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We study gravitational waves induced from the primordial scalar perturbationsat second order around the reheating of the Universe. We consider reheatingscenarios in which a transition from an early matter dominated era to theradiation dominated era completes within a timescale much shorter than theHubble time at that time. We find that an enhanced production of inducedgravitational waves occurs just after the reheating transition because of fastoscillations of scalar modes well inside the Hubble horizon. This enhancementmechanism just after an early matter-dominated era is much more efficient thana previously known enhancement mechanism during an early matter era, and weshow that the induced gravitational waves could be detectable by futureobservations if the reheating temperature $T_{\text{R}}$ is in the range$T_\text{R} \lesssim 7\times 10^{-2}$GeV or $20 \, \text{GeV} \lesssimT_\text{R} \lesssim 2 \times 10^7 \, \text{GeV}$. This is the case even if thescalar perturbations on small scales are not enhanced relative to those onlarge scales, probed by the observations of the cosmic microwave background.

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