Observable Gravitational Waves from Hyperkination in Palatini Gravity and Beyond

TL;DR

This paper explores how a period of hyperkination in Palatini gravity affects primordial gravitational wave spectra, potentially making them observable without disrupting Big Bang Nucleosynthesis.

Contribution

It introduces the concept of hyperkination driven by quartic kinetic terms in Palatini gravity and analyzes its impact on gravitational wave spectra.

Findings

Hyperkination truncates the gravitational wave spectrum peak.

Kinetic domination enhances the gravitational wave amplitude.

Observable gravitational wave signals are possible within parameter space.

Abstract

We consider cosmology with an inflaton scalar field with an additional quartic kinetic term. Such a theory can be motivated by Palatini $R+R^2$ modified gravity. Assuming a runaway inflaton potential, we take the Universe to become dominated by the kinetic energy density of the scalar field after inflation. Initially, the leading kinetic term is quartic and we call the corresponding period hyperkination. Subsequently, the usual quadratic kinetic term takes over and we have regular kination, until reheating. We study, both analytically and numerically, the spectrum of primordial gravitational waves generated during inflation and re-entering the horizon during the subsequent eras. We demonstrate that the spectrum is flat for modes re-entering during radiation domination and hyperkination and linear in frequency for modes re-entering during kination: kinetic domination boosts the spectrum, but hyperkination truncates its peak. As a result, the effects of the kinetic period can be extended to observable frequencies without generating excessive gravitational waves, which could otherwise destabilise the process of Big Bang Nucleosynthesis. We show that there is ample parameter space for the primordial gravitational waves to be observable in the near future. If observed, the amplitude and `knee' of the spectrum will provide valuable insights into the background theory.