Physics

Gravitation

Cosmological constant

Perturbation (astronomy)

Cosmological perturbation theory

Mathematics

Statistics

Spectral density

Dark energy

Perturbation theory (quantum mechanics)

Primordial black hole

Gravitational wave

Geometry

Cosmology

Quantum electrodynamics

Theoretical physics

Astrophysics

Quantum mechanics

Matter power spectrum

Binary black hole

Scalar (mathematics)

Classical mechanics

International Journal of Modern Physics D

Gravitational waves (GWs) are inevitably produced by second-order terms in cosmological perturbation theory. Most notably, the so-called induced (GWs) are a window to the small scales part of the primordial spectrum of fluctuations and a key counterpart to the primordial black hole (PBH) scenario. However, semi-analytical solutions are only known for matter and radiation domination eras. In this paper, we present new analytic integral formulas for the induced GWs on subhorizon scales in a general cosmological background with a constant equation-of-state. We also discuss applications to a peaked primordial scalar power spectrum and the PBH scenario.

Induced gravitational waves in a general cosmological background