Log-dependent slope of scalar induced gravitational waves in the infrared regions

Abstract

We analytically calculate the scalar induced gravitational waves (SIGWs) and find a log-dependent slope of SIGW in the infrared regions (f < fc), namely nGW(f ) = 3 − 2/ ln(fc/f ), and nGW(f ) = 2 − 2/ ln(fc/f ) near the peak if the power spectrum of scalar curvature perturbation is quite narrow, where fc is roughly the frequency at the peak of SIGW. Such a log-dependent slope can be taken as a new template for distinguishing SIGW from other sources.

Scalar Induced Gravitational Waves Review

“…It should be noted that Equation (111) does not recover the logarithmic correction typical of induced GWs in a radiation dominated universe [79]. The main reason is that we assumed the source term to stop at reheating and, therefore, that superhorizon tensor modes at that time behave as free tensor modes.…”

“…[77]; -Induced GW spectral features: There are cases where the induced GW spectrum may be investigated semi-analytically. These are for example, the low frequency tail [74,78,79], the UV tail [80,81] and the log-normal peak in the primordial spectrum [82]. Furthermore, the primordial spectrum may also present oscillatory features which are captured into the induced GW spectrum [83][84][85][86][87].…”

“…This is because when we eventually match our solution at reheating to a free GW propagating in a radiation dominated universe, the upper limit would be x rh = kτ rh ∼ k/k rh 1. The integrals (80) for x → ∞ are derived by Gervois and Navelet [233] and given in Appendix G. Here we just give the form of (79) after integration, which reads…”

Gauge independence of induced gravitational waves

“…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.…”

Merger history of primordial black-hole binaries

“…These LIGO/Virgo BBHs present a much heavier mass distribution (in particular the sourceframe primary mass of GW170729 event can be as heavy as 50.2 +16.2 −10.2 M [7]) than that inferred from X-ray observations [28][29][30][31], which would challenge the formation and evolution mechanisms of astrophysical black holes. One possible explanation for LIGO/Virgo BBHs is the primordial black holes (PBHs) [8][9][10] formed through the gravitational collapse of the primordial density fluctuations [32,33], which may accompany the induced GWs [34][35][36][37]. On the other hand, PBHs can also be a candidate of cold dark matter (CDM), and the abundance of PBHs in CDM has been constrained by various experiments [34,36,[38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56].…”