Narrow Results

In this paper, we introduce a holographic dark energy model that incorporates the first-order approximate Kaniadakis entropy, utilizing the Hubble horizon, $1∕H$, as the infrared cutoff. We investigate the cosmological evolution within this framework. The model introduces an extra parameter relative to the $\mathrm{\Lambda }$CDM model. It posits a Universe that is initially dominated by dark matter, which then evolves to a phase where dark energy becomes the predominant component, with this transition occurring at a redshift of approximately $z\sim 0.419$. The energy density of dark energy is ultimately expected to become constant, thereby circumventing the potential issue of a “big rip”. Employing the most recent Type Ia supernova and Hubble parameter data, we constrain the model’s parameters and find a Hubble constant of $H_0=72.8$ km/s/Mpc, thereby resolving the Hubble tension issue. The estimated age of the Universe, based on the best-fit parameter values, is $14.2$ Gyr. Furthermore, we predict the number of strong gravitational lenses and conduct statefinder and $\mathrm{\text{Om}}$ diagnostic analyses to validate and characterize the model.

We have analyzed the Barrow holographic dark energy (BHDE) in the framework of flat FLRW universe by considering the various estimations of Barrow exponent △. Here, we define BHDE, by applying the usual holographic principle at a cosmological system, for utilizing the Barrow entropy rather than the standard Bekenstein–Hawking. To understand the recent accelerated expansion of the universe, consider the Hubble horizon as the IR cutoff. The cosmological parameters, especially the density parameter $({\mathrm{\Omega }}_D)$, the equation of the state parameter $({\omega }_D)$, energy density $({\rho }_D)$ and the deceleration parameter $(q)$ are studied in this paper and found the satisfactory behaviors. Moreover we additionally focus on the two geometric diagnostics, the statefinder $(r,s)$ and $O_m(z)$ to discriminant BHDE model from the $\mathrm{\Lambda }$CDM model. Here we determined and plotted the trajectories of evolution for statefinder $(r,s)$, $(r,q)$ and $O_m(z)$ diagnostic plane to understand the geometrical behavior of the BHDE model by utilizing Planck 2018 observational information. Finally, we have explored the new Barrow exponent △, which strongly affects the dark energy equation of state that can lead it to lie in the quintessence regime, phantom regime and exhibits the phantom-divide line during the cosmological evolution.

According to the third law of Thermodynamics, it takes an infinite number of steps for any object, including black holes, to reach zero temperature. For any physical system, the process of cooling to absolute zero corresponds to erasing information or generating pure states. In contrast with the ordinary matter, the black hole temperature can be lowered only by adding matter–energy into it. However, it is impossible to remove the statistical fluctuations of the infalling matter–energy. The fluctuations lead to the fact that the black holes have a finite lower temperature and, hence, an upper bound on the horizon radius. We make an estimate of the upper bound for the horizon radius which is curiously comparable to Hubble horizon. We compare this bound with known results and discuss its implications.

In the context of cubic gravity for flat FRW metric we discuss the behavior of cosmological parameters (equation of state (EoS) parameter and square speed of sound) at Hubble horizon with the four different models of Hubble parameter. We observe the validity of generalized second law of thermodynamics (GSLT) and thermal equilibrium condition. It is found that cosmological parameters lie within the observational constraints. Also, GSLT and thermal equilibrium condition holds in almost all cases of Hubble parameter.

In the framework of $f(P)$ gravity, we examine the nature of cosmological parameters by choosing different models of $f(P)$ gravity at past, present as well as future epoch for Hubble parameter from parameterized deceleration parameters. It is found that equation of state parameter leads to quintessence behavior and its ranges lie within Planck data for different constraints. We also study the squared sound speed and the thermodynamics for specific choice of constants. The squared sound speed corresponds to the viable results. Similarly, the validity of GSLT is also investigated for both linear and nonlinear models of $f(P)$ theory. However, the thermal equilibrium condition holds for both $f(P)$ models for specific choice of constants.

In the framework of teleparallel tachyonic model, we explore the stability of the generalized thermodynamical law and equilibrium case at Hubble horizon together with Bekenstein entropy at present as well as past epoch for flat Friedmann–Lemaître–Robertson–Walker metric. For this purpose, we take three distinct models of Hubble parameter in terms of redshift. Also, we choose power-law correction terms and specific coupling of scalar field and take observational values from $\mathrm{\text{CC}}+H_0$ dataset and compare results of all different models.