The detectability of cosmological gravitational-wave backgrounds: a rule of thumb

TL;DR

This paper proposes a practical rule of thumb for estimating the maximum energy density of cosmological gravitational-wave backgrounds across different frequencies, aiding future gravitational-wave observations of the early universe.

Contribution

It introduces a new heuristic guideline for the maximum energy density of primordial gravitational-wave backgrounds based on cosmological scenarios.

Findings

Most cosmological backgrounds have peak energy densities below 10^{-12}

The rule of thumb applies across multiple frequency bands

Implications for future gravitational-wave detection strategies

Abstract

The recent claim by BICEP2 of evidence for primordial gravitational waves from inflation has focused interest on the potential for early-Universe cosmology using observations of gravitational waves. In addition to cosmic microwave background detectors, efforts are underway to carry out gravitational-wave astronomy over a wide range of frequencies including pulsar timing arrays (nHz), space-based detectors (mHz), and terrestrial detectors ($\sim$10-2000 Hz). This multiband effort will probe a wide range of times in the early Universe (each corresponding to a different energy scale), during which gravitational-wave backgrounds may have been produced through processes such as phase transitions or preheating. In this letter, we derive a rule of thumb (not quite so strong as an upper limit) governing the maximum energy density of cosmological backgrounds. For most cosmological scenarios, we expect the energy density spectrum to peak at values of $\Omega_\text{gw}(f)\lesssim10^{-12\pm2}$. We discuss the applicability of this rule of thumb and the implications for gravitational-wave astronomy.