# Stochastic gravitational wave background from accreting primordial black hole binaries during early inspiral stage

## TL;DR

This paper studies the gravitational wave background from accreting primordial black hole binaries in the early universe, highlighting significant correction terms due to rapid mass increase that affect detectability.

## Contribution

It introduces correction terms in gravitational wave amplitude calculations for accreting primordial black hole binaries, showing their importance in the stochastic background.

## Key findings

- Correction terms can dominate the gravitational wave amplitude in certain early universe periods.
- Spectral density from these binaries is within the detection range of current and future detectors.
- Accretion significantly influences the gravitational wave signals from primordial black hole binaries.

## Abstract

We investigate the stochastic gravitational wave background produced by primordial black hole binaries during their early inspiral stage while accreting high-density radiation surrounding them in the early universe. We first show that the gravitational wave amplitude produced from a primordial black hole binary has correction terms because of the rapid rate of increase in masses of the primordial black holes. These correction terms arise due to non-vanishing first and second time derivatives of the masses and their contribution to the overall second time derivative of quadrupole moment tensor. We find that some of these correction terms are not only significant in comparison with the main term but even dominant over the main term for certain ranges of time in the early Universe. The significance of these correction terms is not only for the gravitational wave amplitude produced from an individual PBH-binary, but persists for the overall stochastic gravitational wave background produced from them. We show that the spectral density produced from such accreting primordial black hole binaries lie within the detectability range of some present and future gravitational wave detectors.