2019/11/21 by Chiara M. F. Mingarelli, Mingarelli, Chiara M. F., Stephen R. Taylor +5
Earth and Planetary Sciences · Physics and Astronomy · #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Gravity Measurements #Pulsars and Gravitational Waves Research
paper · doi:10.48550/arxiv.1911.09745
openalex publication_date 2019/11/21 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
In this paper we provide a comprehensive derivation of the energy density in the stochastic gravitational-wave background Ωgw(f), and show how this quantity is measured in ground-based detectors such as Laser Interferometer Gravitational-Wave Observatory (LIGO), space-based Laser Interferometer Space Antenna (LISA), and Pulsar Timing Arrays. By definition Ωgw(f) ∝ Sh(f) -- the power spectral density (PSD) of the Fourier modes of the gravitational-wave background. However, this is often confused with the PSD of the strain signal, which we call Sgw(f), and is a detector-dependent quantity. This has led to confusing definitions of Ωgw(f) in the literature which differ by factors of up to 5 when written in a detector-dependent way. In addition to clarifying this confusion, formulas presented in this paper facilitate easy comparison of results from different detector groups, and how to convert from one measure of the strength of the background (or an upper limit) to another. Our codes are public and on GitHub.