We review the possible mechanisms for the generation of cosmological magnetic fields, discuss their evolution in an expanding Universe filled with the cosmic plasma and provide a critical review of the literature on the subject. We put special emphasis on the prospects for observational tests of the proposed cosmological magnetogenesis scenarios using radio and gammaray astronomy and ultra high energy cosmic rays. We argue that primordial magnetic fields are observationally testable. They lead to magnetic fields in the intergalactic medium with magnetic field strength and correlation length in a well defined range.We also state the unsolved questions in this fascinating open problem of cosmology and propose future observations to address them.

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

In this paper we compute the quantity which is truly measured in a large galaxy survey. We take into account the effects coming from the fact that we actually observe galaxy redshifts and sky positions and not true spatial positions. Our calculations are done within linear perturbation theory for both the metric and the observer velocities but they can be used for non-linear matter power spectra. We shall see that the complications due to the fact that we only observe on our background lightcone and that we do not truly know the distance of the observed galaxy, but only its redshift is not only an additional difficulty, but even more a new opportunity for future galaxy surveys.Comment: 16 pages, 11 figures; v2: 1 table and 4 figures added showing the ratio between the new contributions and the total angular power spectrum. Accepted for publication in PRD. v3: sign typo corrected in eq. (31

The cosmic microwave background (CMB) is the radiation left over from the Big Bang. Recent analysis of the fluctuations in this radiation has given us valuable insights into our Universe and its parameters. Examining the theory of CMB and recent developments, this textbook starts with a brief introduction to modern cosmology and its main successes, followed by a thorough derivation of cosmological perturbation theory. It then explores the generation of initial fluctuations by inflation. The Boltzmann equation governs the evolution of CMB anisotropies and polarization is derived using the total angular momentum method. Cosmological parameter estimation and the lensing of CMB fluctuations and spectral distortions are also discussed. This textbook is the first to contain a full derivation of the theory of CMB anisotropies and polarization. Ideal for graduate students and researchers in this field, it includes end-of-chapter exercises, and solutions to selected exercises are provided.

Liquid crystals are remarkably useful for laboratory exploration of the dynamics of cosmologically relevant defects. They are convenient to work with, they allow the direct study of the "scaling solution" for a network of strings, and they provide a model for the evolution of monopoles and texture. Experiments described here support the simple "one-scale" model for cosmic string evolution, as well as some qualitative predictions of string statistical mechanics. The structure of monopoles and their apparent cylindrical but not spherical symmetry is discussed. A particular kind of defect known as texture is described and is shown to have a dynamical instability-it can decay into a monopole-antimonopole pair. This decay process has been observed occurring in the liquid crystal, and studied with numerical simulations.

We analytically derive the spectrum of gravitational waves due to magneto-hydrodynamical turbulence generated by bubble collisions in a first-order phase transition. In contrast to previous studies, we take into account the fact that turbulence and magnetic fields act as sources of gravitational waves for many Hubble times after the phase transition is completed. This modifies the gravitational wave spectrum at large scales. We also model the initial stirring phase preceding the Kolmogorov cascade, while earlier works assume that the Kolmogorov spectrum sets in instantaneously. The continuity in time of the source is relevant for a correct determination of the peak position of the gravitational wave spectrum. We discuss how the results depend on assumptions about the unequal-time correlation of the source and motivate a realistic choice for it. Our treatment gives a similar peak frequency as previous analyses but the amplitude of the signal is reduced due to the use of a more realistic power spectrum for the magneto-hydrodynamical turbulence. For a strongly first-order electroweak phase transition, the signal is observable with the space interferometer LISA. * 5.9 for turbulence and K peak * 7

We compute the gravity waves induced by anisotropic stresses of stochastic primordial magnetic fields. The nucleosynthesis bound on gravity waves is then used to derive a limit on the magnetic field amplitude as a function of the spectral index. The obtained limits are extraordinarily strong: If the primordial magnetic field is produced by a causal process, leading to a spectral index nу2 on superhorizon scales, galactic magnetic fields produced at the electroweak phase transition or earlier have to be weaker than B р10 Ϫ27 G. If they are induced during an inflationary phase ͑reheating temperature Tϳ10 15 GeV) with a spectral index nϳ0, the magnetic field has to be weaker than B р10 Ϫ39 G. Only very red magnetic field spectra, nϳϪ3, are not strongly constrained. We also find that a considerable amount of the magnetic field energy is converted into gravity waves. The gravity wave limit derived in this work rules out most of the proposed processes for primordial seeds for the large scale magnetic fields observed in galaxies and clusters.

In this paper we discuss some general aspects of the gravitational wave background arising from post-inflationary short-lasting cosmological events such as phase transitions. We concentrate on the physics which determines the shape and the peak frequency of the gravitational wave spectrum. We then apply our general findings to the case of bubble collisions during a first order phase transition and compare different results in the recent literature.