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Inspired by the Covid-$19$ virus structure, Barrow argued that quantum-gravitational effects may introduce intricate, fractal features on the black hole horizon [Phys. Lett. B {\bf808} (2020) 135643]. In this viewpoint, black hole entropy…
Taking into account a fractal structure for the black hole horizon, Barrow argued that the area law of entropy is modified due to quantum-gravitational effects (Barrow in Phys Lett B 808:135643,…
This paper offers an original theoretical framework to quantify the information content associated with cosmological structure formation. By taking into account the growth in perturbations for the matter density field, we are able to…
Based on the relationship between thermodynamics and gravity we propose, with the aid of Verlinde's formalism, an alternative interpretation of the dynamical evolution of the Friedmann-Robertson-Walker Universe. This description takes into…
This thesis explores the cosmological implications of modified gravity, focusing on nonmetricity-based $f(Q)$ gravity as an alternative to the $\Lambda$CDM model in explaining cosmic acceleration. Chapter I lays the theoretical groundwork…
Recently, it was argued (Eur. Phys. J. C {\bf73}, 2487 (2013)) that the total entropy of a gravitational system should be related to the volume of system instead of the system surface. Here, we show that this new proposal cannot satisfy the…
The analysis of phase transitions in cosmological spacetimes shows that their existence requires a time-dependent apparent horizon radius, which in turn implies an equation of state different from that of a dark energy fluid. This condition…
We investigate entropic force cosmological models with the possibility of matter creation and energy exchange between the bulk and the horizon of a homogeneous and an isotropic flat Universe. We consider three different kinds of entropy,…
We explore the derivation of the Friedmann equations from a thermodynamic perspective, applying the unified first law of thermodynamics to the apparent horizon of a flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe. We extend this…
Recently, the R\'{e}nyi and Tsallis generalized entropies have extensively been used in order to study various cosmological and gravitational setups. Here, using a special type of generalized entropy, a generalization of both the R\'{e}nyi…
We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin,…
We revisit Jacobson's thermodynamic derivation of gravitational dynamics in the presence of generalized, non-extensive horizon entropies. Working within a local Rindler-wedge framework, we formulate the Clausius relation as the stationarity…
We explore a cosmological model inspired by the modified Kaniadakis entropy and disclose the influences of the modified Friedmann equations on the evolution of the Universe. We find that in modified Kaniadakis cosmology with only…
We perform a comprehensive cosmographic analysis of Friedmann cosmologies modified by non-extensive entropy frameworks, focusing on Tsallis, R\'enyi, and Kaniadakis entropies within a novel modified energy-momentum tensor approach. In our…
We consider the cosmological implications of a four-dimensional extension of the Gauss-Bonnet $f(G)$ gravity, where $G$ is the Gauss-Bonnet topological invariant, in which the Einstein-Hilbert action is replaced by an arbitrary function…
The relationship between the metric and nonrelativistic matter distribution depends on the theory of gravity and additional fields, providing a possible way of distinguishing competing theories. With the assumption that the geometry and…
The thermodynamics-gravity conjecture reveals that one can derive the gravitational field equations by using the first law of thermodynamics and vice versa. Considering the entropy associated with the horizon in the form of non-extensive…
The observed accelerated expansion of the Universe may be explained by dark energy or the breakdown of general relativity (GR) on cosmological scales. When the latter case, a modified gravity scenario, is considered, it is often assumed…
Cosmological observations are beginning to reach a level of precision that allow us to test some of the most fundamental assumptions in our working model of the Universe. One such an assumption is that gravity is governed by the General…
We investigate the evolution of cosmological perturbations in models of dark energy described by a time-like unit normalized vector field specified by a general function $\mathcal{F}(\mathcal{K})$, so-called Generalized Einstein-Aether…