Primordial black holes and scalar-induced gravitational waves from the generalized Brans-Dicke theory

Abstract

The power spectrum of the scalar-tensor inflation with a quadratic form Ricci scalar coupling function Ω(ϕ) = 1 - 2ϕ/ϕ c + (1 + δ 2)(ϕ/ϕ c )2 can be enhanced enough to produce primordial black holes and generate scalar-induced gravitational waves. The masses of primordial black holes and the frequencies of scalar-induced gravitational waves are controlled by the parameter ϕ c , and their amplitudes are determined by the parameter δ. Primordial black holes with stellar masses, planetary masses, and masses around 10-12 M ⊙ are produced and their abundances are obtained from the peak theory. The frequencies of the corresponding scalar-induced gravitational waves are around 10-9 Hz, 10-6 Hz, and 10-3 Hz, respectively. The primordial black holes with masses around 10-12 M ⊙ can account for almost all of the dark matter, and the scalar-induced gravitational waves with frequencies around 10-9 Hz can explain the NANOGrav 12.5 yrs signal.

Prospects for Taiji to detect a gravitational-wave background from cosmic strings

“…While the PTA window encompasses a wide range of potential sources [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38], the nature of the observed signal, whether it originates from astrophysical phenomena or cosmological processes, remains the subject of ongoing investigation [39][40][41][42][43][44][45][46][47]. The PTA signal can potentially be attributed to various sources [48][49][50][51], such as the SGWB produced by supermassive black hole binaries [52][53][54][55][56], scalar-induced GWs associated with the formation of primordial black holes [81][82][83][84][85][86][87][88][89][90][91][92][93][94][95]...…”

Constant-roll inflation with non-minimally derivative coupling

“…For instance, in the canonical constant-roll inflation with a constant  h f f =f H ̈( ) and η f > 3/2, scalar perturbations outside the horizon continue to evolve [27]. Additionally, the power spectrum of scalar perturbations can exhibit sharp enhancements at small scales in ultra-slow-roll inflation with η f ≈ 3, potentially leading to the formation of primordial black holes and inducing secondary gravitational waves [29][30][31][32][33][34][35][36][37][38][39][40][41]. Despite the differences in the evolution of perturbations between ultra-slow-roll inflation η f = 3 − α and slow-roll inflation η f = α in the canonical inflation model [42], if we neglect the contribution from ò H to the scalar spectral tilt n s , the predictions for the scalar spectral tilt n s and tensor-to-scalar ratio r are the same [43,44].…”