Vector induced Gravitational Waves sourced by Primordial Magnetic Fields
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2025
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| _version_ | 1866908468987822080 |
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| author | Bhaumik, Arko Papanikolaou, Theodoros Ghoshal, Anish |
| author_facet | Bhaumik, Arko Papanikolaou, Theodoros Ghoshal, Anish |
| contents | In this work, we develop a generic formalism for the study of tensor perturbations induced at second order by first-order vector metric perturbations, dubbing these induced tensor modes $\textit{vector-induced gravitational waves}$ (VIGWs). Notably, considering an inflation-inspired power-law type magnetic field power spectrum of the form $P_B(k)\propto k^{n_\mathrm{B}}$ (where $n_{\rm B}$ is the magnetic spectral index), we show that the VIGW signal is enhanced for stiff post-inflationary EoS, with the maximum enhancement happening for $w=1$. We explicitly demonstrate this contribution is dominant over the first-order magnetically-sourced GWs. The VIGW spectrum exhibits a maximum at around the scale crossing the cosmological horizon at the end of reheating, $k_\mathrm{reh}$, with its present day peak amplitude scaling as $Ω_{\rm GW}(k_{\rm reh},η_0)\propto ΔN_{\rm reh}\times(H_{\rm inf}/M_{\rm Pl})^{8}$, where $H_{\rm inf}$ is the Hubble parameter at the end of inflation and $ΔN_{\rm reh}$ the duration of the post-inflationary era in $e$-folds. For $w=1$ (kination) and $n_{\rm B}>-3/2$, one further obtains a nearly $n_{\rm B}$-independent frequency scaling of the GW spectrum of the form $Ω_{\rm GW}(f,η_0)\propto \left(\frac{f}{f_{\rm reh}}\right)^{-2.8}$ for $f>f_\mathrm{reh}\equiv k_\mathrm{reh}/(2π)$. Finally, we highlight that the VIGW signal can be well within the detection bands of several next-generation interferometric GW missions at small scales. Indicatively, for $H_{\rm inf} \sim O(10^{7})\:\mathrm{GeV}$ and $O(10^{14})\:\mathrm{GeV}$, and $ΔN_{\rm reh} \sim 15$ and $10$, the VIGW signal is expected to be detectable by LISA and ET respectively. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_10477 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vector induced Gravitational Waves sourced by Primordial Magnetic Fields Bhaumik, Arko Papanikolaou, Theodoros Ghoshal, Anish Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory In this work, we develop a generic formalism for the study of tensor perturbations induced at second order by first-order vector metric perturbations, dubbing these induced tensor modes $\textit{vector-induced gravitational waves}$ (VIGWs). Notably, considering an inflation-inspired power-law type magnetic field power spectrum of the form $P_B(k)\propto k^{n_\mathrm{B}}$ (where $n_{\rm B}$ is the magnetic spectral index), we show that the VIGW signal is enhanced for stiff post-inflationary EoS, with the maximum enhancement happening for $w=1$. We explicitly demonstrate this contribution is dominant over the first-order magnetically-sourced GWs. The VIGW spectrum exhibits a maximum at around the scale crossing the cosmological horizon at the end of reheating, $k_\mathrm{reh}$, with its present day peak amplitude scaling as $Ω_{\rm GW}(k_{\rm reh},η_0)\propto ΔN_{\rm reh}\times(H_{\rm inf}/M_{\rm Pl})^{8}$, where $H_{\rm inf}$ is the Hubble parameter at the end of inflation and $ΔN_{\rm reh}$ the duration of the post-inflationary era in $e$-folds. For $w=1$ (kination) and $n_{\rm B}>-3/2$, one further obtains a nearly $n_{\rm B}$-independent frequency scaling of the GW spectrum of the form $Ω_{\rm GW}(f,η_0)\propto \left(\frac{f}{f_{\rm reh}}\right)^{-2.8}$ for $f>f_\mathrm{reh}\equiv k_\mathrm{reh}/(2π)$. Finally, we highlight that the VIGW signal can be well within the detection bands of several next-generation interferometric GW missions at small scales. Indicatively, for $H_{\rm inf} \sim O(10^{7})\:\mathrm{GeV}$ and $O(10^{14})\:\mathrm{GeV}$, and $ΔN_{\rm reh} \sim 15$ and $10$, the VIGW signal is expected to be detectable by LISA and ET respectively. |
| title | Vector induced Gravitational Waves sourced by Primordial Magnetic Fields |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2504.10477 |