in which neutrinos would be either enhanced (e.g. by the decay of other particles) or suppressed (e.g. in case of low-temperature reheating).

Our forecasts consist in fitting these models to mock data, with a choice of fiducial parameters slightly different from the previous section8, including in particular neutrino masses summing up to  meV.

Parameter Planck, TEP LiteCORE-80, TEP LiteCORE-120, TEP CORE-M5, TEP COrE+, TEP
(68%CL) (68%CL) (68%CL) (68%CL) (68%CL)
(meV) (68%CL)
(km/s/Mpc)
Parameter Planck, TEP LiteCORE-80, TEP LiteCORE-120, TEP CORE-M5, TEP COrE+, TEP
+ DESI + DESI + DESI + DESI + DESI
(68%CL) (68%CL) (68%CL) (68%CL) (68%CL)
(meV)
(km/s/Mpc)
Parameter Planck, TEP LiteCORE-80, TEP LiteCORE-120, TEP CORE-M5, TEP COrE+, TEP
+ DESI + Euclid + DESI + Euclid + DESI + Euclid + DESI + Euclid + DESI + Euclid
(68%CL) (68%CL) (68%CL) (68%CL) (68%CL)
(meV)
(km/s/Mpc)
Table 6:  CL constraints on cosmological parameters in the CDM + + model (accounting for standard massive neutrino plus extra massless relics, with ) from the different CORE experimental specifications and with or without external data sets (DESI BAOs, Euclid cosmic shear). For Planck alone, we quote the results from the 2015 data release, while for combinations of Planck with future surveys, we fit mock data with a fake Planck likelihood mimicking the sensitivity of the real experiment (although a bit more constraining).
Parameter Planck, TEP LiteCORE-80, TEP LiteCORE-120, TEP CORE-M5, TEP COrE+, TEP
(meV) (68%CL) (68%CL)
(km/s/Mpc)
Parameter Planck, TEP LiteCORE-80, TEP LiteCORE-120, TEP CORE-M5, TEP COrE+, TEP
+ DESI + DESI + DESI + DESI + DESI
(meV)