Hearing beyond the standard model with cosmic sources of Gravitational Waves

In this talk we will review the dynamics of warm inflation and the effect of dissipation on the primordial spectrum. When inflation occurs in the so-called strong dissipative regime, this effect will lead to the enhancement of the spectrum over all scales. An in particular to large enough fluctuations over the last 10-20 efolds of inflation which on re-entry may form Primordial Black Holes and act as a source for the tensors at second order. We will discuss different realisations consistent with CMB observations, i.e., different combinations of potentials and dissipative coefficients. Typically the enhancement is maximal near the end of inflation, which result in a spectral density of Gravitational Waves (GW) peaked at large frequencies today, in the range of MHz. Although the frequency range is outside the reach of present and planned GW detectors, it might be reached in future high-frequency gravitational waves detectors, designed to search for cosmological stochastic GW backgrounds above MHz frequencies.

We study the impact of Leptogenesis on Gravitational Waves from phase transition. We consider a heavy scalar field that decays into radiation and heavy right-handed neutrinos. These heavy right-handed neutrinos decay eventually and generate the lepton asymmetry. A part of the lepton asymmetry transfers into the baryon asymmetry of the Universe via the sphaleron transitions. We identify the parameter space of Leptogenesis where it maybe probed due to the Gravitational Wave spectral shapes. We show that a Gravitational Wave signal which can be detectable in the low-frequency range of future predictions of LISA that is consistent with Leptogenesis.

When cosmic strings are formed during inflation, they regrow to reach a scaling regime, leaving distinct imprints on the stochastic gravitational wave background (SGWB). Such signatures, associated with specific primordial features, could be detectable by upcoming gravitational wave observatories like LISA, Einstein Telescope (ET), and others. Our analysis explores scenarios where cosmic strings form either before or during inflation. We examine how the number of e-folds experienced by the cosmic strings during inflation correlates with the predictions of inflationary models observable in CMB measurements. This correlation provides a testable link between inflationary physics and associated gravitational wave signals in a complementary manner. Focusing on α-attractor models of inflation,with the Polynomial α-attractor serving as an illustrative example, we find constraints, for instance, on the spectral index ns to 0.962 ≲ ns ≲ 0.972 for n = 1, 0.956 ≲ ns ≲ 0.968 for n = 2, 0.954 ≲ ns ≲ 0.965 for n = 3 and 0.963 ≲ ns ≲ 0.964 for n = 4 which along with the GW signals from LISA are capable of detecting local cosmic strings that have suffered ∼ 34 − 47 e-folds of inflation consistent with current Planck data and also testable in the upcoming CMB experiments like LiteBIRD and CMB-S4.

we investigate the impact of scalar fluctuations ($\chi$) non-minimally coupled to gravity, $\xi\chi^2 R$, as a potential source of secondary gravitational waves (SGWs).
Our study reveals that when reheating EoS $\wre < 1/3$ and $\xi \lesssim 1/6$ or $\wre > 1/3$ and $\xi \gtrsim 1/6$, the super-horizon modes of scalar field experience a \textit{Tachyonic instability}
during the reheating phase. Such instability causes a substantial growth in the scalar field amplitude leading to pronounced production of SGWs in the low and intermediate-frequency ranges that are strong enough to be detected by PLANCK and future gravitational wave detectors. Such growth in super-horizon modes of the scalar field and associated GW production may have a significant effect on the strength of the tensor fluctuation at the Cosmic Microwave Background (CMB) scales (parametrized by $r$) and the number of relativistic degrees of freedom (parametrized by $\dneff$) at the time of CMB decoupling.
To prevent such overproduction, the PLANCK constraints on tensor-to-scalar ratio $r \leq 0.036$ and $\dneff \leq 0.284$ yield a strong lower bound on $\xi$ for $\wre < 1/3$, and upper bound on the value of $\xi$ for $\wre > 1/3$. Taking into account all the observational constraints we found the value of $\xi$ should be $ \gtrsim 0.02$ for $\wre =0$, and $\lesssim 4.0$ for $\wre \geq 1/2$ for a wide range of reheating temperature within $10^{-2} \lesssim \Tre \lesssim 10^{14}$ GeV, and for a wide range of inflationary energy scales. Further, as one approaches $\wre$ towards $1/3$, the value of $\xi$ remains unconstrained. Finally, we identify the parameter regions in $(\Tre,\xi)$ plane which can be probed by the upcoming GW experiments namely BBO, DECIGO, LISA, and ET.

A stochastic gravitational wave background (GWB) produced in the early universe would necessarily exhibit anisotropies analogous to the CMB. In multi-field inflationary scenarios, anisotropies in GWB could differ significantly from those of the CMB if sourced by a quantum field different from the one sourcing CMB. In these scenarios, however, the more interesting case of highly anisotropic GWB typically comes at the cost of suppressed isotropic GWB signal. In this talk, I will present models of modified post-inflationary cosmology in which this tradeoff is made less severe. Such models significantly improve the detection prospects of these highly anisotropic GWBs at future GW experiments.

In these lectures, I discuss how GWs are produced by cosmological phase transitions. We start by a short recap of gravitational waves and then move to early attempts using pairs of bubbles and the envelope approximation. Next we cover the energy budget of phase transitions and the impact of sound waves. Finally I comment on recent developments.