Primordial gravitational waves from spontaneous Lorentz symmetry breaking

Abstract: We study the effect of Spontaneous Lorentz Symmetry Breaking (SLSB) on Primordial Gravitational Waves (PGWs) generated during inflation. The SLSB is induced by a time-like Bumblebee vector field which is non-minimally coupled to the Ricci tensor in the Friedmann-Lema^itre-Robertson-Walker background. The power spectrum and GW amplitude are computed to investigate how Lorentz violation leaves observable imprints. We calculate the GW strain amplitude over frequencies $(10^{-10}~\mathrm{Hz}, 10^4~\mathrm{Hz})$, for a range of the dimensionless Lorentz-violating parameter, $ -10^{-3} \leq l \leq 10^{-4} $, which essentially comes from a slight sensitivity to the equation of state for dark energy. For positive $ l $ values, the amplitude of GW shows a mild suppression compared to the standard cosmological scenario $( l = 0) $. This effect could be observable with detectors like SKA, $\mu$-Ares, and BBO. Conversely, negative $ l $ values amplify the GW amplitude, enhancing detectability by both SKA, $\mu$-Ares, and BBO, as well as by THEIA and DECIGO. Notably, the GW strain amplitude increases by an order of magnitude as $ l $ moves from 0 to $ -10^{-3} $, improving prospects for detection in high-sensitivity detectors like THEIA and DECIGO.