arXiv subjects

Krishna P B

Publications and source records attributed to Krishna P B.

6 recordsLinked to original sources

arXiv2025

Evolution of fluctuations in horizon energy and its dependence on the degrees of freedom

Taking account of the thermal nature of the Hubble horizon of the expanding universe, we analysed the evolution of relative fluctuations of horizon energy. For this analysis, we used two approaches: (i) by treating the Hubble horizon as a system in canonical ensemble, and (ii) by considering the microscopic degrees of freedom on the horizon. In both approaches, we obtained the relative fluctuations by using two different definitions of the horizon temperature; first, the Gibbons-Hawking temperature, and second, the Kodama-Hayward temperature. For a given temperature, both approaches yield the same general evolution for the fluctuations. In the asymptotic limit, the relative energy fluctuations corresponding to the Gibbons-Hawking temperature, is $[{\hbar G}/{2π}] H^2,$ and $2/N_{sur}$ for the first and second approaches respectively. Similarly, using the Kodama-Hayward temperature, the asymptotic fluctuations are $[{5\hbar G}/{2π}] H^2,$ and $10/N_{sur}.$ This implies that, the magnitude of the relative fluctuations of the horizon energy is higher in the case of Kodama-Hayward temperature. The inverse dependence of the fluctuation on $N_{sur},$ the number of degrees of freedom on the horizon, reflects a familiar behaviour in ordinary thermal systems: fluctuations decrease as the number of degrees of freedom increases. Notably, we also found that the relative energy fluctuations establish a connection between the Planck length scale $L_p,$ characteristic length scale of the very early epoch of the universe, and $\sqrt{3/Λ},$ the length scale associated with the late-time accelerated phase. This relationship can offer valuable insights that could help in addressing the cosmological constant problem.

gr-qc↗

arXiv2021

Emergence of cosmic space and the maximization of horizon entropy

The spatial expansion of the universe can be described as the emergence of space with the progress of cosmic time, through a simple equation, $ΔV = Δt\left(N_{surf}- N_{bulk}\right)$. This law of emergence suggested by Padmanabhan in the context of general relativity for a flat universe has been generalized by Sheykhi to Gauss Bonnet and Lovelock gravity for a universe with any spacial curvature. We investigate whether this generalized holographic equipartition effectively implies the maximization of horizon entropy. First, we obtain the constraints imposed by the maximization of horizon entropy in Einstein, Gauss Bonnet and Lovelock gravities for a universe with any spacial curvature. We then analyze the consistency of the law of emergence in \cite{Sheykhi}, with these constraints obtained. Interestingly, both the law of emergence and the horizon entropy maximization demands an asymptotically de Sitter universe with $ω\geq -1$. More specifically, when the degrees of freedom in the bulk $( N_{bulk})$ becomes equal to the degrees of freedom on the boundary surface $(N_{surf}),$ the universe attains a state of maximum horizon entropy. Thus, the law of emergence can be viewed as a tendency for maximizing the horizon entropy, even in a non flat universe. Our results points at the deep connection between the law of emergence and horizon thermodynamics, beyond Einstein gravity irrespective of the spacial curvature.

gr-qc↗

arXiv2020

Dynamical system analysis and thermal evolution of the causal dissipative model

The dynamical system behaviour and thermal evolution of a homogeneous and isotropic dissipative universe are analyzed. The dissipation is driven by the bulk viscosity $ξ= αρ^s $ and the evolution of bulk viscous pressure is described using the full causal Israel-Stewart theory. We find that for $s=1/2$ the model possesses a prior decelerated epoch which is unstable and a stable future accelerated epoch. From the thermodynamic analysis, we have verified that the local as well as the generalised second law of thermodynamics are satisfied throughout the evolution of the universe. We also show that the convexity condition $S''<0$ is satisfied at the end stage of the universe which implies an upper bound to the evolution of the entropy. For $s\neq1/2,$ the case $s<1/2$ is ruled out since it does not predict the conventional evolutionary stages of the universe. On the other hand, the case $s>1/2$ does imply a prior decelerated and a late de Sitter epochs, but both of them are unstable fixed points. The thermal evolution corresponding to the same case implies that GSL is satisfied at both the epochs but convexity condition is violated by both, so that entropy growth is unbounded. Hence for $s>1/2$ the model does not give a stable evolution of the universe.

gr-qc↗

arXiv2020

Does Holographic equipartition demand a pure cosmological constant?

The spacial expansion of the universe could be described as a tendency for satisfying holographic equipartition which inevitably demands the presence of dark energy. We explore whether this novel idea proposed by Padmanabhan give any additional insights into the nature of dark energy. In particular, we obtain the constraints imposed by the law of emergence on the equation of state parameter, $ω$. We also present a thermodynamic motivation for the obtained constraints on $ω$. Further, we explicitly prove the feasibility of describing a dynamic dark energy model through the law of emergence. Interestingly, both holographic equipartition and the entropy maximization demands an asymptotically de Sitter universe with $ω\geq-1$, rather than a pure cosmological constant.

gr-qc↗

arXiv2019

Entropy Maximization in the Emergent Gravity Paradigm

The accelerated expansion of the universe can be interpreted as a quest for satisfying holographic equipartition. It can be expressed by a simple law, $ΔV = Δt\left(N_{surf}- N_{bulk}\right)$ which leads to the standard Friedmann equation. This novel idea suggested by Padmanabhan in the context of general relativity has been generalized by Cai and Yang et al. to Gauss-Bonnet and Lovelock gravities for a spatially flat universe in different methods. We investigate the consistency of these generalizations with the constraints imposed by the maximum entropy principle. Interestingly, both these generalizations imply entropy maximization even if their basic assumptions are different. Further, we analyze the consistency of Verlinde's emergent gravity with the maximum entropy principle in the cosmological context. In particular, we consider the generalization suggested by Shu and Gong, in which an energy flux through the horizon is assumed, in addition. Even though the conceptual formulations are different, these two emergent perspectives of gravity describes a universe which behaves as an ordinary macroscopic system. Our results provide further support to the emergent gravity paradigm.

gr-qc↗

arXiv2017

Holographic equipartition and the maximization of entropy

\begin{abstract} The accelerated expansion of the universe can be interpreted as a tendency to satisfy the holographic equipartition. It can be expressed by a simple law, $ΔV = Δt\left(N_{surf}-εN_{bulk}\right),$ where $V$ is the Hubble volume in Plank units, $t$ is the cosmic time plank units and $N_{surf/bulk}$ is the degrees of freedom on the horizon/bulk of the universe. We show that this holographic equipartition law effectively implies the maximization of entropy. In the cosmological context, a system that obeys the holographic equipartition law behaves as an ordinary macroscopic system that proceeds to an equilibrium state of maximum entropy. We consider the standard $Λ$CDM model of the universe and have shown that it is consistent with the holographic equipartition law. Analyzing the entropy evolution we find that it also proceeds to an equilibrium state of maximum entropy.

gr-qc↗