Running of the Spectral index in Deformed Matter Bounce Scenarios with Hubble-rate-dependent Dark Energy

TL;DR

This paper explores a deformed matter bounce cosmological model with a running vacuum dark energy component, analyzing its spectral index and running to compare with inflationary predictions and observational data.

Contribution

It introduces a deformed matter bounce scenario with a Hubble-rate-dependent dark energy modeled as a power series, extending previous models to include higher-order terms for better observational consistency.

Findings

Spectral index can match observations in some cases.

Positive running of the spectral index is obtained, conflicting with inflation.

Including H^4 terms yields a small negative running and tensor-to-scalar ratio.

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 is written as a power series of $H^2$ and $\dot H$ with a constant equation of state parameter same as the cosmological constant. Our results in analytical and numerical point of views show that in some cases same as LCDM bounce scenario, although the spectral index may achieve a good consistency with observations, a positive value of running of spectral index 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 reval a degeneracy between deformed matter bounce scenario with RVM-DE and inflationary cosmology.