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The aim of this paper is to analyze the cosmological evolution of holographic dark energy in

The surprising discovery of the accelerated expansion of the Universe is one of the exciting progress areas in cosmology. This tremendous change in cosmic history has been proved from a diverse set of high-precision observational data accumulated from various astronomical sources. The accelerating paradigm is considered as a consequence of an exotic type of force dubbed as dark energy (DE) which possesses repulsive characteristics with negatively large pressure. It may predict the ultimate future of the Universe but its salient features are still not known. To explore the perplexing nature of DE, different approaches have been presented. The cosmological constant

Gauss-Bonnet (GB) invariant being a particular linear combination of quadratic curvature invariants has gained much attention in cosmology. This four-dimensional topological invariant is free from spin-2 ghost instabilities and is defined as [

The nonminimal curvature-matter coupling in modified gravitational theories has gained significant attention, since it can describe consistently the late-time acceleration phenomenon. Harko et al. [

Dynamical DE models have been constructed in the framework of general relativity and quantum gravity which play an important role in exploring the mystery of cosmic expansion. Li [

The accelerated expansion of the Universe is also successfully discussed in literature via correspondence scheme of dynamical DE models with modified theories of gravity. In this mechanism, generic function of the considered gravity is reconstructed by comparing the corresponding energy densities. A variety of reconstructed holographic DE models in different modified theories have gained remarkable importance in describing the present cosmic phase. Setare [

Houndjo and Piattella [

In curvature-matter coupled gravitational theories, various dynamical DE models have also gained significant importance in describing the cosmic evolutionary phases. Sharif and Zubair [

In this paper, we investigate the cosmological evolution of holographic DE in

In this section, we briefly discuss basic concepts related to

In curvature-matter coupled theories, the generic function and matter Lagrangian density play a pivotal role in exploring their dynamics. Some particular forms are as follows.

The line element for flat FRW Universe model is

The energy density of holographic DE model is given by [

Now we reconstruct the holographic DE

In order to obtain its solution, we consider power-law form of the scale factor which has a significant importance in cosmology since it elegantly illustrates different cosmic evolutionary phases given by [

Figure

Evolution of holographic DE

In this section, we analyze the EoS and deceleration parameters as well as examining the cosmological planes such as

The EoS parameter for the obtained model using the correspondence scenario of energy densities is given by

We use scale factor in terms of red-shift parameter as

Evolution of EoS parameter versus

The deceleration parameter is defined as

Evolution of deceleration parameter versus

Sahni et al. [

The plane of these cosmological parameters (dubbed as

Plot of state-finder diagnostic parameters for

Caldwell and Linder [

Plot of

In this paper, we have explored cosmological reconstruction of

We have examined the evolutionary paradigm of reconstructed holographic

The trajectory of EoS parameter indicates the phantom phase of the Universe for the considered value of

The evolution of deceleration parameter against cosmic time gives accelerated phase of the Universe throughout the evolution (Figure

The state-finder diagnostic plane for the reconstructed model only corresponds to Chaplygin gas model (Figure

The trajectory in

No data were used to support this study.

The authors declare that they have no conflicts of interest.

We would like to thank the Higher Education Commission, Islamabad, Pakistan, for its financial support through the