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 postinflation reheating phase remains limited due to its small-scale dynamics. Traditional observations, such as those of the cosmic microwave background, 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 wave (GW) spectra, resulting from electromagnetic fields generated during inflation, can offer valuable insights both into the magnetogenesis model and reheating dynamics. We investigate how the spectral shape of GWs varies across different frequency ranges, depending on the model parameters, the magnetogenesis parameters, and reheating dynamics. For this, we consider a well-known nonhelical 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 ($w_{\mathrm{re}}$). We identify spectral breaks in the GW spectra for both $w_{\mathrm{re}}<1/3$ and $w_{\mathrm{re}}>1/3$ 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. Finally, we attempt to constrain the nonhelical models under consideration utilizing the latest NANOGrav 15-year observation campaign. We find that, in order to explain the observed GW spectrum in the nano-Hz range, the required magnetic field spectrum needs to be very stiff. However, such a stiff magnetic field spectrum in turn yields a strongly blue-tilted GW spectrum, which conflicts with other cosmological observations.

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• Cosmology
• Evolution of the Universe
• Gravitational waves
• Inflation
• Primordial magnetic fields