Vector induced gravitational waves sourced by primordial magnetic fields

Authors

• Arko Bhaumik, Indian Statistical Institute, Kolkata
• Theodoros Papanikolaou, Scuola Superiore Meridionale
• Anish Ghoshal, University of Warsaw

Article Type

Research Article

Publication Title

Journal of Cosmology and Astroparticle Physics

Abstract

In this work, we develop a generic formalism for the study of cosmological tensor perturbations induced at second order by first-order vector metric perturbations, dubbing these induced tensor modes vector-induced gravitational waves (VIGWs). In the presence of an active source such as primordial magnetic fields (PMFs), the vector perturbations of the metric do not necessarily decay rapidly with Hubble expansion, but may remain significantly large in amplitude depending upon the background equation-of-state (EoS) parameter, w, during reheating. Considering an inflation-inspired PMF power spectrum of the power-law form PB (k) ∝ k ^{n B} (where n B is the magnetic spectral index), we show that the VIGW signal is enhanced for a stiff post-inflationary EoS, with the maximum enhancement happening for w = 1 (kination). The VIGW spectrum exhibits a maximum around the scale crossing the cosmological horizon at the end of reheating, k reh, while its present day peak amplitude scales as ΩGW(k reh,η 0) ∝ [10^{ΔN reh}(H inf/M Pl)]⁸, where H inf is the Hubble parameter at the end of inflation and ΔN reh is the duration of the post-inflationary era in e-folds. For w = 1 and n B > -3/2, one further obtains a nearly n B-independent frequency scaling of the GW spectrum of the form ΩGW(f,η 0) ∝ (f/f reh)^-2.8 for f > f reh ≡ k reh/(2π). We also explicitly demonstrate that the VIGW spectrum is dominant over that of the first-order magnetically-sourced GWs from the reheating era. Finally, it is highlighted that the VIGW signal may lie well within the detection bands of several next-generation interferometric GW missions at small scales. Indicatively, for H inf ∼ O(10⁷) GeV and O(10¹⁴) GeV, and ΔN reh ∼ 15 and 10, the VIGW signal is found to be detectable by LISA and ET respectively.

DOI

10.1088/1475-7516/2025/08/054

Publication Date

8-1-2025

Recommended Citation

Bhaumik, Arko; Papanikolaou, Theodoros; and Ghoshal, Anish, "Vector induced gravitational waves sourced by primordial magnetic fields" (2025). Journal Articles. 5658.
https://digitalcommons.isical.ac.in/journal-articles/5658