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 $\Omega (\varphi )=1-2\varphi /{\varphi }_c+(1+{\delta }^2)(\varphi /{\varphi }_c{)}^2$ 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 ${\varphi }_c$, and their amplitudes are determined by the parameter $\delta$. Primordial black holes with stellar masses, planetary masses, and masses around $10^{-12}{M}_{\odot }$ 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 $10^{-12}{M}_{\odot }$ 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 12.5yrs signal.

arXiv comment26 pages, 3 figures

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