Massive neutrinos and cosmology

Abstract

The present experimental results on neutrino flavour oscillations provide evidence for non-zero neutrino masses, but give no hint on their absolute mass scale, which is the target of beta decay and neutrinoless double-beta decay experiments. Crucial complementary information on neutrino masses can be obtained from the analysis of data on cosmological observables, such as the anisotropies of the cosmic microwave background or the distribution of large-scale structure. In this review we describe in detail how free-streaming massive neutrinos affect the evolution of cosmological perturbations. We summarize the current bounds on the sum of neutrino masses that can be derived from various combinations of cosmological data, including the most recent analysis by the WMAP team. We also discuss how future cosmological experiments are expected to be sensitive to neutrino masses well into the sub-eV range.

Introduction

Neutrino cosmology is a fascinating example of the fecund interaction between particle physics and astrophysics. At the present time, the researchers working on neutrino physics know that the advances in this field need a combined effort in the two areas.

From the point of view of cosmologists, the idea that massive neutrinos could play a significant role in the history of the Universe and in the formation of structures has been discussed for more than thirty years, first as a pure speculation. However, nowadays we know from experimental results on flavour neutrino oscillations that neutrinos are massive. At least two neutrino states have a large enough mass for being non-relativistic today, thus making up a small fraction of the dark matter of the Universe. At a stage in which cosmology reaches high precision thanks to the large amount of observational data, it is unavoidable to take into account the presence of massive neutrinos. In particular, the observable matter density power spectrum is damped on small scales by massive neutrinos. This effect can range from a few per cent for 0.05–0.1 eV masses, the minimal values of the total neutrino mass compatible with oscillation data, up to 10–20% in the limit of three degenerate masses.

From the point of view of particle physicists, fixing the absolute neutrino mass scale (or, equivalently, the lightest neutrino mass once the data on flavour oscillations are taken into account) is the target of terrestrial experiments such as the searches for neutrinoless double beta decay or tritium beta decay experiments, a difficult task in spite of huge efforts and very promising scheduled experiments. At the moment, the best bounds come from the analysis of cosmological data, from the requirement that neutrinos did not wash out too much of the small-scale cosmological structures. Recently the cosmological limits on neutrino masses progressed in a spectacular way, in particular thanks to the precise observation of the cosmic microwave background (CMB) anisotropies by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite, and to the results of a new generation of very deep galaxy redshift surveys. Neutrino physicists look with anxiety at any new development in this field, since in the next years many cosmological observations will be available with unprecedented precision.

At this very exciting moment, which might be preceding a breaking discovery within a few years, our aim is to present here a clear and comprehensive review of the role of massive neutrinos in cosmology, including a description of the underlying theory of cosmological perturbations, a summary of the current bounds and a review of the sensitivities expected for future cosmological observations. Our main goal is to address this manuscript simultaneously to particle physicists and cosmologists: for each aspect, we try to avoid useless jargon and to present a self-contained summary. Compared to recent short reviews on the subject, such as Refs. [1], [2], [3], [4], we tried to present a more detailed discussion. At the same time, we will focus on the case of three flavour neutrinos with masses in accordance with the current non-cosmological data. A recent review on primordial neutrinos can be found in [5], while for many other aspects of neutrino cosmology we refer the reader to [6]. Finally, a more general review on the connection between particle physics and cosmology can be found in [7].

We begin in Section 2 with an introduction to flavour neutrino oscillations, and their implications for neutrino masses in the standard three-neutrino scenario. We also briefly review the limits on neutrino masses from laboratory experiments. Then, in Section 3, we describe some basic properties of the cosmic neutrino background. According to the big bang cosmological model, each of the three flavour neutrinos were in thermal equilibrium in the Early universe, and then decoupled while still relativistic. We review the consequences of this simple assumption for the phase-space distribution and number density of the relic neutrinos, and we summarize how this standard picture is confirmed by observations from big bang nucleosynthesis (BBN) and cosmological perturbations. Finally we explain why neutrinos are expected to constitute a fraction of the dark matter today.

In Section 4, we describe the impact of massive neutrinos on cosmological perturbations. This section is crucial for understanding the rest, since current and future bounds rely precisely on the observation of cosmological perturbations. Although the theory of cosmological perturbations is a very vast and technical topic, we try here to be accessible both to particle physicists willing to learn the field, and to cosmologists willing to understand better the specific role of neutrinos. We introduce the minimal number of concepts, technicalities and equations for understanding the main results related to neutrinos. Still this section is quite long because we wanted to make it self-contained, and to explain many intermediate steps that are usually hidden in most works on the subject.

In Section 4.1, we define the quantities that can be observed, i.e. those that we want to compute. In Section 4.2, we describe the evolution of homogeneous quantities and in Section 4.3 we define the general setup for the theory of cosmological perturbations. Then in Section 4.4 we described in a rather simplified way what the evolution of perturbations would look like in absence of neutrinos. For a cosmologist, these four sections are part of common knowledge and can be skipped. In Section 4.5, we present a detailed description of the impact of neutrinos on cosmological perturbations. This long section is the most technical part of this work, so the reader who wants to avoid technicalities and to know the results can go directly to Section 4.6, for a comprehensive summary of the effects of neutrino masses on cosmological observables.

Then, in Section 5 we review the current existing bounds on neutrino masses, starting from those involving only CMB observations, and then adding different sets of data on the distribution of the large scale structure (LSS) of the Universe, which include those coming from galaxy redshift surveys and the Lyman-$\alpha$ forest. We explain why a unique cosmological bound on neutrino masses does not exist, and why there are significant variations from paper to paper, depending on the data included and the assumed cosmological model.

Finally, in Section 6 we describe the prospects for the next ten or fifteen years. We summarize the forecasts which can be found in the literature concerning the sensitivity to neutrino masses of future CMB experiments, galaxy redshift surveys, weak lensing observations (either from the CMB or from galaxy ellipticity) and galaxy cluster surveys. We conclude with some general remarks in Section 7.