Gravitational wave signatures from reheating in axion-Chern-Simons running-vacuum cosmology

Within the context of a axion-Chern-Simons running-vacuum-model (RVM) cosmology, one expects an early matter dominated (eMD) reheating period after RVM inflation driven by the axion field. Treating thus in this work Chern-Simons RVM cosmology as an effective $f(R)$ gravity theory characterized by logarithmic corrections of the spacetime curvature, we study the gravitational-wave (GW) signal induced by the nearly scale invariant inflationary adiabatic curvature perturbations during the transition from the eMD era driven by the axion to the late radiation-dominated era. Remarkably, by accounting for the extra GW scalaron polarization present within $f(R)$ gravity theories, we find regions in the parameter space of the theory where one is met with a distinctive induced GW signal with a universal ${f}^{6}$ high-frequency scaling compared to the ${f}^{7}$ scaling present in general relativity (GR). In particular, for axion masses ${m}_{a}$ higher than 1 GeV and axion gauge couplings ${f}_{a}$ above ${10}^{\ensuremath{-}3}$ reduced Planck masses, one can produce induced GW spectra within the sensitivity bands of future GW observatories such as the Einstein Telescope (ET), the Laser Interferometer Space Antenna (LISA), the Big Bang Observer (BBO) and the Square Kilometer Arrays (SKA).