Running of the spectral index in deformed matter bounce scenarios with Hubble-rate-dependent dark energy

Abstract

As a deformed matter bounce scenario with a dark energy component, we propose a deformed one with running vacuum model (RVM) in which the dark energy density rho _{Lambda } is written as a power series of H^2 and dot{H} with a constant equation of state parameter, same as the cosmological constant, w=-1. Our results in analytical and numerical point of views show that in some cases same as Lambda CDM bounce scenario, although the spectral index may achieve a good consistency with observations, a positive value of running of spectral index (alpha _s) is obtained which is not compatible with inflationary paradigm where it predicts a small negative value for alpha _s. However, by extending the power series up to H^4, rho _{Lambda }=n_0+n_2 H^2+n_4 H^4, and estimating a set of consistent parameters, we obtain the spectral index n_s, a small negative value of running alpha _s and tensor to scalar ratio r, which these reveal a degeneracy between deformed matter bounce scenario with RVM-DE and inflationary cosmology.