arXiv subjects

Titus K Mathew

Publications and source records attributed to Titus K Mathew.

34 records · Page 2Linked to original sources

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

First Law of Thermodynamics and Emergence of Cosmic Space in a Non-Flat Universe

The emergence of cosmic space as cosmic time progresses is an exciting idea advanced by Padmanabhan to explain the accelerated expansion of the universe. The generalization of Padmanabhan's conjecture to the non-flat universe has resulted in scepticism about the choice of volume such that the law of emergence can not be appropriately formulated if one uses proper invariant volume. The deep connection between the first law of thermodynamics and the law of emergence \cite{mahith}, motivate us to explore the status of the first law in a non-flat universe when one uses proper invariant volume. We have shown that the first law of thermodynamics, $dE = TdS +WdV$ cannot be formulated properly for a non-flat universe using proper invariant volume. We have also investigated the status of the first law of the form $-dE = TdS$ in a non-flat universe. We have shown that the energy change dE within the horizon and the outward energy flux are not equivalent to each other in a non-flat universe when we use the proper invariant volume. We have further shown that the consistency between the above two forms of the first law claimed in Ref. \cite{caiakb} will hold only with the use of the areal volume of the horizon. Thus, a consistent formulation of the above two forms of the first law of thermodynamics demands the use of areal volume.

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↗

arXiv2018

Probing the dynamical system and thermal behaviours of the model, $Λ_0+3 βH^2.$

In this work we study the cosmological evolution of a two component model with non-relativistic dark matter and decaying vacuum of the form $Λ= Λ_0 + 3 βH^2.$ We contrast the model the model with the supernovae data and found that the model parameter $β=-0.010$ when the interaction parameter is zero and is $β=-0.002$ when $b=0.001.$ The thermal evolution study of the model indicates that it obeys the generalized second of entropy and also satisfies the convexity condition, $\ddot S <0$ so that the model behaves like an ordinary macroscopic system which approaching a stable equilibrium thermal state is the asymptotic condition. The dynamical system analysis reveals that, the model posses a prior decelerated epoch represented by a saddle critical point and the late critical point represents an accelerating epoch which posses a convergence of phase-space trajectories form both the regions of the point hence can be considered as stable.

gr-qc↗

arXiv2018

Interacting holographic Ricci dark energy as running vacuum

Earlier studies have shown that, in a two component model of the universe with dark matter and the running vacuum energy which is phenomenologically a combination of $H^2$ and $\dot{H},$ produces either eternal deceleration or acceleration in the absence of a bare constant in the density of the running vacuum. In this paper we have shown that, in the interaction scenario, where the interaction between matter and vacuum is introduced through a phenomenological term, the two component model is capable of causing a transition from a prior decelerated to a later accelerated epoch without a bare constant in the running vacuum density. On contrasting the model with the cosmological data, we have found that the interaction coupling constant, is small enough, for a slow decay of the running vacuum. The model is subjected to dynamical system analysis which revealed that the end de Sitter phase of the model is a stable one. We did an analysis on the thermal behavior of the system, which shows that the entropy is bounded at the end stage so that the system is behaving like an ordinary macroscopic system. Apart from these we have also performed the state finder diagnostic analysis which implies the quintessence nature of running vacuum and confirms that the model will approach the standard $Λ$CDM in the future.

gr-qc↗

arXiv2018

Bulk viscous matter and recent acceleration of the universe based on causal viscous theory

Evolution of the bulk viscous matter dominated universe has been analysed using the full causal, Israel-Stewart theory for the evolution of bulk viscous pressure in the context of recent acceleration of the universe. The form of bulk viscosity is taken as $ξ=αρ^{1/2}. $ We obtained analytical solutions for the Hubble parameter and scale factor of the universe. The model parameters have been computed using the Type Ia supernovae observational data. The evolution of the prominent cosmological parameters were obtained. The age of the universe for the best estimated model parameters is found to be less than observational value. The viscous matter behaves like stiff fluid in the early evolutionary phase and then evolves to a negative pressure fluid in the later phase. The equation of state is found to be stabilized with value $ω>-1$ and thus, the model is not showing any of the phantom behaviour during the evolution. The local as well as generalized second law of thermodynamics are satisfied in this model, while it was shown by many that the local second law is breaking in the Eckart formalism approach. The statefinder geometric diagnostic shows that the present model is distinct from the standard $Λ$CDM model of the universe. One of the marked deviation seen in this model compared to a corresponding model using Eckart approach is that the bulk viscosity decreases with expansion of the universe, while in it increases from negative value in the early universe towards positive values values in the Eckart formalism.

gr-qc↗

arXiv2018

Bayesian analysis of bulk viscous matter dominated universe

In our previous works, we have analyzed the evolution of bulk viscous matter dominated universe with a more general form for bulk viscous coefficient, $ζ=ζ_{0}+ζ_{1}\frac{\dot{a}}{a}+ζ_{2}\frac{\ddot{a}}{\dot{a}}$ and also carried out the dynamical system analysis. We found that the model reasonably describes the evolution of the universe if the viscous coefficient is a constant. In the present work we are contrasting this model with the standard $Λ$CDM model of the universe using the Bayesian method. We have shown that, even though the viscous model gives a reasonable back ground evolution of the universe, the Bayes factor of the model indicates that, it is not so superior over the $Λ$CDM model, but have a slight advantage over it.

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↗

arXiv2016

Phase space analysis of bulk viscous matter dominated universe

We consider a Friedmann model of the universe with bulk viscous matter and radiation as the cosmic components. We study the asymptotic properties in the equivalent phase space by considering the three cases for the bulk viscous coefficient as (i) $ζ= ζ_{0}$, a constant (ii) $ζ= ζ_{0} + ζ_{1}\frac{\dot{a}}{a}$, depending on velocity of the expansion of the universe and (iii) $ζ= ζ_{0} + ζ_{1}\frac{\dot{a}}{a} + ζ_{2}\frac{\ddot{a}}{\dot{a}}$, depending both on velocity and acceleration of the expansion of the universe. It is found that all the three cases predicts the late acceleration of the universe. However, a conventional realistic behaviour of the universe, i.e., a universe having an initial radiation dominated phase and then followed by decelerated matter dominated phase and then finally evolving to accelerated epoch, is shown only when $ζ= ζ_{0}$, a constant. For the other two cases, it does not show either a prior conventional radiation dominated phase or a matter dominated phase of the universe.

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arXiv2015

Holographic Ricci dark energy as running vacuum

Holographic Ricci dark energy has been proposed ago has faced with problems of future singularity. In the present work we consider the Ricci dark energy with an additive constant in it's density as running vacuum energy. We have analytically solved the Friedmann equations and also the role played by the general conservation law followed by the cosmic components together. We have shown that the running vacuum energy status of the Ricci dark energy helps to remove the possible future singularity in the model. The additive constant in the density of the running vacuum played an important role, such that, without that, the model predicts either eternal deceleration or eternal acceleration. But along with the additive constant, equivalent to a cosmological constant, the model predicts a late time acceleration in the expansion of the universe, and in the far future of the evolution it tends to de Sitter universe.

gr-qc↗

arXiv2014

Cosmology and thermodynamics of FRW universe with bulk viscous stiff fluid

We consider a cosmological model dominated by stiff fluid with a constant bulk viscosity. We classify all the possible cases of the universe predicted by the model and analyzing the scale factor, density as well as the curvature scalar. We find that when the dimensionless constant bulk viscous parameter is in the range $0 < \barζ<6$ the model began with a Big Bang, and make a transition form the decelerating expansion epoch to an accelerating epoch, then tends to the de Sitter phase as $ t\to \infty$. The transition into the accelerating epoch would be in the recent past, when $4<\barζ<6.$ For $\barζ>6$ the model doesn't have a Big Bang and suffered an increase in the fluid density and scalar curvature as the universe expands, which are eventually saturates as the scale factor $a \to \infty$ in the future. We have analyzed the model with statefinder diagnostics and find that the model is different from $Λ$CDM model but approaches $Λ$CDM point as $a \to \infty.$ We have also analyzed the status of the generalized second law of thermodynamics with apparent horizon as the boundary of the universe and found that the law is generally satisfied when $0 \leq \barζ<6$ and for $\barζ>6$ the law is satisfied when the scale factor is larger than a minimum value.

gr-qc↗

arXiv2013

Holographic Ricci dark energy and generalized second law

We explore the validity of the generalized second law (GSL) of thermodynamics in flat FRW universe with apparent horizon and event horizon as the boundary. We found that in a universe with holographic Ricci dark energy and dark matter, interacting with each other, the GSL is satisfied at the apparent horizon and partially satisfied at the event horizon under thermal equilibrium conditions. We also analyses the GSL under non-equilibrium conditions and shows that the fulfillment of GSL at the apparent horizon implies that the temperature of the dark energy is greater than that of the horizon. Thus there occurs a flow of dark energy towards the apparent horizon. As a result the entropy of the dark energy decreases and that of horizon increases. This is verified by finding the evolution of the dark energy entropy and horizon entropy in a dark energy dominated universe under non-equilibrium conditions.

gr-qc↗

arXiv2013

Interacting modified holographic Ricci dark energy model and statefinder diagnosis in flat universe

In this work we have considered the modified holographic Ricci dark energy interacting with dark matter through a non-gravitational coupling. We took three phenomenological forms for the interaction term $Q$ in the model, where in general $Q$ is proportional to the Hubble parameter and densities of the dark sectors, $ρ_{de}+ρ_m, \, ρ_m$ and $ρ_{de}$ respectively. We have obtained analytical solutions for the three interacting models, and studied the evolutions of equations of state parameter, deceleration parameter. The results are compared with the observationally constrained values for the best parameters of the model. We have also done the statefinder analysis of the model to discriminate the model from other standard models. In general we have shown that the model is showing a de Sitter type behavior in the far future of the evolution of the universe.

astro-ph.CO↗

arXiv2013

Cosmological horizon entropy and generalised second law for flat Friedmann Universe

We discuss the generalized second law (GSL) and the constraints imposed by it for two types of Friedmann universes. The first one is the Friedmann universe with radiation and a positive cosmological constant, and the second one consists of non-relativistic matter and a positive cosmological constant. The time evolution of the event horizon entropy and the entropy of the contents within the horizon are analyses in an analytical way by obtaining the Hubble parameter. It is shown that the GSL constraint the temperature of both the radiation and matter of the Friedmann universe. It is also shown that, even though the net entropy of the radiation (or matter) is decreasing at sufficiently large times as the universe expand, it exhibit an increase during the early times when universe is decelerating. That is the entropy of the radiation within the comoving volume is decreasing only when the universe has got an event horizon.

astro-ph.CO↗

arXiv2012

Modified holographic Ricci dark energy model and statefinder diagnosis in flat universe

Evolution of the universe with modified holographic Ricci dark energy model is considered. Dependency of the equation of state parameter and deceleration parameter on the redshift and model parameters are obtained. It is shown that the density evolution of both non-relativistic matter and dark energy are the same until recent times. The evolutionary trajectories of the model for different model parameters are obtained in the statefinder planes, r-s and r-q planes. The present statefinder parameters are obtained for different model parameter values, using that the model is differentiated from other standard models like $Λ$CDM model etc. We have also shown that the evolutionary trajectories are depending on the model parameters, and at past times the dark energy is behaving like cold dark matter, with equation of state equal to zero.

astro-ph.CO↗