arXiv subjects

Titus K. Mathew

Publications and source records attributed to Titus K. Mathew.

At least 19 recordsLinked to original sources

arXiv2026

Horizon energy fluctuations beyond Einstein's gravity: Gauss-Bonnet, Lovelock and Quantum deformed frameworks

We study thermal energy fluctuations of cosmological horizons within the canonical ensemble framework, treating the horizon as a thermodynamic system characterized by temperature and entropy. The analysis is performed for a class of gravitational theories, including (n+1)-dimensional Einstein gravity, Gauss-Bonnet gravity, Lovelock gravity, and models incorporating quantum deformed entropy corrections. We find that horizon energy fluctuations stabilize to a constant value in the asymptotic de Sitter limit, independent of the underlying gravity theory and robust against higher-curvature and quantum corrections. It is worth mentioning that in its final de Sitter state, the universe obeys holographic equipartition condition and in consequence the horizon entropy attains a maximum constant value, just like an ordinary macroscopic system. These findings establish a unified thermodynamic picture in which entropy maximization, holographic equipartition, and the suppression of energy fluctuations collectively characterize the asymptotic de Sitter universe as the equilibrium end state of cosmic evolution.

gr-qc↗

arXiv2024

Emergence of space from the first law of thermodynamics in the braneworld scenarios

Expansion of the universe is caused by the departure from the holographic equipartition. This principle, the law of emergence, first postulated in the context of Einstein's gravity has been extended successfully to more general gravity theories like Gauss-Bonnet and Lovelock gravity. We derive the law of emergence for braneworld models of gravity, starting from the more fundamental and well established principle, the first law of thermodynamics. More specifically, we derive the law of emergence in the context of RS II braneworld, Warped DGP model and Gauss-Bonnet braneworld and compare the derived law with the one proposed by Sheykhi for the braneworld models. We further show that the law of emergence leads to the maximization of horizon entropy in all these braneworld models. While the law of emergence effectively implies the maximization of horizon entropy, it could be derived from the first law of thermodynamics. Our results suggest that the horizon thermodynamics is the backbone of the law of emergence in the braneworld scenarios.

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arXiv2023

Thermal evolution and stability analysis of phenomenologically emergent dark energy model

The phenomenologically emergent dark energy (PEDE) model is a varying dark energy model with no extra degrees of freedom proposed by Li and Shafieloo\citep{Li_2019} to alleviate the Hubble tension. The statistical consistency of the model has been discussed by many authors. Since the model depicts a phantom dark energy that increases with redshift, its cosmic evolution, particularly during the late phase, must be examined. We discover that the model's Hubble and deceleration parameters display unusual behaviour in the future, which differs from $Λ$CDM cosmology. We find the model also follows a distinct evolution in the statefinder plane. The phantom nature of the model leads to the violation of the null energy condition and a decrease in horizon entropy. The asymptotic future epoch also seems to be unstable based on our dynamical system analysis as well as the stability analysis based on dark energy sound speed.

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arXiv2023

Unified formalism for the emergence of space from the first law of thermodynamics

We derive a unified expansion law for our universe from the first law of thermodynamics on the apparent horizon, where entropic evolution depicts the emergence of cosmic space. The derivation advances a general form for degrees of freedom on the surface and bulk, which provides a natural generalization for the expansion law proposed by Padmanabhan. The general expression for the surface degrees of freedom differs from the natural expectation, $ N_{sur }= 4S $ in the emergent gravity paradigm for general theories of gravity. The derivation also provides justification for the selection of Gibbons-Hawking temperature in the original expansion law and for the use of areal volume in the non-flat FRW universe. Since the unified expansion law exclusively depends on the form of entropy, the method is applicable to obtain the expansion law in any gravity theory without any additional ad hoc assumptions. From the general expansion law, we have obtained the expansion law corresponding to different theories of gravity like (n+1) Einstein, Gauss-Bonnet, Lovelock, and Horava-Lifshitz. We also obtained the expansion law for non-extensive entropy like Tsallis entropy from the unified expansion law.

gr-qc↗

arXiv2023

Holographic dark energy from the laws of thermodynamics with Rényi entropy

This article investigates the relationship between the holographic principle and the laws of thermodynamics in explaining the late-time acceleration of the universe. First, we explore the possibilities of generating the standard holographic dark energy (SHDE) from the laws of horizon thermodynamics. Except for entropies that follow an exponent stretched area law, unless we redefine the horizon temperature, we found it challenging to construct a one-to-one correspondence between the dark energies defined by the holographic principle and the laws of thermodynamics. Secondly, in SHDE models, unless we invoke some phenomenological interactions, it is impossible to explain the late-time cosmic acceleration with the Hubble horizon as the IR cutoff. On the other hand, it is possible to induce dark energy as an integration constant using the laws of thermodynamics on the Hubble horizon. These motivated us to explore a feasible way to invoke the holographic principle from the laws of horizon thermodynamics. We show that the additional terms that appear in the modified Friedmann equations on using entropies other than the Bekenstein-Hawking entropy in the first law of thermodynamics can behave like a dynamic holographic dark energy (HDE). We study the features of such an HDE with Rényi entropy as the choice without considering any non-standard interactions. Interestingly, the resulting form of dark energy reduces to the standard cosmological constant when Rényi entropy reduces to the Bekenstein-Hawking entropy. By examining different parameters, we affirm the validity of our approach to dark energy, which respects both holographic principle and thermodynamics.

gr-qc↗

arXiv2022

Emergence of cosmic space in Tsallis modified gravity from equilibrium and non-equilibrium thermodynamic perspective

In this paper, we obtain the law of emergence with Tsallis entropy from the thermodynamic laws. We first derive the law of emergence from the equilibrium description of the unified first law and Clausius relation. However, it has been shown that considering Tsallis entropy as the horizon entropy, the Clausius relation $δQ=T dS$ does not hold due to non-equilibrium thermodynamics and is replaced by the entropy-balance relation $dS=\frac{δQ}{T}+d_{i}S$, where $d_iS$ is the additional entropy produced due to the irreversible thermodynamic process. Hence, we derive the law of emergence from the non-equilibrium description of thermodynamic laws. The comparison between the law of emergence in both cases shows that the law of emergence from the non-equilibrium approach describes the expansion of the universe in terms of the areal volume, unlike the effective volume in the equilibrium case. We have further shown that the law of emergence also satisfies the condition of the maximization of entropy for a de Sitter universe; thus, the entropy of the universe evolves to a bounded value in the asymptotic future.

gr-qc↗

arXiv2022

Tsallis Holographic Dark Energy Reconsidered

We consider the interacting Tsallis Holographic Dark Energy (THDE), with the Granda-Oliveros (GO) scale as the infrared (IR) cutoff, as dynamical vacuum. We analytically solved for the Hubble parameter, in a spatially flat FLRW universe with dark energy and matter as components, and the solution traces the evolutionary path from the prior decelerated to the late accelerated epoch. Without interaction, the model predicts a $Λ$CDM like behavior with an effective cosmological constant. We used Pantheon Supernovae type Ia, observational Hubble data (OHD), cosmic microwave background (CMB), and baryon acoustic oscillation (BAO) data to constrain the free parameters of the model. The estimated values of the cosmological parameters were consistent with observational results. We analyzed the behavior of the model using the statefinder and $ω^\prime_{e}-ω_{e}$ plane where $ω_{e}$ and $ω^\prime_{e}$ corresponds to the effective equation of state and its evolution, respectively. The model shows a quintessence behavior in general, and the model trajectory ends in a point that corresponds to the de Sitter phase. We performed a dynamical analysis of the model, concluding that the prior decelerated and late accelerated phases are unstable and stable equilibria, respectively. We also investigated the thermodynamical nature of the model and found that the generalized second law remains valid in the dynamical vacuum treatment of the model.

gr-qc↗

arXiv2022

Modified expansion law with Kodama-Hayward temperature for the horizon

The expansion law proposed by Padmanabhan suggests that the evolution of the volume of the horizon is due to the difference between the degrees of freedom on the horizon and the degrees of freedom in the bulk enclosed by the horizon. In formulating this law, Padmanabhan used the temperature, $T=H/2π$, for a dynamical expansion. In this work, we modified the expansion law using Kodama-Hayward temperature, the dynamical temperature, for the horizon, first in (3+1) Einstein's gravity and extended it to higher order gravity theories such as (n+1) Einstein gravity, Gauss-Bonnet gravity, and more general Lovelock gravity. Contrary to the conventional approach, we expressed degrees of freedom of the horizon in terms of the surface energy of the horizon. Also, we have expressed modified expansion law in terms of cosmic components. It then turns out that it is possible to express the modified expansion law in a form as if $T=H/2π$ is the temperature of the dynamical horizon.

gr-qc↗

arXiv2022

Emergence of space and expansion of universe

According to the principle of emergence, the expansion of the universe can be explained as the emergence of space with the progress of cosmic time. We have analytically solved the equation of emergence proposed by Padmanabhan by assuming the Komar energy density $ρ+3P$ as a function of the Hubble parameter. The resulting model describes the evolution of the universe, which proceeds towards a final de Sitter state. Model parameters have been extracted using the cosmological observational data. Further, the horizon entropy evolution of the model has been studied. The model predicts a universe having a transition from a prior decelerated epoch to a late accelerated epoch and reasonably predicts the cosmological constant.

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arXiv2021

Emergence of space from non-equilibrium thermodynamics in f(R) gravity

It has shown that the accelerated expansion of the FRW Universe can be explained as the quest towards the holographic equipartition ($N_{sur} = N_{bulk}$), satisfies the expansion law $\frac{dV}{dt} = l_{P}^{2} \left( N_{sur} - εN_{bulk} \right)$, from which one can derive the Friedmann equation of the FRW Universe in Einstein gravity \cite{paddy2012jun}. We introduce a generic derivation of the expansion law from the generalized first law of thermodynamics $-dE=TdS$ and $dE=TdS + WdV$. The generic derivation provides an expression for $N_{sur}$ in terms of entropy $S$ and the expansion law consistent with gravity theories having different entropy $S$, like Gauss-Bonnet and more general Lovelock gravity. We extended the same idea to the non-equilibrium situation and obtained the expansion law in f(R) gravity as a specific case. For this, we used the first law of thermodynamics in non-equilibrium description having the extra entropy production term $Td_{i}S.$

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arXiv2021

Running vacuum model versus $Λ$CDM -- a Bayesian analysis

We study the running vacuum model in which the vaccum energy density depends on square of Hubble parameter in comparison with the $Λ$CDM model. In this work, the Bayesian inference method is employed to test against the standard $Λ$CDM model to appraise the relative significance of our model, using the combined data sets, Pantheon+CMB+BAO and Pantheon+CMB+BAO+Hubble data. The model parameters and the corresponding errors are estimated from the marginal likelihood function of the model parameters. Marginalizing over all model parameters with suitable prior, we have obtained the Bayes factor as the ratio of Bayesian evidence of our model and the $Λ$CDM model. The analysis based on Jeffrey's scale of bayesian inference shows that the evidence of our model against the $Λ$CDM model is weak for both data combinations. Even though the running vacuum model gives a good account of the evolution of the universe, it is not superior to the $Λ$CDM model.

gr-qc↗

arXiv2021

Pancharatnam-Berry phase in neutrino mixing

The Pancharatnam - Berry phase (PBP) of purely geometric origin appears as a reparametrization invariant quantity of ray Space. In this article, we investigate the properties exhibited by PBP in neutrino mixing. We map the neutrino flavour modes to independent flavour vacuum states and compute PBP using Bargmann invariant. We derive the exact formula for PBP in two flavour approximation using the kinematic approach. Our result reproduces previous results of Blasone et al. under cyclic condition. Inspired by the work of Mukunda and Simon, we investigate the total and dynamical phases separately. This method leads us to identify the existence of nodal points in the mixing parameter space. At nodal points, PBP changes by a value $π$, and it originates from the total phase. We report the direct relation between nodal points and MSW resonance, giving physical meaning to nodal points. Our analysis shows the ability of PBP to differentiate between different mass hierarchies and set numerical bounds to $Δm^2$ by changing total energy. We extend our studies to three flavour model and found that PBP is sensitive to the Dirac $CP$ phase ($δ_{CP}$). Using our $N$-qubit architecture of the $N$-flavour neutrino model, one can immediately study the dynamical characteristics like mode entanglement between neutrino flavour modes.

hep-ph↗

arXiv2021

Decaying vacuum and evolution from early inflation to late acceleration

Decaying vacuum models are a class of models that incorporate the vacuum energy density as a time-evolving entity that has the potential to explain the entire evolutionary history of the universe in a single framework. A general solution to the Friedmann equation can be obtained by considering vacuum energy density as a function of the Hubble parameter. We have obtained the asymptotic solution by choosing the appropriate equation of state for matter and radiation. Finite boundaries in the early and late de Sitter epoch could be defined by considering the evolution of primordial perturbation wavelength. An epoch invariant number $N_c$ determines the number of perturbation modes that cross the Hubble radii during each epoch has been obtained.

gr-qc↗

arXiv2018

Expansion Law From First Law of Thermodynamics

Padmanabhan in his paper [arxiv: 1206.4916] put forth an intriguing idea arguing that the accelerated expansion of the universse can be viewed as the emergence of cosmic space as cosmic time progresses, with the expansion triggered due to the difference in the degrees of freedom on a holographic surface and the one in its emerged bulk. We show that the modified expansion law of the universe proposed by Sheykhi in a non-flat Friedmann- Robertson-Walker (FRW) universe and by Cai in a flat FRW universe could be derived starting from the first law of thermodynamics, in (n+1) dimensional Einstein gravity, Gauss-Bonnet and more general Lovelock gravity theories. We have also derived the modified versions of the expansion law for a flat universe due to Yang et al, in the case of Gauss-Bonnet and Lovelock gravities, from the first law of thermodynamics. This approach is unique in the sense that all these modified versions of the expansion law is derived from a thermodynamic identity that has the same form regardless of the gravity theory and irrespective of whether the universe is flat or non-flat

gr-qc↗

arXiv2018

A model of the late universe with viscous Zel'ldovich fluid and decaying vacuum

Many have speculated about the presence of a stiff fluid in very early stage of the universe. Such a stiff fluid was first introduced by Zel'dovich. Recently the late acceleration of the universe was studied by taking bulk viscous stiff fluid as the dominant cosmic component, but the age predicted by such a model is less than the observed value. We consider a flat universe with viscous stiff fluid and decaying vacuum energy as the cosmic components and found that the model predicts a reasonable background evolution of the universe with de Sitter epoch as end phase of expansion. More over the model also predicts a reasonable value for the age of the present universe. We also perform a dynamical system analysis of the model and found that the end de Sitter phase predicted by the model is stable.

gr-qc↗

arXiv2016

Bulk viscous matter and recent acceleration of the Universe

We consider a cosmological model dominated by bulk viscous matter with total bulk viscosity coefficient proportional to the velocity and acceleration of the expansion of the universe in such a way that $ζ=ζ_{0}+ζ_{1}\frac{\dot{a}}{a}+ζ_{2}\frac{\ddot{a}}{\dot{a}}.$ We show that there exist two limiting conditions in the bulk viscous coefficients, ($ζ_{0}$, $ζ_{1}$, $ζ_{2}$) which corresponds to a universe having a Big-Bang at the origin, followed by an early decelerated epoch and then making a smooth transition into an accelerating epoch. We have constrained the model using the type Ia Supernovae data, evaluated the best estimated values of all the bulk viscous parameters and the Hubble parameter corresponding to the two limiting conditions. We found that even though the evolution of the cosmological parameters are in general different for the two limiting cases, they show identical behavior for the best estimated values of the parameters from both the limiting conditions. A recent acceleration would occur if $\tildeζ_{0}+\tildeζ_{1}>1$ for the first limiting conditions and if $\tildeζ_{0}+\tildeζ_{1}<1$ for the second limiting conditions. The age of the universe predicted by this model is found to be less than that predicted from the oldest galactic globular clusters. The total bulk viscosity seems to be negative in the past and becomes positive when $z\leq0.8$. So the model violates the local second law of thermodynamics. However, the model satisfies the generalized second law of thermodynamics at the apparent horizon throughout the evolution of the universe. We also made a statefinder analysis of the model and found that it is distinguishably different from the standard $Λ$CDM model at present, but shows a de Sitter type behavior in the far future of the evolution.

gr-qc↗

arXiv2015

Evolution of entropic dark energy and its phantom nature

Assuming the form of the entropic dark energy as arises form the surface term in the Einstein-Hilbert's action, it's evolution were analyzed in an expanding flat universe. The model parameters were evaluated by constraining model using the Union data on Type Ia supernovae. We found that the model predicts an early decelerated phase and a later accelerated phase at the background level. The evolution of the Hubble parameter, dark energy density, equation of state parameter and deceleration parameter were obtained. The model is diagnosed with $Om$ parameter. The model is hardly seems to be supporting the linear perturbation growth for the structure formation. We also found that the entropic dark energy shows phantom nature for redshifts $z<0.257.$ During the phantom epoch, the model predicts big-rip effect at which both the scale factor of expansion and the dark energy density become infinitely large and the big rip time is found to be around 36 Giga Years from now.

gr-qc↗

arXiv2015

Bulk viscous Zel'dovich fluid model and it's asymptotic behavior

In this paper we have considered a flat FLRW universe with bulk viscous Zel'dovich as the cosmic component. Being considered the bulk viscosity as per the Eckart formalism, we have analyzed the evolution of the Hubble parameter and constrained the model with the Type Ia Supernovae data thus extracting the constant bulk viscous parameter and present Hubble parameter. Further we have analyzed the scale factor, equation of state and deceleration parameter. The model predicts the late time acceleration and is also compatible with the age of the universe as given by the oldest globular clusters. We have also studied the phase-space behavior of the model and found that a universe dominated by bulk viscous Zel'dovich fluid is stable. But on the inclusion of radiation component in addition to the Zel'dovich fluid, makes the model unstable. Hence, even though the bulk viscous Zel'dovich fluid dominated universe is a feasible one, the model as such failed to predict a prior radiation dominated phase.

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