Narrow Results

In this work, two originally separate adjustments for the Friedmann equations are concurrently considered. First, the fractal structure of the black hole horizon region is imposed by the Barrow entropy. The second adjustment is the $f(\mathcal{𝒯})$ gravity, which is based on a teleparallel framework generalization of the Einstein–Hilbert action, where $\mathcal{𝒯}$ is the scalar torsion. This can be considered as a Barrow entropy modification of the $f(\mathcal{𝒯})$ gravity thus yielding a new model. Gravity thermodynamics hypothesis principles are used to integrate these two models under a unified framework. We derive the modified Friedmann equation and note the corrections obtained. To understand the implications of such dual modifications, an application is analyzed and a particular $f(\mathcal{𝒯})$ toy model is chosen for the purpose. The equation of the state parameter of the resulting model, the dimensionless density parameters of matter and dark energy, and the deceleration parameter are explored to check the viability of the new model. A discussion of the dynamic evolution of the universe follows from these results. It is seen that the results comply with the observations. The newly developed model is promising and demands further study.

Quantum gravitational effects, on the one hand, lead to a limitation in the accuracy of measuring spatial and time intervals, and, on the other hand, they generate a discrete of spacetime structure (quantum foam). The common source of both measurement limitations and discreteness of spacetime is quantum fluctuations, so their characteristics must be related to each other. We study such a relationship using Barrow entropy as a source of fractal spacetime structure. The minimum inaccuracy in measuring spacetime intervals is expressed through the Barrow entropy parameter. The connection between the level of fractality and the speed of information processing is considered.

In this research, we have reconstructed the extended $f({𝒫})$ cubic gravity and symmetric $f({𝒬})$ teleparallel gravity from the $(m,n)$-type Barrow Holographic Dark Energy (BHDE) model. We have derived the unknown functions $f({𝒫})$ and $f({𝒬})$ in terms of ${𝒫}$ and ${𝒬}$, assuming a flat, homogeneous, and isotropic universe. To constrain our model parameters, we employed cosmic chronometer datasets and Baryon Acoustic Oscillation (BAO) datasets, utilizing Markov Chain Monte Carlo (MCMC) method. We analyzed the behavior and stability of each model throughout the universe’s evolution by studying crucial parameters such as the deceleration parameter, equation of state (EoS) parameter ${\omega }_{\mathrm{\text{DE}}}$, density parameter $\mathrm{\Omega }(z)$ and the square of the speed of sound $v_s^2$. Additionally, we explored the cosmographic behavior by plotting the jerk parameter, snap parameter, and lerk parameter against the redshift. Furthermore, we examined the ${\omega }_{\mathrm{\text{DE}}}^{\prime }-{\omega }_{\mathrm{\text{DE}}}$ phase plane, the $(r,s^{\ast })$, $(r,q)$ statefinder parameters, and the $Om(z)$ parameter offers profound revelations about the dynamics of the universe and the distinctive features of dark energy. Our analyses indicated that our model could produce a universe undergoing accelerated expansion with quintessence-type dark energy. These findings contribute to our understanding of the nature of dark energy and the evolution of the cosmos.

In this paper, we consider an exponential potential $V_{(\varphi )}=V_0{e}^{-\alpha \varphi }$ in the framework of Barrow entropy under the constant-roll inflation and check their viability in the light of observable Planck 2020 data. By applying the first law of thermodynamics to the apparent horizon of the Universe, a modification of the Friedmann–Robertson–Walker (FRW) metric is derived in the context of Barrow entropy. We consider the early inflationary period of the universe to consist phenomenologically of a single inflationary state, that is, a state of the costant-roll inflation in which inflation is driven by an exponential potential field function. By fitting the constant-roll inflationary models to the observations, we examined the effect of the Barrow parameter $\mathrm{\Delta }$ on the inflation mechanism with the constant-roll parameter $\gamma$. As a result, we concluded that for a viable inflation, the observation limits of the inflation parameters determine that the constant-roll parameter is in the range $0.011\le \gamma \le 0.016$.

In this paper, we explore the impact of Barrow’s entropy on the topological classification of d-dimensional black holes (BHs). Specifically, we examine the Gauss–Bonnet (GB) and singly rotating Kerr black holes (KBHs) as well as their AdS counterparts. We notice that Barrow’s entropy significantly influences the topological numbers of these BHs. To understand these effects, we use the thermodynamic domain — the space defined by thermodynamic variables like temperature and pressure — to study topologically inspired defects in the BHs. These defects are points in the thermodynamic domain where singular or discontinuous behavior occurs. By computing the winding numbers of these defects, which are integers that count how many times a loop around the defect encircles the origin, we can understand the local and global topology of the BHs. Our analysis suggest that the topological number $(\mathcal{𝒯})$ derived from Barrow’s statistics differs from the one obtained using Gibbs–Boltzmann statistics. Furthermore, we observe that BHs can undergo topological phase transitions that characterize them in different thermodynamic topological classes. Overall, these findings demonstrate the importance of Barrow’s entropy in understanding the topological classification of BHs, and highlight the potential for further research in this area.

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 $\mathrm{\Delta }$. Furthermore, we mention the consequences of the presence of interaction among the universe sectors.

Recently, Barrow holographic dark energy (BHDE), based on Barrow entropy, has been proposed to describe the late acceleration of the universe. Contrary to the earlier analysis of this model in the literature, we consider the BHDE with the Granda–Oliveros length as IR cut-off, as a dynamical vacuum, having a constant equation of state ${\omega }_{\mathrm{\Lambda }}=-1.$ We have analytically solved for the Hubble parameter and studied the evolution of cosmological parameters. The model is compared with the observational data on Hubble parameter (OHD36) and Supernovae type Ia (SN Ia), the pantheon data. In the absence of interaction between the dark sectors, we found that the model predicts a $\mathrm{\Lambda }$CDM-like evolution of the universe with an effective cosmological constant. In this case, the model is found to satisfy the generalized second law (GSL), irrespective of the value of the Barrow index. The interaction also shows the safe validity of GSL, for the extracted value of the Barrow index, $\mathrm{\Delta }=0.063\pm 0.029$. The thermodynamic analysis of the model predicts an end de Sitter phase of maximum entropy. We performed a dynamical system analysis, which reveals that the end de Sitter phase is stable. Furthermore, we performed the Information Criterion analysis using Akaike and Bayesian Information Criterion to compare the statistical compatibility of the present model with the standard $\mathrm{\Lambda }$CDM model.

In this work, we study a constant-roll inflation model embedded in the Barrow entropy scenario. In this regards, we derive the modified of the Friedmann–Robertson–Walker (FRW) universe from the Barrow entropy using the first law of thermodynamics for the apparent horizon of the universe. We consider the inflation dynamics of the early universe under the constant-roll condition where the inflation is driven by a power-law scalar potential field, $V_{(\mathrm{\Phi })}={\mathrm{\Phi }}^n$. We calculated the tensor-to-scalar ratio $r$ and scalar spectral index $n_s$ by applying the constant-roll condition with some other parameters and compared them with the Planck 2020 observable data. To reveal the effect of the Barrow parameter $\mathrm{\Delta }$ on the inflation, we fixed the constant-roll inflation parameter as $\gamma =0.014$ and focused on the exponent of potential in the range $0<n<1$. We observed that as the value of the Barrow parameter approaches zero in the range $0\le \mathrm{\Delta }\le 1$, a long and sufficient inflation occurs, consistent with the observation data. This strengthens the claim that the observable values of the Barrow parameter occur at very small values. In addition, the obtained results were also examined numerically.

This study examines the structure of the universe during its high-energy era. In this context, we examine Barrow’s proposal of entropy, which forecasts a fractal configuration for the geometric properties of the black hole’s horizon. By applying the principles of thermodynamics, we get the equation of motion using the Barrow entropic consideration. A quasi-de Sitter phase, in which fractal and non-fractal states may coexist, is determined. This is an uncertainty state (coexistence of fractal and non-fractal states), and so a deformation for de Sitter spacetime, which contains a high-energy scale in the framework of the COBE normalization. With the kinetic energy term of the inflation field, we remove this ambiguity owing to the field oscillations. However, the oscillatory behavior of the inflation field continues and causes the universe to enter a new phase state. At this point, in which the inflation field oscillations are over, we obtain a solution that provides the universe transition to the radiation and dust phases.