Abstract
Here, in this work we establish the main cosmological parameters namely the deceleration parameter $q$, the equation of state parameter $w$ and the diagnostic omega $Om$ for $f(R)$ modified gravity using Sharma-Mitall Holographic Dark Energy model ($SMHDE$).Our model shows a type of stability of achieved by studying the behavior of the square speed of sound parameter which has a positive behavior over the given range . For the considered red shift $z$ range, we study the evolution of energy conditions for our model and the growth of dark energy the results fit the observations that the dark energy increase with time and the universe in an accelerated expansion epoch. Thermal analysis is considered through the quantum correction for power law and logarithmic entropy, consequently we study the validity of the generalized second law of thermodynamic the results show that the the generalized second law of thermodynamic holds using power law corrected scenario.
Highlights
The accelerated expansion behaviour of the universe has attracted many scientises in the last 20 years
In section (II) we consider our model, in section (III) we study the diagnostic state finder parameter, the stability of the model considered using the square speed of sound and energy conditions and in section (IV) thermal evolution of the model are studied and in last section the conclusion is present
The entropy-area relation is corrected using what called the entanglement of quantum fields in and out the black hole horizon [35, 36]. Following these quantum effects which is motivated by loop quantum mechanics a type of curvature correction is obtained in the Einstein-Hilbert action that leads to the modification of both power law corrected entropy (PLCE) and logarithmic corrected entropy (LCE) [38, 39], namely: SP
Summary
The accelerated expansion behaviour of the universe has attracted many scientises in the last 20 years. Dark energy (DE) is a one of the biggest challenging questions, it is considerd as the main candidate of accelerated expansion behavior of the AJBAS Volume 2, Issue II, 2021. The holographic dark energy model (HDE) assumed by M. li [13] as a promissing model used to understand DE nature. This model based on the holographic principle [14], where the degrees of freedom of the system are represented by using the boundary area rather that its volume. The behavior f(R) modified gravity model is studied within the context of (S − M) Holographic Dark Energy, the structure of the paper is as follows. In section (II) we consider our model, in section (III) we study the diagnostic state finder parameter, the stability of the model considered using the square speed of sound and energy conditions and in section (IV) thermal evolution of the model are studied and in last section the conclusion is present
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