Minimal-supersymmetric extended inflation field in Horava–Lifshitz gravity

Abstract

We study the Friedmann inflation in general covariant Horava–Lifshitz gravity (HLG) without the projectability conditions and with detailed and nondetailed balance conditions. Accordingly, we derive modifications in the Friedmann equations due to a single-scalar field potential describing minimal-supersymmetrically extended inflation. By implementing two time-independent equations of state (EoS) characterizing the cosmic background geometry filled up with dark energy, the dependence of the tensorial and scalar density fluctuations and their ratios on the inflation field are determined. The latter refers to the time evolution of the inflationary field relative to the Hubble parameter. Furthermore, the ratios of tensorial-to-spectral density fluctuations are calculated in dependence on the spectral index. For cold dark energy EoS [Formula: see text], we find that the tensorial-to-spectral density fluctuations are not depending on the different theories of gravity and the results are very small relative to the recent BICEP2/Keck Array-Planck observations, [Formula: see text]. We have also calculated the tensorial and scalar perturbations of the primordial spectra.