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.Comment: 27 pages, 6 figure

Exploring Modifications to FLRW Cosmology with General Entropy and Thermodynamics: A new Approach

This paper investigates modifications to the FLRW cosmology resulting from considering general entropy for the cosmological apparent horizon. Although the Bekenstein-Hawking entropy has been successful in the study of the thermodynamics of black holes and cosmology, according to the laws of thermodynamics, considering this entropy, it imposes a $w=-1$ limit on the equation of state of the cosmic fluid. To address this limitation, Nojiri and colleagues in 2022, introduced generalized entropies with four-parameters that may tend to familiar entropies and can solve some problems of cosmology. In this paper, we explore how correcting the entropy affects the Energy-momentum tensor of the cosmic flux from the outset. Our calculations show that in any way, the modified Bekenstein-Hawking entropy can be still considered as a general entropy after a modification energy-momentum density tensor with a correction function $f(\rho)$. The function $f(\rho)$ can be easily reconstructed, by considering the thermodynamics of the apparent horizon. We also study the first and second laws of thermodynamics in this context and show how the problem of limited cosmic flux can be resolved based on the model's parameters. At last, In order to study the kinematics of the universe, cosmography parameters are also calculated and we see that the correction function $f(\rho)$ has a non-negligible role in cosmography parameters. This paper provides valuable insights into using general entropies on the apparent horizon of the universe.Comment: 12 page