Stochastic Limit of Growing Gravitational Wave Memory from Sources in the Early Universe and Astrophysical Sources

TL;DR

This paper demonstrates that the stochastic gravitational wave memory from early universe and astrophysical sources exhibits a growing fractional Brownian motion, providing a new method to identify such signals in observational data and explore conditions after the Big Bang.

Contribution

It introduces a novel model of gravitational wave memory as a growing fractional Brownian motion with Hurst parameter between 1/2 and 1, applicable to cosmological and astrophysical sources.

Findings

Memory grows faster than t, surpassing Brownian motion scaling.

Expansion of the universe enhances gravitational wave memory signals.

Provides a new approach to detect and analyze gravitational wave memory in observational data.

Abstract

We show that the stochastic background of gravitational wave memory of growing type leads to a fractional Brownian motion increasing at the order of $t^{H}$ for large $t$ where $\frac{1}{2} < H <1$. This beats the scaling law of Brownian motion. In this article we investigate sources of gravitational waves in the early universe as well as in astrophysical settings. Cosmological sources may include primordial black holes or other sources immediately after the Big Bang when there were pockets of hot material, and large density fluctuations. Gravitational waves from mergers of primordial black holes produce memory. We show that due to the conditions in which these are taking place the gravitational wave memory will be increasing in time following a certain power law. Corresponding results hold for any gravitational wave memory from a cosmological source where the surrounding conditions are similar. The stochastic limit of these memories is a stochastic process growing in time faster than the $\sqrt{t}$ scaling law of Brownian motion. The latter is also typical for noise and for the limit of memory events as they have been mostly considered in the literature. In an expanding universe, the memory is enhanced by the expansion itself. Our results provide a tool to extract gravitational wave sources of this type from data using this memory signature. This would be particularly useful for the PTA data that has been already observed, answering the long-standing question on how to extract memory signals from the data. Further, the new results open up a new door to explore the conditions right after the Big Bang using the long-range dependence and further probability analysis.