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We have developed a Bianchi I cosmological model of the universe in $f(R,T)$ gravity theory which fit good with the present day scenario of accelerating universe. The model displays transition from deceleration in the past to the acceleration at the present. As in the $\Lambda$CDM model, we have defined the three energy parameters $\Omega_m$, $\Omega_{\mu}$ and $\Omega_{\sigma}$ such that $\Omega_m$ + $\Omega_{\mu}$ + $\Omega_{\sigma}$ = 1. The parameter $\Omega_m$ is the matter energy density (baryons + dark matter), $\Omega_{\mu}$ is the energy density associated with the Ricci scalar $R$ and the trace $T$ of the energy momentum tensor and $\Omega_{\sigma}$ is the energy density associated with the anisotropy of the universe. We shall call $\Omega_{\mu}$ dominant over the other two due to its higher value. We find that the $\Omega_{\mu}$ and the other two in the ratio 3:1. 46 Hubble OHD data set is used to estimate present values of Hubble $H_0$, deceleration $q_0$ and jerk $j$ parameters. 1$\sigma$, 2$\sigma$ and 3$\sigma$ contour region plots for the estimated values of parameters are presented. 580 SNIa supernova distance modulus data set and 66 pantheon SNIa data which include high red shift data in the range $0\leq z\leq 2.36$ have been used to draw error bar plots and likelihood probability curves for distance modulus and apparent magnitude of SNIa supernova's. We have calculated the pressures and densities associated with the two matter densities, viz., $p_{\mu}$, $\rho_{\mu}$, $p_m$ and $\rho_m$, respectively. The present age of the universe as per our model is also evaluated and it is found at par with the present observed values., Comment: 19 pages, 19 figures. The European Physical Journal Plus. 2023. arXiv admin note: text overlap with arXiv:2303.14136

In the present work, we investigate the power-law entropy corrected holographic dark energy (PLECHDE) model with Hubble horizon cutoff. We use 46 observational Hubble data points in the redshift range $0 \leq z \leq 2.36$ to determine the present Hubble constant $H_0$ and the model parameter $n$. It represents a phase transition of the universe from deceleration to acceleration and has the transition point at $z_t = 0.71165$. We investigate the observational constraints on the model and calculate some relevant cosmological parameters. We examine the model's validity by drawing state-finder parameters that yield the result compatible with the modern observational data. The model's physical and geometrical characteristics are also explored, and they are shown to match well with current observations of observational Hubble data (OHD) and the latest joint light curves(JLA) datasets., Comment: 18 pages, 12 figures

In this paper, we examine the (LRS) Bianchi-type-I cosmological model with holographic dark energy. The exact solutions to the corresponding field equations are obtained by using generalized hybrid expansion law (HEL). The EoS parameter $\omega$ for DE is found to be time dependent and redshift dependent and its exiting range for derived model is agreeing well with the current observations. Here we likewise apply two mathematical diagnostics, the statefinder ({r, s}) and $\omega_{d}-\omega^{'}_{d}$ plane to segregate HDE model from the $\Lambda CDM$ model. Here the $\omega_{d}-\omega^{'}_{d}$ diagnostic trajectories is the good tool to classifying the dynamical DE model. We found that our model lies in both thawing region and freezing region. We have also construct the potential as well as dynamics of the quintessence and tachyon scalar field. Some physical and geometric properties of this model along with the physical acceptability of cosmological solution have been discussed in detail., Comment: 19 pages, 15 figures