Probing the early universe with future GW observatories

One of the fundamental characteristics of slow roll inflation is its generation of tensor perturbations, which manifest as stochastic gravitational waves (GWs). Slow roll inflation results in a nearly scale-invariant GW spectrum that maintains its scale invariance as it transitions into the radiation-dominated era. However, introducing an intermediate reheating phase can modify the spectral tilt, depending on the equation of state governing that particular epoch. These GWs, especially on smaller scales, are anticipated to be observable by forthcoming GW detectors. In this study, we initially delineate the parameter space encompassing the inflationary energy scale, reheating temperature, and equation of state in a model-independent manner, focusing on the spectra detectable by GW detectors such as LISA, ET, DECIGO, and BBO. We also examine the implications for the $\alpha$-attractor model of inflation and explore the observational constraints on $n_s-r$ prediction in the light of GW detection. Then, we point out the probable ranges for various non-gravitational and gravitational coupling between the inflaton and Standard Model particles considering the perturbative reheating. If one assumes PBHs were formed during the early reheating era, such detection of GW signal also sheds light on the probing PBH parameters. Note that for the case of PBH domination, we also consider the contribution of the induced GWs due to the density fluctuation in PBH distribution, which helps to decode the phase of early PBH domination. Finally, to test the production of other cosmological relics through future GW missions, we consider dark matter produced via gravitational interaction in the early universe.