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.



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