Enhancement of gravitational waves induced by scalar perturbations due to a sudden transition from an early matter era to the radiation era

Abstract

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 matterdominated 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 TR is in the range TR 7 × 10 −2 GeV or 20 GeV TR 2 × 10 7 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.

Gauge independence of induced gravitational waves

“…7 A corollary of this discussion is that the large enhancement of the induced GWs found in Ref. [19], which one may suspect a gauge artifact, is not a gauge artifact. They are produced in a RD era, just after a sudden reheating transition, and the late-time time dependence of I(u, v, x) is that of genuine gravitational waves, i.e.…”

“…Table 1 summarizes the correspondence of the notations in this paper (as well as Refs. [14,18,19,42]) and in Ref. [41].…”

“…Gravitational waves (GWs) are a useful probe of small-scale curvature perturbations [3][4][5][6][7][8] since if the latter is enhanced, a sizable amount of GWs is produced at the second order of the cosmological perturbation. We call it the induced GWs 1 (see early works [9][10][11][12] and recent developments [13][14][15][16][17][18][19][20][21][22]). Such an enhancement of the curvature perturbations are often considered in the context of the primordial black hole (PBH) [23][24][25] (see also Refs.…”

The First Three Seconds: a Review of Possible Expansion Histories of the Early Universe

“…For a sudden transition between MD and RD eras, however, an enhanced production of GWs occurs just after the reheating transition concludes, due to fast oscillations of scalar modes well inside the Hubble horizon as shown in Ref. [978]. They claim that this enhancement mechanism just after an early MD era is in fact much more efficient than any previously known enhancement mechanism during such MD period, leading to a detectable GW signal by BBO/DECIGO if the reheating temperature is in the range T reh < 7 × 10 −2 GeV or 20 GeV < T reh < 2 × 10 7 GeV.…”

Measuring the scalar induced gravitational waves from observations

“…The gauge dependence or independence of induced gravitational waves are discussed in these papers [11][12][13][14][15][16]. The induced gravitational waves in different cosmological backgrounds are explored in [17][18][19][20][21][22][23][24][25]. The induced gravitational waves not only probe the primordial density perturbation spectrum on small scales, but also probe the thermal history of the universe [28][29][30].…”