arXiv subjects

Titus K Mathew

Publications and source records attributed to Titus K Mathew.

At least 19 recordsLinked to original sources

arXiv2026

Generalized Mass-to-Horizon Entropy and Horizon Thermodynamics

We investigate the cosmological implications of generalized mass-to-horizon entropy, a two-parameter extension of the standard Bekenstein entropy based on the mass-to-horizon relation. Assuming the entropy balance relation, we derive the change in the generalized mass-to-horizon entropy, which entirely accounts for the heat exchange across the horizon as measured by an observer near the apparent horizon. We have then derived the Friedmann equation, using the Clausius relation, and also using modified law of thermodynamics. The thermodynamic consistency of the entropy, is examined through entropy evolution and entropy maximization conditions, where the generalized entropy and its higher-order derivatives indicate that the universe evolves toward a stable maximum entropy configuration consistent with the generalized second law of thermodynamics. In addition, fluctuations in horizon energy are investigated to probe the thermal stability and thermodynamic behavior of the cosmic horizon. The fluctuation analysis reveals finite and physically stable behavior throughout cosmic evolution, supporting the thermodynamic viability of the proposed model. The present work therefore establishes the generalized mass-to-horizon entropy as a viable thermodynamic framework for describing modified cosmological dynamics and also the accelerated expansion of the universe as well.

gr-qc↗

arXiv2026

Subtleties in non-equilibrium horizon thermodynamics of modified gravity theories

Thermodynamic interpretations of gravity often arise from applying the Clausius relation to spacetime horizons. In modified gravity theories with higher-order equations of motion, such as f(R) and scalar-tensor gravity, this relation generally acquires additional entropy-production term. In this context, two distinct formulations have been proposed in literature: the non-equilibrium approach of Eling, Guedens, and Jacobson based on local Rindler horizons, and the thermodynamic formulation of cosmological apparent horizons in FLRW spacetimes. In this article, we present a detailed analysis of these approaches, and show that, even though both employ identical entropy balance relations that resemble non-equilibrium thermodynamics, the exact origin and role of each entropy-production term is fundamentally different. In the Rindler-horizon framework the extra term follows directly from consistency requirements related to the Bianchi identity, whereas in the apparent-horizon approach it is introduced solely to recover the Friedmann equations. Furthermore, we will see that the latter non-equilibrium contribution enters directly into dynamical equations of gravity, while the former does not. Finally, we also highlight the fact that thermodynamic descriptions of horizons in such modified gravity are not unique, and that equilibrium, and non-equilibrium descriptions can arise from different choices of thermodynamic variables. A clear understanding of these distinctions is therefore crucial for establishing a consistent and physically meaningful thermodynamic foundation for gravity beyond general relativity.

gr-qc↗

arXiv2025

Cosmology with non-linear barotropic Israel-Stewart fluid with causal relaxation time

We derive an extended expression for the relaxation time of a barotropic Israel-Stewart (IS) fluid using the non-linear causality constraint, and propose a new formulation for modeling causal viscous dissipation in barotropic fluids. With this generalized relaxation time, the non-linear IS equation simplifies to a first-order non-linear expression connecting bulk viscous pressure and energy density, which remains valid in any homogeneous and isotropic spacetime. In the case of spatially flat Friedmann universe, adopting this extended relation in the generalized non-linear IS theory, provides new class of analytical solutions in both, the linear, and the non-linear regimes. We also find that, the resulting effective equation of state in the linear regime naturally reproduces the generalized polytropic form which is often introduced phenomenologically in literature. Resulting dynamical implications are investigated and the constraints necessary for ensuring an acceptable evolutionary behavior for the fluid are determined. A detailed dynamical system analysis of the coupled Einstein-Israel-Stewart (EIS) system is also performed. Finally, we solve the coupled EIS equations numerically, and show that the model can support a transient Hubble slow-roll expansion phase with a smooth exit to a radiation-dominated universe, which is challenging to obtain in standard inflationary models.

gr-qc↗

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↗

arXiv2025

$Λ$vCF: Extending $Λ$CDM into a Unified Model with Particle Creation

We present a novel extended version of the $Λ$CDM model that provides analytical solution for Hubble parameter uniting all epochs of cosmic evolution starting from inflation to late-acceleration, with intermediate radiation and matter-dominated epochs. This is achieved by relaxing the perfect fluid assumption in the standard model and considering a general viscous cosmic fluid (vCF) with non-zero particle creation rate and evolving adiabatic equation of state. Transition points of the Universe and the finite boundary connecting them is exactly determined. We then propose a novel method to determine the early-time viscous coefficient and inflation energy scale using the Cosmic Mode Index value postulated by Padmanabhan. Considering the data from the Planck 2018 analysis, this yields an inflationary Hubble parameter of $H_{I}\approx10^{13}$\,GeV. An equivalent scalar-field description for the inflationary epoch is then constructed and inferences are made regarding the nature of inflation. Notably, we find that the model describes an ultra-slow-roll hilltop inflation scenario with a graceful exit to radiation-dominated epoch. Subsequently, we show that bulk viscosity in this model can be expressed as Israel-Stewart equation in relativistic dissipative hydrodynamics with an appropriate underlying viscous coefficient and relaxation time that satisfy the causality constraint in its extreme limit. Finally, by comparing the evolution of this causal relation and its Navier-Stokes counterpart, we infer that the evolution from inflation to radiation era signifies a fluid transitioning from viscoelastic to pseudoplastic behavior.

astro-ph.CO↗

arXiv2024

Dissipative $Λ$CDM model with causal sign-switching bulk viscous pressure

Extending the standard $Λ$CDM model by considering dissipative effects within a causal viscous framework, and obtaining an analytical solution for the Hubble parameter remains a challenge in the literature. In this work, we resolve this dilemma by deriving a complete and original solution for the Hubble parameter by introducing a novel form for the bulk viscous coefficient associated with bulk viscous dark matter (vDM). A thorough analysis of the model is conducted by deriving theoretical constraints on the parameters and comparing the model with the latest observational data sets. Intriguingly, we find that the model predicts a sign-switching bulk viscous pressure, which facilitates both the early decelerated expansion and the late accelerated expansion of the universe. Also, the redshift at which the viscous pressure switches sign is found to be strongly correlated with the relaxation time parameter of the viscous fluid. Thermodynamic analysis revealed that, the model satisfies both the covariant and generalized second law of thermodynamics as well as the convexity condition for entropy. Additionally, we reconstructed the model by unifying viscous dark matter and dark energy into a single unified dark matter (UDM) component, and found that this unified model predicts identical dynamical evolution for the Universe, while satisfying the necessary near-equilibrium condition throughout that evolution (both in early and late phases).

astro-ph.CO↗

arXiv2024

Constraining the bulk viscous coefficients in a viscous universe with cosmological constant

In this paper we consider dissipative effects in $Λ$CDM model, i.e., we consider a universe with cosmological constant having viscous matter. We assume the most general form for bulk viscous coefficient, $ζ=ζ_{0}+ζ_{1}\frac{\dot{a}}{a}+ζ_{2}\frac{\ddot{a}}{\dot{a}}$ and obtained various constrains for $ζ$'s . We also studied the background study of the model with $ζ=ζ_{0}$ and $ζ=ζ_{1}\frac{\dot{a}}{a}$. Extracted the value of $ζ_1$ using the Pantheon data and also obtained its thermodynamic evolution and the age.

gr-qc↗

arXiv2023

Bulk viscous late acceleration under near equilibrium conditions in f(R, T) gravity with mixed matter

Various studies have shown that the late acceleration of the universe can be caused by the bulk viscosity associated with dark matter. But recently, it was indicated that a cosmological constant is essential for maintaining Near Equilibrium Conditions (NEC) for the bulk viscous matter during the accelerated expansion of the universe. In the present study, we investigate a model of the universe composed of mixed dark matter components, with viscous dark matter (vDM), and inviscid cold dark matter (CDM) as it's constituents, in the context of $f(R,T)$ gravity and showed that the model predicts late acceleration by satisfying NEC throughout the evolution, without cosmological constant. We have also compared the model predictions with combined Type Ia Supernovae and observational Hubble data sets and thereby determined the estimated values of different cosmological parameters.

gr-qc↗

arXiv2023

Near Equilibrium Constraints on Bulk Viscous Models in $f(R,T)=R+2λT$ Gravity

Recent studies indicate that, near equilibrium condition could not be maintained for bulk viscous matter models during the accelerated expansion of the universe in the context of Einstein's gravity, without including the cosmological constant. But from our investigation in $f(R,T)$ gravity, it is observed that, this condition can be satisfied in this modified gravity regime by properly constraining the coupling and viscous parameters. Accordingly, strict constraints are developed for free parameters in bulk viscous models in $f(R,T)=R+2λT$ gravity based on fulfillment near equilibrium condition. Then, for assessing the validity of NEC during different stages of evolution, two cosmological models are studied for each case based on the developed constraints. Initially, the data analysis of the models is performed using the Observational Hubble Data (OHD) and then later, model showing the best result is analyzed using combined OHD+SNe Ia data sets. From the obtained best fit values of model parameters, inferences are made regarding the possibilities of achieving recent acceleration for viscous models in $R+2λT$ gravity while simultaneously satisfying the required conditions both in the presence and absence of cosmological constant.

gr-qc↗

arXiv2023

Emergence of cosmic space with Barrow entropy, in non-equilibrium thermodynamic conditions

Recently, Barrow accounts for the quantum gravitational effects to the black hole surface. Thus the conventional area-entropy relation has modified, $S=(A/A_{0})^{1+Δ/2},$ with an exponent $Δ$, ranges $0\leΔ\le1$, quantifies the amount of quantum gravitational deformation effect to the black hole surface. In recent literature, this horizon entropy has been extended to the cosmological context. Following this, we consider an n+1 dimensional non-flat universe with an apparent horizon as the boundary with appropriate temperature and associated entropy is Barrow entropy. We derived the modified form of the law of emergence from the equilibrium and non-equilibrium thermodynamic principles. Later studied the entropy maximization condition due to the modified law of emergence. On distinguishing the obtained result, it speculates that in order to hold the energy-momentum conservation, the universe with Barrow entropy as the horizon entropy should have non-equilibrium behaviour with an additional entropy production. However, the additional entropy production rate decreases over time, so the system eventually approaches equilibrium. Because of this, the constraint relation for entropy maximization looks similar for both equilibrium and non-equilibrium approaches.

gr-qc↗

arXiv2023

Barrow Holographic Dark Energy Model with GO Cut-off -- An Alternative Perspective

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 $ω_Λ=-1.$ 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 $Λ$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, $Δ=0.063\pm 0.029$. 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 $Λ$CDM model.

gr-qc↗

arXiv2022

Geometric phases in neutrino mixing

Neutrinos can acquire both dynamic and geometric phases due to the non-trivial mixing between mass and flavour eigenstates. In this article, we derive the general expressions for all plausible gauge invariant diagonal and off-diagonal geometric phases in the three flavour neutrino model using the kinematic approach. We find that diagonal and higher order off-diagonal geometric phases are sensitive to the mass ordering and the Dirac CP violating phase $δ$. We show that, third order off-diagonal geometric phase ($Φ_{μeτ}$) is invariant under any cyclic or non-cyclic permutations of flavour indices when the Dirac CP phase is zero. For non-zero $δ$, we find that $Φ_{μeτ}(δ)=Φ_{e μτ}(-δ)$. Further, we explore the effects of matter background using a two flavour neutrino model and show that the diagonal geometric phase is either 0 or $π$ in the MSW resonance region and takes non-trivial values elsewhere. The transition between zero and $π$ occurs at the point of complete oscillation inversion called the nodal point, where the diagonal geometric phase is not defined. Also, in two flavour approximations, two distinct diagonal geometric phases are co-functions with respect to the mixing angle. Finally, in the two flavour model, we show that the only second order off-diagonal geometric phase is a topological invariant quantity and is always $π$.

hep-ph↗

arXiv2022

Emergence of cosmic space and its connection with thermodynamic principles

The recent research on the connection between gravity and thermodynamics suggests that gravity could be an emergent phenomenon. Following this, Padmanabhan proposed a novel idea that the expansion of the universe can be interpreted as equivalent to the emergence of space with the progress of cosmic time. In this approach, the expansion of the universe is described by what is known as the law of emergence, which states that the expansion of the universe is driven by the difference between the number of bulk and surface degrees of freedom in a region bounded by the Hubble radius. This principle correctly reproduces the standard evolution of a Friedmann universe. We establish the connection of the law of emergence, which is conceptually different from the conventional paradigm to describe cosmology, with other well-established results in thermodynamics. It has been shown that the law of emergence can be derived from the unified first law of thermodynamics, which can then be considered as the backbone of the law. However, the law of emergence is rich in structure than implied by the First law thermodynamics alone. It further explains the evolution of the universe towards a state of maximum horizon entropy. Following this, it can be considered that the first law of thermodynamics, along with the additional constraints imposed by the maximisation of the horizon entropy, can together lead to the law of emergence. In the present article, we first make a brief review of Padmanabhan's proposal and then studies its connection with the thermodynamics of the horizon in the context of Einstein's, Gauss-Bonnet, and more general Lovelock gravity theories.

gr-qc↗

arXiv2022

Running vacuum cosmology with bulk viscous matter

We study the late acceleration of the universe by incorporating bulk viscous matter with the running vacuum. The vacuum energy density varies as the squares of the Hubble parameter ($ρ_Λ\propto H^2$), and the coefficient of bulk viscosity of matter is proportional to the velocity of expansion ($ξ\propto H$). We obtained an analytical solution to the Friedmann equations and estimated the model parameters using the combined data set SN1a+CMB+BAO+OHD. We have evaluated the universe's age as 14 Gyr, which is slightly higher than the age-predicted by the $Λ$CDM model. However, it is an improved result compared to the age-predicted by a class of bulk viscous matter-dominated models. Interestingly, we have obtained the coefficient of bulk viscosity of the matter component as $1.316\times 10^5$ kg $\textnormal m^{-1}$ $\textnormal s^{-1}$ which is one to two orders of magnitude less than the value predicted by most of the bulk viscous matter-dominated models and it falls in the range of highly viscous materials found on the earth. The Hubble parameter is a decreasing function of the scale factor, and it attains a constant value in the far future that corresponds to an end deSitter phase of evolution. The deceleration parameter shows a transition from matter-dominated decelerated phase to vacuum energy-dominated accelerating phase, and the transition redshift is obtained as $z_T = 0.73$. The statefinder analysis distinguishes our model from the $Λ$CDM model at present, and the $r-s$ trajectory reveals the quintessence behaviour of the vacuum energy. The phase space analysis shows that the universe is evolving towards a mechanically stable state in the far future. The entropy evolution satisfies the generalised second law of thermodynamics, and the entropy is maximised in the far future evolution.

gr-qc↗

arXiv2021

Contrasting the bulk viscous model with the standard $Λ$CDM using Bayesian statistics

Causal dissipative model is a plausible choice to explain the late accelerated epoch of universe. At the same time $Λ$CDM is considered to be standard model to explain the cosmological data corresponding to the late evolution of the universe. We consider a bulk viscus model in which the dissipation is driven by the bulk viscosity $ζ=αρ^{1/2}$, described using the full causal Israel-Stewart theory. We computed the model parameters using the latest observational data (Pantheon). We contrasted this model with $Λ$CDM model for the late accelerated phase using Bayesian inference method. The Bayes factor has been obtained by calculating the likelihood for Pantheon data. Suitable prior values has been assumed for model parameters for calculating the likelihood. It shows that the evidence for $Λ$CDM against this viscous model is very strong according to Jeffrey's scale.

gr-qc↗

arXiv2021

On the feasibility of truncated Israel-Stewart model in the context of late acceleration

A dissipative model of the Universe based on the causal relativistic truncated Israel-Stewart theory is analysed in the context of recent accelerated expansion of the Universe. The bulk viscosity and relaxation time are taken as $ξ=αρ^s$ and $τ=\fracα{εγ(2-γ)}ρ^{s-1}$ respectively. For $s=1/2,$ we found an analytical solution for the Hubble parameter of the model. We have estimated the model parameters by treating $γ=1$ and $γ$ as a free parameter using the latest cosmological data. The model predicts a prior decelerated phase and an end de Sitter phase as in the standard $Λ$CDM model. The dynamical system analysis shows that the prior decelerated epoch is an unstable equilibrium, while the far future de Sitter epoch is stable. The age of the Universe obtained around $13.66$ Gyr, which is close to the recent observations. The second law of thermodynamics is found to be satisfied throughout the evolution in this model. The feasibility of the model has been checked by contrasting with models based on the full Israel-Stewart and the Eckart viscous theories. The truncated viscous model appears more compatible with astronomical observations than the Eckart and full causal viscous models.

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

Bayesian analysis of running holographic Ricci dark energy

Holographic Ricci dark energy evolving through its interaction with dark matter is a natural choice for the running vacuum energy model. We have analyzed the relative significance of two versions of this model in the light of SNIa, CMB, BAO and Hubble data sets using the method Bayesian inferences. The first one, model 1, is the running holographic Ricci dark energy (rhrde) having a constant additive term in its density form and the second is one, model 2, having no additive constant, instead the interaction of rhrde with dark matter is accounted through a phenomenological coupling term. The Bayes factor of these models in comparison with the standard $Λ$CDM have been obtained by calculating the likelihood of each model for four different data combinations, SNIa(307)+CMB+BAO, SNIa(307)+CMB+BAO+Hubble data, SNIa(580)+CMB+BAO and SNIa(580)+CMB+BAO+Hubble data. Suitable flat priors for the model parameters has been assumed for calculating the likelihood in both cases. Our analysis shows that, according to the Jeffreys scale, the evidence for $Λ$CDM against both model 1 and model 2 is very strong as the Bayes factor of both models are much less than one for all the data combinations.

gr-qc↗