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

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.