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...

We study the details of preheating in an inflationary scenario in which the standard model Higgs, strongly nonminimally coupled to gravity, plays the role of the inflaton. We find that the Universe does not reheat immediately through perturbative decays, but rather initiates a complex process in which perturbative and nonperturbative effects are mixed. The Higgs condensate starts oscillating around the minimum of its potential, producing W and Z gauge bosons nonperturbatively, due to violation of the socalled adiabaticity condition. However, during each semioscillation, the created gauge bosons partially decay (perturbatively) into fermions. The decay of the gauge bosons prevents the development of parametric resonance, since bosons cannot accumulate significantly at the beginning. However, the energy transferred to the decay products of the bosons is not enough to reheat the Universe, so after about a hundred oscillations, the resonance effects will eventually dominate over the perturbative decays. Around the same time (or slightly earlier), backreaction from the gauge bosons into the Higgs condensate will also start to be significant. Soon afterwards, the Universe is filled with the remnant condensate of the Higgs and a nonthermal distribution of fermions and bosons (those of the standard model), which redshift as radiation and matter, respectively. We compute the distribution of the energy budget among all the species present at the time of backreaction. From there until thermalization, the evolution of the system is highly nonlinear and nonperturbative, and will require a careful study via numerical simulations.

Abstract. We investigate the potential for the LISA space-based interferometer to detect the stochastic gravitational wave background produced from different mechanisms during inflation. Focusing on well-motivated scenarios, we study the resulting contributions from particle production during inflation, inflationary spectator fields with varying speed of sound, effective field theories of inflation with specific patterns of symmetry breaking and models leading to the formation of primordial black holes. The projected sensitivities of LISA are used in a model-independent way for various detector designs and configurations. We demonstrate that LISA is able to probe these well-motivated inflationary scenarios beyond the irreducible vacuum tensor modes expected from any inflationary background.-1 -

We present a set of tools to assess the capabilities of LISA to detect and reconstruct the spectral shape and amplitude of a stochastic gravitational wave background (SGWB). We first provide the LISA power-law sensitivity curve and binned power-law sensitivity curves, based on the latest updates on the LISA design. These curves are useful to make a qualitative assessment of the detection and reconstruction prospects of a SGWB. For a quantitative reconstruction of a SGWB with arbitrary power spectrum shape, we propose a novel data analysis technique: by means of an automatized adaptive procedure, we conveniently split the LISA sensitivity band into frequency bins, and fit the data inside each bin with a power law signal plus a model of the instrumental noise. We apply the procedure to SGWB signals with a variety of representative frequency profiles, and prove that LISA can reconstruct their spectral shape. Our procedure, implemented in the code SGWBinner, is suitable for homogeneous and isotropic SGWBs detectable at LISA, and it is also expected to work for other gravitational wave observatories.

The reheating of the universe after hybrid inflation proceeds through the nucleation and subsequent collision of large concentrations of energy density in the form of bubble-like structures moving at relativistic speeds. This generates a significant fraction of energy in the form of a stochastic background of gravitational waves, whose time evolution is determined by the successive stages of reheating: First, tachyonic preheating makes the amplitude of gravity waves grow exponentially fast. Second, bubble collisions add a new burst of gravitational radiation. Third, turbulent motions finally sets the end of gravitational waves production. From then on, these waves propagate unimpeded to us. We find that the fraction of energy density today in these primordial gravitational waves could be significant for GUT-scale models of inflation, although well beyond the frequency range sensitivity of gravitational wave observatories like LIGO, LISA or BBO. However, low-scale models could still produce a detectable signal at frequencies accessible to BBO or DECIGO. For comparison, we have also computed the analogous gravitational wave background from some chaotic inflation models and obtained results similar to those found by other groups. The discovery of such a background would open a new observational window into the very early universe, where the details of the process of reheating, i.e. the Big Bang, could be explored. Moreover, it could also serve in the future as a new experimental tool for testing the Inflationary Paradigm.