Gravitational waves in minimal Maxwell $f(R)$ gravity

TL;DR

The paper investigates gravitational wave production in minimal Maxwell-coupled $f(R)$ gravity by treating a massive scalaron and massless tensor GWs in a Minkowski background with a constant magnetic field. It derives a scalaron-to-GW conversion mechanism, obtaining a small-$P$ expression $P_{S\rightarrow GW} \approx \frac{\kappa^{4} B^{4} d^{2}}{16 \omega^{2}}$ and showing that the process is unidirectional and highly sensitive to the magnetic field strength. Applying this to early-universe primordial magnetic fields and to magnetar magnetospheres, the authors estimate GW spectra with amplitudes up to $\Omega_{GW} \sim 10^{-12}$ (and down to $10^{-16}$ in some regimes) in frequency bands accessible to future detectors such as DECIGO, BBO, CE, and ET, suggesting a potential observational window for scalaron-induced GWs. The work also discusses the suppression of GW-photon mixing and outlines future extensions including dynamical EM fields, plasma effects, and richer cosmological backgrounds.

Abstract

We discuss the conversion mechanism from scalar field to gravitational waves in magnetic background in $f(R)$ gravity minimal coupled to the Maxwell electrodynamics. Applying the conversion in early universe with primordial magnetic field and the neutron star with strong magnetosphere, the generated gravitational waves, converted from the scalar field, exhibit distinct power spectra which can be potentially probed by future experiments such as DECIGO, BBO, CE and ET.

Figures (1)

• Figure 1: The power spectrum of GWs converted from the scalaron propagating in the primordial magnetic field in early universe (Left) and the strong magnetic field generated by magnetars (Right). The scalaron source is assumed to be in a scale invariant spectrum with density $\Omega_\varphi=0.06 \Omega_\gamma$ in the whole post-inflationary epoch. The converting GW spectra are compared to various experiments with their sensitivity curves obtained from Schmitz:2020syl. The blue shade in right panel denotes the maximum of GW density by varying magnetic strength of the magnetar and effective magnetosphere size. The damping effect is expected to be dominant when $f\lesssim \sqrt{\kappa B_0 m_S}/2 \pi$ (Left) or $f\lesssim \kappa B /2\pi$ (Right), which is schematically shown in dashed lines.