Enhancement of Gravitational Waves Induced by Scalar Perturbations due to a Sudden Transition from an Early Matter Era to the Radiation Era

We study gravitational waves induced from the primordial scalar perturbations at second order around the reheating of the Universe. We consider reheating scenarios in which a transition from an early matter dominated era to the radiation dominated era completes within a timescale much shorter than the Hubble time at that time. We find that an enhanced production of induced gravitational waves occurs just after the reheating transition because of fast oscillations of scalar modes well inside the Hubble horizon. This enhancement mechanism just after an early matter-dominated era is much more efficient than a previously known enhancement mechanism during an early matter era, and we show that the induced gravitational waves could be detectable by future observations if the reheating temperature $T_{\text{R}}$ is in the range $T_\text{R} \lesssim 7\times 10^{-2}$GeV or $20 \, \text{GeV} \lesssim T_\text{R} \lesssim 2 \times 10^7 \, \text{GeV}$. This is the case even if the scalar perturbations on small scales are not enhanced relative to those on large scales, probed by the observations of the cosmic microwave background.Comment: 13 pages, 5 figures, v2: minor changes, version accepted for publication in PR

Gravitational Waves Induced by Scalar Perturbations during a Gradual Transition from an Early Matter Era to the Radiation Era

We revisit the effects of an early matter-dominated era on gravitational waves induced by scalar perturbations. We carefully take into account the evolution of the gravitational potential, the source of these induced gravitational waves, during a gradual transition from an early matter-dominated era to the radiation-dominated era, where the transition timescale is comparable to the Hubble time at that time. Realizations of such a gradual transition include the standard perturbative reheating with a constant decay rate. Contrary to previous works, we find that the presence of an early matter-dominated era does not necessarily enhance the induced gravitational waves due to the decay of the gravitational potential around the transition from an early matter-dominated era to the radiation-dominated era.Comment: 14 pages, 5 figures, a minor correction in Eq.(3.9) after the published version which does not affect the result