Université Pierre Et Marie Curie

UniversitéPierre et Marie Curie Sorbonne Universités Ecole´ doctorale de Physique en Île-de-France Institut d'Astrophysique de Paris (IAP) et Institut de Physique Théorique(IPhT) du Commissariat àl'Energie´ Atomique et aux Energies´ Alternatives (CEA) de Saclay Precision cosmology with the large-scale structure of the universe par HélèneDupuy Thèsede doctorat en cosmologie dirigéepar Francis Bernardeau (chercheur CEA, directeur de l'IAP) présentéeet soutenue publiquement le 11/09/2015 devant un jury composéde (par ordre alphabétique): Dr. Francis Bernardeau IAP, CEA Examinateur Dr. Diego Blas CERN (TH-Division) Examinateur Pr. Michael Joyce LPNHE Examinateur Pr. Eiichiro Komatsu Max-Planck-Institut für Rapporteur Astrophysik Pr. Julien Lesgourgues RWTH Aachen University Rapporteur Dr. Jean-Philippe Uzan IAP, CNRS, IHP Invité Contents Introduction4 1 An illustration of what precision cosmology means9 1.1 Is the cosmological principle stringent enough for precision cosmology?9 1.2 Questioning the cosmological principle analytically.......... 12 1.2.1 Redshift, luminosity distance and Hubble diagram...... 12 1.2.2 Misinterpretation of Hubble diagrams............. 13 1.2.3 An idea to test analytically the impact of inhomogeneities.. 15 1.3 Generalities about propagation of light in a Swiss-cheese model... 16 1.3.1 The homogeneous background................. 16 1.3.2 Geometry inside the holes.................... 19 1.3.3 Junction of the two metrics................... 20 1.3.4 Light propagation........................ 23 1.4 Impact of inhomogeneities on cosmology................ 27 1.5 Article \Interpretation of the Hubble diagram in a nonhomogeneous universe"................................. 29 1.6 Article \Can all observations be accurately interpreted with a unique geometry?"................................ 54 1.7 Continuation of this work........................ 60 2 A glimpse of neutrino cosmology 61 2.1 Basic knowledge about neutrinos.................... 61 2.2 Why are cosmologists interested in neutrinos?............. 62 2.2.1 An equilibrium that does not last long............. 63 2.2.2 The effective number of neutrino species, a parameter relevant for precision cosmology..................... 64 1 Contents 2.2.3 Neutrino masses: small but decisive.............. 70 2.3 How cosmic neutrinos are studied.................... 74 2.3.1 Observation............................ 74 2.3.2 Modeling............................. 75 3 Refining perturbation theory to refine the description of the growth of structure 83 3.1 A brief presentation of cosmological perturbation theory....... 84 3.2 The Vlasov-Poisson system, cornerstone of standard perturbation theory................................... 85 3.3 The single-flow approximation and its consequences.......... 87 3.4 Perturbation theory at NLO and NNLO................ 90 3.5 Eikonal approximation and invariance properties........... 92 3.5.1 Eikonal approximation...................... 92 3.5.2 Invariance properties....................... 95 3.6 Perturbation theory applied to the study of massive neutrinos.... 97 4 A new way of dealing with the neutrino component in cosmology 99 4.1 Principle of the method......................... 99 4.2 Derivation of the equations of motion................. 102 4.2.1 Conservation of the number of particles............ 102 4.2.2 Conservation of the energy-momentum tensor......... 104 4.2.3 An alternative: derivation from the Boltzmann and geodesic equations............................. 105 4.3 Comparison with standard results.................... 107 4.3.1 Linearized equations of motion................. 107 4.3.2 Linearized multipole energy distribution............ 109 4.3.3 Initial conditions......................... 110 4.3.4 Numerical tests and discussion on the appropriateness of the multi-fluid approach....................... 113 4.4 Article \Describing massive neutrinos in cosmology as a collection of independent flows"............................ 115 5 Towards a relativistic generalization of nonlinear perturbation theory 141 5.1 Generic form of the relativistic equations of motion.......... 141 2 Contents 5.2 Useful properties in the subhorizon limit................ 142 5.3 Consistency relations........................... 147 5.4 Article \Cosmological Perturbation Theory for streams of relativistic particles"................................. 147 6 A concrete application of the multi-fluid description of neutrinos 168 6.1 Generalized definitions of displacement fields in the eikonal approximation................................... 168 6.2 Impact on the nonlinear growth of structure.............. 170 6.2.1 Qualitative description...................... 170 6.2.2 Quantitative results in the case of streams of massive neutrinos172 6.3 Article \On the importance of nonlinear couplings in large-scale neutrino streams"............................... 174 Conclusions and perspectives 188 Acknowledgments 193 Remerciements 195 Résuméde la thèseen fran¸cais 218 3 Introduction The title of my PhD thesis, \Precision cosmology with the large-scale structure of the universe", encompasses a wide range of searches, all equally exciting. Cosmology is an ancient questioning: understanding what the universe is made of, how it formed, how it evolved since then and what its future is. Yet it is entering a new era, whence the denomination precision cosmology. The investigation method is still the same, i.e. switching back and forth between observations of the sky and formulation of theories, but lately the level of description has amazingly evolved. The twentieth century has been a golden period for cosmology. On the theo- retical side, about a hundred years ago, Albert Einstein's general relativity ([64]) brought the mathematical tools allowing to represent appropriately time and space in a gravitation theory. Soon after appeared the first models based on this theory to describe the structure of the universe and its time evolution. The expansion of the universe has been discovered at the same epoch, jointly thanks to the observations of the astrophysicist Edwin Hubble (carried out and discussed between 1925 and 1929, [94]) and to the relativistic calculations of several theorists, such as Georges Lema^ıtre(in 1927, [103]), Alexandre Friedmann (in 1922, [79]) and Willem de Sitter (in 1917, [53]). A cosmological model naturally emerged from the study of the physics at play in an expanding universe. It is the Big Bang theory, accord- ing to which the universe was born 13.8 billion of years ago (from a process called Big Bang and involving unimaginably high energies) and then progressively cooled down and dilated. In this context, cooling down means dropping from a temperature1 T 1019 ∼ GeV to T 2:73 K. Such different temperatures lead perforce to extremely di- ≈ 1In cosmology, it is common to use the electronvolt as unit of temperature, or more precisely the electronvolt divided by the Boltzmann constant since 1 eV / kB 11604:5 K, kB being the Boltz- 23 2 2 1 ≈ mann constant (kB = 1:3806488 10− m .kg.s− .K− ). In practice, one omits the Boltzmann × constant so that T (K) 11604:5 T (eV). ≈ 4 versified physical processes. The chain of cosmological eras, each characterized by specific physical processes, is called thermal history of the universe. All stages of the thermal history are not equally understood. In particular, understanding mech- anisms involving energies that are not accessible in laboratories is very challenging. Some epochs are thus described very speculatively. Conversely, the Big Bang nu- cleosynthesis and the recombination era are particularly well depicted. The former is the process during which nuclei heavier than the lightest isotope of hydrogen are created thanks to the trapping of protons and neutrons that previously freely evolved in the cosmic plasma (T 1 MeV). The latter refers to the epoch at which ∼ electrons and protons first became bound to form electrically neutral hydrogen atoms (T 3000 K). ∼ One specificity of the Big Bang model is that it predicts the existence of a radiation which started to propagate freely about 380 000 years after the Big Bang. This \cosmic microwave background", detected incidentally in 1964 by the two physicists Arno Penzias and Robert Wilson ([128]), is nothing but the photons that emerged when the temperature of the cosmic plasma became lower than the temperature of ionization of hydrogen. Its detection was such a strong argument in favor of the Big Bang model that this discovery has been awarded the Nobel Prize in 1978. Nowadays, observing and studying carefully the cosmic microwave background is still one of the driving force of cosmology. So far, the Big Bang model has not been ruled out by observations. Rather, each new set of cosmological data provided by exploration of space strengthens the so-called \standard model of cosmology". This model relies on the Big Bang theory and assumes the existence of a cosmological constant, which mimics the acceleration of the expansion of the universe, and of cold dark matter, a form of matter proposed in response to some unexpected observations. More precisely, two observational projects realized in 1998 by the scientific teams headed by the cosmologists Saul Perlmutter, Brian P. Schmidt and Adam Riess showed independently that the expansion of the universe is accelerating ([129, 148]). This breakthrough has been honored with the Nobel Prize in 2011. Gravity being an attractive unstoppable force, astrophysicists originally thought that expansion could only decelerate.

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