Probing reheating phase via nonhelical magnetogenesis and secondary gravitational waves

In the past two decades, significant advancements have been made in observational techniques to enhance our understanding of the universe and its evolutionary processes. However, our knowledge of the post-inflation reheating phase remains limited due to its small-scale dynamics. Traditional observations, such as those of the Cosmic Microwave Background (CMB), primarily provide insights into large-scale dynamics, making it challenging to glean information about the reheating era. In this paper, our primary aim is to explore how the generation of Gravitational Waves (GWs) spectra, resulting from electromagnetic fields in the early universe, can offer valuable insights into the Reheating dynamics. We investigate how the spectral shape of GWs varies across different frequency ranges, depending on the initial magnetic profile and reheating dynamics. For this, we consider a well-known non-helical magnetogenesis model, where the usual electromagnetic kinetic term is coupled with a background scalar. Notably, for such a scenario, we observe distinct spectral shapes with sufficiently high amplitudes for different reheating histories with the equation of state parametrized by ($w_{\rm re}$). We identify spectral breaks in the GW spectra for both $w_{\rm re}<1/3$ and $w_{\rm re}>1/3$ scenarios. We find that future GW experiments such as BBO, LISA, SKA, and DECIGO are well within the reach of observing those distinct spectral shapes and can potentially shed light on the underlying mechanism of the reheating phase.