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In this work, we propose a new dark energy (DE) model by applying the Barrow entropy and the holographic principle, with a time scale as IR cut-off. Analyzing the conformal time as well as universe’s age as infrared cut-offs, we explore the cosmological importance of the suggested DE models and examine the universe evolution filled with the proposed DE applicants and a pressure-less matter. We observe that the equation of state, deceleration, the density parameters can present adequate nature, and these models may also explain the late-time acceleration though the proposed models are unstable except for some values of Barrow exponent [Formula: see text]. Furthermore, we mention the consequences of the presence of interaction among the universe sectors.

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In this research, we examine a spatially homogeneous anisotropic locally rotationally symmetric (LRS) Bianchi type-I cosmological model in [Formula: see text] gravity, for some choices of the function [Formula: see text] ( arXiv:1104.2669 [gr-qc]). The precise solutions of the field equations are introduced for the periodic-time varying deceleration parameter that can adjust to meet the [Formula: see text]CDM model. We have reviewed the physical and dynamic characteristics of these models to understand the accelerated expansion of the Universe in the current era. Furthermore, SNe Ia union data ( arXiv:0811.2379 [astro-ph]), SN Ia with BAO and CMB observations ( arXiv:1203.3213 [astro-ph.CO]) and OHD[Formula: see text]+[Formula: see text]JLA data ( arXiv:1711.03437 [astro-ph.CO]) are used to estimate the statefinder diagnostics to get the geometric dynamics of the Universe at distinct stages and also to find the luminosity distance, angular-diameter distance, and distance modulus. We have also investigated the transit points for the deceleration parameter [Formula: see text] in the framework of these three observations within the range of redshift [Formula: see text].

This research study investigates Barrow holographic dark energy with an energy density of ρΛ=CH2−Δ by considering the Hubble horizon as the IR cut-off in the f(R, T) gravity framework. We employ Barrow holographic dark energy to obtain the equation of the state for the Barrow holographic energy density in a flat FLRW Universe. Concretely, we study the correspondence between quintessence, k-essence, and dilation scalar field models with the Barrow holographic dark energy in a flat f(R, T) Universe. Furthermore, we reconstruct the dynamics and potential for all these models for different values of the Barrow parameter: Δ. Via this study, we can show that for Barrow holographic quintessence, k-essence, and dilation scalar field models, if the corresponding model parameters satisfy some limitations, the accelerated expansion can be achieved.

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In this paper, we investigate a non-interacting model considering a spatially anisotropic and homogeneous Bianchi type-[Formula: see text] Universe, filled with Barrow holographic dark energy (BHDE) and pressureless dark matter. We examine some important cosmological parameters for the evolutionary report and to witness adequate nature in BHDE model as including deceleration parameter, the jerk parameter, equation of state parameter and density parameter. To study more briefly, we diagnose statefinder parameters, [Formula: see text] analysis and explain that the model parameter significantly modifies the evolutionary trajectories in these planes.