We investigate the potential for the eLISA space-based interferometer to detect the stochastic gravitational wave background produced by strong first-order cosmological phase transitions. We discuss the resulting contributions from bubble collisions, magnetohydrodynamic turbulence, and sound waves to the stochastic background, and estimate the total corresponding signal predicted in gravitational waves. The projected sensitivity of eLISA to cosmological phase transitions is computed in a model-independent way for various detector designs and configurations. By applying these results to several specific models, we demonstrate that eLISA is able to probe many wellmotivated scenarios beyond the Standard Model of particle physics predicting strong first-order cosmological phase transitions in the early Universe.

Gravitational waves (GWs) have a great potential to probe cosmology. We review early universe sources that can lead to cosmological backgrounds of GWs. We begin by presenting definitions of GWs in flat space-time and in a cosmological setting, and discussing the reasons why GW backgrounds from the early universe are of a stochastic nature. We recap current observational constraints on stochastic backgrounds, and discuss some of the characteristics of present and future GW detectors including advanced LIGO, advanced Virgo, the Einstein Telescope, KAGRA, LISA. We then review in detail early universe GW generation mechanisms proposed in the literature, as well as the properties of the GW backgrounds they give rise to. We classify the backgrounds in five categories: GWs from quantum vacuum fluctuations during standard slow-roll inflation, GWs from processes that operate within extensions of the standard inflationary paradigm, GWs from post-inflationary preheating and related non-perturbative phenomena, GWs from first order phase transitions (related or not to the electroweak symmetry breaking), and GWs from topological defects, in particular from cosmic strings. The phenomenology of early universe processes that can generate a stochastic background of GWs is extremely rich, and some backgrounds are within the reach of near-future GW detectors. A future detection of any of these backgrounds will provide crucial information on the underlying high energy theory describing the early universe, probing energy scales well beyond the reach of particle accelerators. 157 * Alternatively, the gauge freedom in Lorentz coordinate systems, amounts to 8 free functions depending on the 3 spatial coordinates, determining the initial data hyper-surface. * Another example are e.g. static space-times.†Note that, in this context, one also finds a wave-like equation for the scalar Bardeen potential, * The case of inflation does not verify this condition, but we analyse this later on in the section. * The total entropy of the universe is very large and dominated by the relativistic species: extra entropy production due to known decoupling processes is sub-dominant with respect to the total entropy. * In reality, there is always a small degree of deviation from gaussianity in the inflationary perturbations, as they are created over a dynamical quasi-de Sitter background that also evolves (even if slowly) during inflation [47]. In practice, the amount of non-gaussianity is slow-roll suppressed. * The predictions for 6 Li and 7 Li are in contrast with observations [58,59], and this remains an open problem today. * With this definition we also encompass the possibility that n T is a function of the scale k, even if this is not the case in canonical SFSR scenarios. * An interesting perspective on how much PBH constraints limit the ability of observation of GWs by LISA can be found e.g. in [233] * Otherwise the spectral index would be also contributed by the standard red tilted slow-roll term given by Eq. ( 192), which here is considered negligi...