arXiv subjects

D. Panigrahi

Publications and source records attributed to D. Panigrahi.

18 recordsLinked to original sources

arXiv2025

Emergent Universe Scenario in the Modified Chaplygin gas : Towards an Exact Solution and Observational Constraints

The Modified Chaplygin Gas (MCG) model is revisited as a unified framework for describing cosmic evolution. Due to the nonlinear field equations, exact solutions in cosmic time are generally unavailable; hence, a first-order approximation is employed to obtain the scale factor and flip time. The effective equation-of-state parameter evolves from a positive value in the early universe to $w_{\mathrm{eff}}\approx -1$ at late times, yielding a transition from deceleration to acceleration and approaching the $\Lambda$CDM limit. In the phantom regime, the model admits an emergent solution with a finite minimum scale factor and a late-time de~Sitter--like phase. The emergent solution is geodesically complete and free from curvature singularities, as confirmed by the regular Kretschmann scalar. CMB constraints for all considered cases remain consistent with observations within the $1\sigma$ confidence level, while the combined Hubble-$57$ and CMB analysis provides improved parameter constraints. The solutions are further verified independently using the Raychaudhuri equation, providing an additional consistency check. Overall, the results establish the MCG model as a self-consistent and observationally viable framework for cosmic evolution within general relativity.

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arXiv2025

Higher-Dimensional Cosmology in the Framework of Generalized Chaplygin Gas: An Approximation Method

We present a higher-dimensional cosmological model with a generalized Chaplygin-type gas to explain the late-time acceleration of the Universe. The model admits dimensional reduction and reproduces the standard $4D$ Chaplygin cosmology for $d=0$. Using Hubble-$57$ data, we obtain observational constraints on the model parameters. Due to the highly nonlinear nature of the field equations, the model successfully describes both matter-dominated and accelerating phases of the Universe. By adopting a first-order approximation, we derive exact time-dependent solutions for the scale factors in both ordinary and extra dimensions, along with an exact expression for the flip time. The model approaches the $\Lambda$CDM scenario at large scale factors and exhibits the desired transition from deceleration to acceleration. The evolution of the deceleration parameter, effective EoS parameter, and jerk parameter is also discussed. The constrained value of the Chaplygin parameter $\alpha \ll 1$ disfavors the pure Chaplygin gas model $(\alpha = 1)$ and suggests that smaller values of $\alpha$ are favored at late times.

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arXiv2025

Studies of the Inhomogeneous Cosmology in Higher Dimensional space-time with a Cosmological Constant

We have studied the inhomogeneous cosmology in Kaluza-Klein spacetime with a positive cosmological constant in a dust dominated era ($p = 0$). Depending on the integration constant we have derived two types of solutions. The dimensional reduction of extra dimensional scale factor is possible due to inhomogeneity depending on the curvature of the metric for positive cosmological constant for all solutions. The high value of entropy in present observable universe and the possible matter leakage in $4D$ world due to reduction of extra dimension are also discussed. Our solutions show the early deceleration and late accelerating nature of the universe. Findings are verified by the wellknown Raychaudhuri equation.

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arXiv2021

Accelerating Universe in Higher Dimensional Space Time : an alternative approach

We have discussed here a higher dimensional cosmological model and explained the recent acceleration with a Chaplygin type of gas. Dimensional reduction of extra space is possible in this case. Our solutions are general in nature because all the well known results of 4D Chaplygin driven cosmology are recovered when $d = 0$. We have drawn the best fit graph using the data obtained by the differential age method (CC) and it is seen that the graph favours only one extra dimension. That means the Chaplygin gas is apparently dominated by a 5D world. Relevant to point out that the final equation in this case are highly nonlinear in nature. Naturally it is not possible to obtain explicit solution of the 4D scale factor with time. To circumvent this difficulty, we consider a first order approximation of the key equation which has made it possible to get time explicit solution of 4D scale factor in exact form as well as the expression of extra dimensions. It may be pointed out that for large four dimensional scale factor this solution mimics $Λ$CDM model. An analysis of flip time is also studied both analytically and graphically in some detail. It clearly shows that early \emph{flip} occurs for higher dimensions. It is also seen that the rate of dimensional reduction is faster for higher dimensions. So we may conclude that the effect of compactification of extra dimension helps the acceleration.

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arXiv2019

Tolman-Bondi-Lemaître spacetime with a generalised Chaplygin gas

The Tolman-Bondi-Lemaître type of inhomogeneous spacetime with generalised Chaplygin gas equation of state given by $p = -\frac{A}{ρ^α}$ is investigated where $ α$ is a constant. We get an inhomogeneous spacetime at early stage but at the late stage of universe the inhomogeneity disappear with suitable radial co-ordinate transformation. For the large scale factor our model behaves like $Λ$CDM type which is in accord with the recent WMAP studies. We have calculated $\frac{\partial ρ}{\partial r}$ and it is found to be negative for $α> 0$ which is in agreement with the observational analysis. A striking difference with Chaplygin gas ($ α= 1$) lies in the fact that with any suitable co-ordinate transformation our metric cannot be reduced to the Einstein-de Sitter type of homogeneous spacetime as is possible for the Chaplygin gas. We have also studied the effective deceleration parameter and find that the desired feature of \emph{flip} occurs at the late universe. It is seen that the flip time depends explicitly on $α$. We also find that flip is not synchronous occurring earlier at the outer shells, thus offering a natural path against occurrence of wellknown shell crossing singularity. This is unlike the Tolman-Bondi case with perfect gas where one has to impose stringent external conditions to avoid this type of singularity. We further observe that if we adopt separation of variables method to solve the field equations the inhomogeneity in matter distribution disappears. The whole situation is later discussed with the help of Raychaudhury equation and the results compared with previous cases. This work is the generalisation of our previous article where we have taken $α=1$.

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arXiv2019

Evolution of FRW universe in variable modified Chaplygin gas model

In this paper we study the evolution of the FRW universe filled with variable modified Chaplygin gas (VMCG). We begin with a thermodynamical treatment of VMCG described by the equation of state $P = Aρ-Bρ^{-α}$, and obtain its temperature as a function of redshift $z$. We show that the results are consistent with similar works on other types of Chaplygin gas models. In addition to deriving the exact expression of temperature of the fluid in terms of the boundary conditions and redshift, we also used observational data to determine the redshift at the epoch of transition from the decelerated to the accelerated phase of expansion of the universe. The values of other relevant parameters like the Hubble parameter, the equation-of-state parameter and the speed of sound are obtained in terms of the redshift parameter, and these values are compared with the results obtained from previous works on MCG and other Chaplygin gas models for the various values of $n$ permitted by thermodynamic stability. We assume the present value of temperature of the microwave background radiation to be given by $ T_0 = 2.7 K $, and the parameter $ A $ in the equation of state is taken as $ 1/3 $ since it corresponds to the radiation-dominated phase of the universe. The value of the parameter $Ω_x$ has been assumed to be $0.7$ in our calculation. Since it is known that the redshift of photon decoupling is $ z\simeq 1100 $, we used this value to calculate the temperature of decoupling.

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arXiv2016

Viability of Variable Generalised Chaplygin gas - a thermodynamical approach

The viability of the variable generalised Chaplygin gas (VGCG) model is analysed from the standpoint of its thermodynamical stability criteria with the help of an equation of state, $P = - \frac{B}{ρ^α}$, where $B = B_{0}V^{-\frac{n}{3}}$. Here $B_{0}$ is assumed to be a positive universal constant, $n$ is a constant parameter and $V$ is the volume of the cosmic fluid. We get the interesting result that if the well-known stability conditions of a fluid is adhered to, the values of $n$ are constrained to be negative definite to make $ \left(\frac{\partial P}{\partial V}\right)_{S} <0$ \& $ \left(\frac{\partial P}{\partial V}\right)_{T} <0$ throughout the evolution. Moreover the positivity of thermal capacity at constant volume $c_{V}$ as also the validity of the third law of thermodynamics are ensured in this case. For the particular case $n = 0$ the effective equation of state reduces to $Λ$CDM model in the late stage of the universe while for $n <0$ it mimics a phantom-like cosmology which is in broad agreement with the present SNe Ia constraints like VGCG model. The thermal equation of state is discussed and the EoS parameter is found to be an explicit function of temperature only. Further for large volume the thermal equation of state parameter is identical with the caloric equation of state parameter when $ T \rightarrow 0$. It may also be mentioned that like Santos et al our model does not admit of any critical points. We also observe that although the earlier model of Lu explains many of the current observational findings of different probes it fails to explain the crucial tests of thermodynamical stability.

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arXiv2016

Thermodynamics of the Variable Modified Chaplygin gas

A cosmological model with a new variant of Chaplygin gas obeying an equation of state(EoS), $P = Aρ- \frac{B}{ρ^α}$ where $B= B_{0}a^{n}$ is investigated in the context of its thermodynamical behaviour. Here $B_{0}$ and $n$ are constants and $a$ is the scale factor. We show that the equation of state of this `Variable Modified Chaplygin gas' (VMCG) can describe the current accelerated expansion of the universe. Following standard thermodynamical criteria we mainly discuss the classical thermodynamical stability of the model and find that the new parameter, $n$ introduced in VMCG plays a crucial role in determining the stability considerations and should always be \emph{negative.} We further observe that although the earlier model of Lu explains many of the current observational findings of different probes it fails the desirable tests of thermodynamical stability. We also note that for $n < 0$ our model points to a phantom type of expansion which, however, is found to be compatible with current SNe Ia observations and CMB anisotropy measurements. Further the third law of thermodynamics is obeyed in our case. Our model is very general in the sense that many of earlier works in this field may be obtained as a special case of our solution. An interesting point to note is that the model also apparently suggests a smooth transition from the big bang to the big rip in its whole evaluation process.

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arXiv2014

Constraining Modified Chaplygin gas parameters

We investigate the evolution of a FRW model fuelled by a modified Chaplygin gas with an equation of state $p = Aρ-\frac{B}{ρ^α}$. An attempt is made here to constrain the free parameters of MCG model through the wellknown contour plot technique using observational data. The permissible range of values of the pair of free parameters are determined to study the viability of cosmological models \emph{vis-a-vis} observational results. Aside from allowing the desirable feature of \emph{flip} of the sign of deceleration parameter we also find that the transition from the decelerating to the accelerating phase occurs at relatively low value of redshift in accordance with the observational prediction that the acceleration is a recent phenomenon. It is found that the effective acoustic speed may become imaginary depending upon the initial conditions signalling that perturbations associated with instability sets in resulting in structure formation. As one considers more negative values of $A$ the \emph{flip} in sign is delayed resulting the density parameter to change fast. Again it is found from the contour plot that compatibility with observational results is admitted with a value of $A$ which is very near to zero or a small negative number.

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arXiv2012

FRW type of cosmology with a Chaplygin gas

The evolution of a universe modelled as a mixture of generalised Chaplygin gas and ordinary matter field is studied for a Robertson Walker type of spacetime. This model could interpolate periods of a radiation dominated, matter dominated and a cosmological constant dominated universe. Depending on the arbitrary constants appearing in our theory the instant of flip changes. Interestingly we also get a bouncing model when the signature of one of the constants changes. The velocity of sound may become imaginary under certain situations pointing to a perturbative state and consequently the possibility of structure formation. We also discuss the whole situation in the backdrop of wellknown Raychaudhury equation and a comparison is made with the previous results.

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arXiv2011

Spherically symmetric inhomogeneous model with Chaplygin gas

We investigate the late time acceleration with a Chaplygin type of gas in spherically symmetric inhomogeneous model. At the early phase we get Einstien-deSitter type of solution generalised to inhomogeneous spacetime. But at late stage of the evolution our solutions admit the accelerating nature of the universe. For a large scale factor our model behaves like a ?CDM model. We calculate the deceleration parameter for this anisotropic model, which, unlike its homogeneous counterpart, shows that the flip is not syn- chronous occurring early at the outer shells. This is in line with other physical processes in any inhomogeneous models. Depending upon initial conditions our solution also gives bouncing universe. In the absence of inhomogeneity our solution reduces to wellknown solutions in homogeneous case. We have also calculated the effective deceleration parameter in terms of Hubble parameter. The whole situation is later discussed with the help of wellknown Raychaudhury equation and the results are compared with the previous case. This work is an extension of our recent communication where an attempt was made to see if the presence of extra dimensions and/or inhomogeneity can trigger an inflation in a matter dominated Lemaitre Tolman Bondi model.

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arXiv2010

Quintessential Phenomena in Higher Dimensional Space Time

The higher dimensional cosmology provides a natural setting to treat, at a classical level, the cosmological effects of vacuum energy. Here we discuss two situations where starting with an ordinary matter field without any equation of state we end up with a Chaplygin type of gas apparently as a consequence of extra dimensions. In the second case we study the quintessential phenomena in higher dimensional spacetime with the help of a Chaplygin type of matter field. The first case suffers from the disqualification that no dimensional reduction occurs, which is, however, rectified in the second case. Both the models show the sought after feature of occurrence of \emph{flip} in the rate of expansion. It is observed that with the increase of dimensions the occurrence of \emph{flip} is delayed for both the models, more in line with current observational demands. Interestingly we see that depending on some initial conditions our model admits QCDM, $Λ$CDM and also Phantom like evolution within a unified framework. Our solutions are general in nature in the sense that when the extra dimensions are switched off the known 4D model is recovered.

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arXiv2009

Dimension Driven Accelerating Universe

The current acceleration of the universe leads us to investigate higher dimensional gravity theory, which is able to explain acceleration from a theoretical view point without the need of introducing dark energy by hand. We argue that the terms containing higher dimensional metric coefficients produce an extra negative pressure that apparently drives an acceleration of the 3D space, tempting us to suggest that the accelerating universe seems to act as a window to the existence of extra spatial dimensions. Interesting to point out that in this case our cosmology apparently mimics the well known quintessence scenario fuelled by a generalised Chaplygin-type of fluid where a smooth transition from a dust dominated model to a de Sitter like one takes place. Correspondence to models generated by a tachyonic form of matter is also briefly discussed.

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arXiv2009

Alfven wave in higher dimensional space time

Following the wellknown spacetime decomposition technique as applied to (d+1) dimensions we write down the equations of magnetohydrodynamics (MHD) in a spatially at generalised FRW universe. Assuming an equation of state for the background cosmic fluid we find solutions in turn for acous- tic waves and also for Alfven waves in a warm (cold) magnetised plasma. Interestingly the different plasma modes closely resemble the at space coun- terparts except that here the field variables all redshift with their time due to the expansion of the background. It is observed that in the ultrarelativistic limit the field parameters all scale as the free photon. The situation changes in the prerelativistic limit where the frequencies change in a bizarre fashion depending on initial conditions. It is observed that for a fixed magnetic field in a particular medium the Alfven wave velocity decreases with the number of dimensions, being the maximum in the usual 4D. Further for a fixed dimension the velocity attenuation is more significant in dust compared to the radiation era. We also find that in an expanding background the Alfven wave propaga- tion is possible only in the high frequency range, determined by the strength of the external magnetic field, the mass density of the medium and also the dimensions of the spacetime. Further it is found that with expansion the cosmic magnetic field decays more sharply in higher dimensional cosmology, which is in line with observational demand.

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arXiv2008

General relativistic plasma in higher dimensional space time

The well known (3+1) decomposition of Thorne and Macdonald is invoked to write down the Einstein-Maxwell equations generalised to (d+1) dimensions and also to formulate the plasma equations in a flat FRW like spacetime in higher dimensions (HD). Assuming an equation of state for the background metric we find solutions as also dispersion relations in different regimes of the universe in a unified manner both for magnetised(un) cold plasma. We find that for a free photon in expanding background we get maximum redshift in 4D spacetime, while for a particular dimension it is so in pre recombination era. Further wave propagation in magnetised plasma is possible for a restricted frequency range only, depending on the number of dimensions. Relevant to point out that unlike the special relativistic result this allowed range evolves with time. Interestingly the dielectric constant of the plasma media remains constant, not sharing the expansion of the background, which generalises a similar 4D result of Holcomb-Tajima in radiation background to the case of higher dimensions with cosmic matter obeying an equation of state . Further, analogous to the flat space static case we observe the phenomenon of Faraday rotation in higher dimensional case also.

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arXiv2007

Accelerating Universe from an Evolving Lambda in Higher Dimension

We find exact solutions in five dimensional inhomogeneous matter dominated model with a varying cosmological constant. Adjusting arbitrary constants of integration one can also achieve acceleration in our model. Aside from an initial singularity our spacetime is regular everywhere including the centre of the inhomogeneous distribution. We also study the analogous homogeneous universe in (4+d) dimensions. Here an initially decelerating model is found to give late acceleration in conformity with the current observational demands. We also find that both anisotropy and number of dimensions have a role to play in determining the time of flip, in fact the flip is delayed in multidimensional models. Some astrophysical parameters like the age, luminosity distance etc are also calculated and the influence of extra dimensions is briefly discussed. Interestingly our model yields a larger age of the universe compared to many other quintessential models.

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arXiv2006

Accelerating Universe as Window for Extra Dimensions

Homogeneous cosmological solutions are obtained in five dimensional space time assuming equations of state $ p = kρ$ and $ p_{5}= γρ$ where p is the isotropic 3 - pressure and $p_{5}$, that for the fifth dimension. Using different values for the constants k and $γ$ many known solutions are rediscovered. Further the current acceleration of the universe has led us to investigate higher dimensional gravity theory, which is able to explain acceleration from a theoretical view point without the need of introducing dark energy by hand. We argue that the terms containing higher dimensional metric coefficients produce an extra negative pressure that apparently drives an acceleration of the 3D space, tempting us to suggest that the accelerating universe seems to act as a window to the existence of extra spatial dimensions. Interestingly the 5D matter field remains regular while the \emph{effective} negative pressure is responsible for the inflation. Relaxing the assumptions of two equations of state we also present a class of solutions which provide early deceleration followed by a late acceleration in a unified manner. Interesting to point out that in this case our cosmology apparently mimics the well known quintessence scenario fuelled by a generalised Chaplygin-type of fluid where a smooth transition from a dust dominated model to a de Sitter like one takes place.

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arXiv2004

Multidimensional inhomogeneous cosmology in scalar tensor theory

Exact cosmological solutions are obtained for a five dimensional inhomogeneous fluid distribution along with a Brans-Dicke type of scalar field. The set includes varied forms of matter field including $ρ+p=0$, where p is the 3D isotropic pressure. Depending on the signature of 4-space curvature our solutions admit of indefinite expansion in the usual 3-space and dimensional reduction of the fifth dimension. Due to the presence of the scalar field the case $p=-ρ$ does not yield an exponential expansion of the scale factor, which strikingly differs from our earlier investigations without scalar field.The \emph{effective} four dimensional values of entropy and matter are calculated and possible consequences of entropy and matter generation in the 4D world as a result of dimensional reduction of the extra space are also discussed. Encouraging to point out that aside from the well known big bang singularity our inhomogeneous cosmology is spatially regular everywhere. Further our model seems to suggest an alternative mechanism pointing to a smooth pass over from a primordial, inhomogeneous cosmological phase to a 4D homogeneous one.

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