  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 GW due to the
density function 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.
