Strong scale-dependence does not enhance the kinematic boosting of gravitational wave backgrounds
File(s)
Published version
Author(s)
Mentasti, G
Contaldi, CR
Peloso, M
Type
Journal Article
Abstract
Existing expressions in the literature appear to indicate that Doppler boosting, due to our proper motion with respect to the isotropic frame of the universe, can amplify stochastic gravitational wave backgrounds whose energy spectra exhibit strong scale dependence, for example, those generated by large scalar perturbations in models of primordial black holes or by astrophysical populations with broken power-law behaviour. It has been suggested that this enhancement could increase the signal-to-noise ratio of such backgrounds in pulsar timing measurements, as well as in ground- and space-based observatories. We show that the reported enhancement is an artefact of a Taylor expansion of the boosted signal, typically performed in the literature under the assumption of a small boosting parameter. This approximation fails to reproduce the correct result for signals with strong scale dependence. When Doppler boosting is treated exactly, the apparent amplification disappears. Using representative spectra, we demonstrate that Doppler motion induces only blue- and red-shifting by the expected amount; it does not lead to additional amplification or introduce new spectral features. The exact expression for the kinematic boost can and should be easily applied in analysing such backgrounds.
Date Issued
2026-02-01
Date Acceptance
2025-12-01
Citation
Journal of Cosmology and Astroparticle Physics, 2026, 2026 (02)
ISSN
1475-7516
Publisher
IOP Publishing
Journal / Book Title
Journal of Cosmology and Astroparticle Physics
Volume
2026
Issue
02
Copyright Statement
© 2026 The Author(s). Published by IOP Publishing Ltd on behalf of Sissa Medialab. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, https://doi.org/10.1088/1475-7516/2026/02/068 JCAP02(2026)068 journal citation and DOI.
License URL
Publication Status
Published
Date Publish Online
2026-02-18