Gravitational waves induced by scalar perturbations as probes of the small-scale primordial spectrum

Abstract

Compared to primordial perturbations on large scales, roughly larger than 1 megaparsec, those on smaller scales are not severely constrained. We revisit the issue of probing small-scale primordial perturbations using gravitational waves (GWs), based on the fact that, when large-amplitude primordial perturbations on small scales exist, GWs with relatively large amplitudes are induced at second order in scalar perturbations, and these induced GWs can be probed by both existing and planned gravitational-wave projects. We use accurate methods to calculate these induced GWs and take into account sensitivities of different experiments to induced GWs carefully, to report existing and expected limits on the small-scale primordial spectrum.

Gauge independence of induced gravitational waves

“…7 We also comment on the gauge dependence from the viewpoint of the diffusion damping [45], which occurs on small scales, since many authors focus on the GWs induced by the small-scale scalar perturbations (often in the context of PBHs). After inducing GWs, the small-scale pertur- 6 Note that u and v cannot be small simultaneously because of momentum conservation: see the integration region in Eq. (3).…”

“…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]).…”

Scalar induced gravitational waves in inflation with gravitationally enhanced friction

“…Here Θ is the Heaviside theta function. Between the energy spectra of the induced GWs at present and at η c there exists a relation [20] Ω GW,0 h 2 = 0.83 g c 10.75…”

Primordial black hole formation in inflationary α -attractor models

“…where u = (t + s + 1)/2, v = (t − s + 1)/2 and x = kτ. The function I 2 RD (v, u, x) is expressed in terms of a rather complicated combination of terms, the exact form of which can be found in [58,59]. Although the integral can be simplified if the P R (k) are modelled using lognormal distributions, the second order tensor power spectrum is computed exactly using the curvature power spectra data obtained by solving the Mukhanov-Sasaki equation.…”