arXiv subjects

Arijit Panda

Publications and source records attributed to Arijit Panda.

11 recordsLinked to original sources

arXiv2025

Observational Insights on DBI K-essence Models Using Machine Learning and Bayesian Analysis

We perform a late-time cosmological study; we compare the performance of two Dirac-Born-Infeld (DBI)-type k-essence scalar field extensions of the $\Lambda$CDM model to the standard framework and a wCDM scenario using the Chevallier-Polarski-Linder (CPL) equation of state parametrization. We solve background dynamics numerically as functions of redshift and incorporate them into a Bayesian inference pipeline accelerated by machine learning. We use a Flax-based surrogate emulator to replace repeated direct integrations of the ODE system, reducing computational cost. A hybrid scheme that combines Stochastic Variational Inference (SVI) with No-U-Turn Hamiltonian Monte Carlo constrains cosmological parameters using the Pantheon$+$SH0ES Type Ia supernova sample, DESI BAO (DR2) data, and cosmic chronometer $H(z)$ measurements without CMB-based priors. In both DBI k-essence formulations, present-day dark energy equations of state are consistent with cosmic acceleration, indicating a $\Lambda$CDM-like regime with a modest redshift dependence. The $w$CDM model is marginally favored by conventional model selection measures such as $\chi^2$, AIC, BIC, and DIC, which are based on goodness of fit and penalized. However, Bayesian predictive measures like WAIC and PSIS-LOO show no significant differences between $\Lambda$CDM, $w$CDM, and DBI k-essence scenarios. All have similar model weights and out-of-sample predictive performance for the datasets. Thus, DBI k-essence models mimic the success of the classic $\Lambda$CDM paradigm while allowing controlled, redshift-dependent deviations from a strict cosmological constant that are consistent with present late-time observations.

astro-ph.CO↗

arXiv2025

Exploring Cosmological Implications of the Modified Raychaudhuri Equation in Non-Gravitating Vacuum Energy Theory

This article investigates the modified Raychaudhuri Equation (RE) in the context of Non-Gravitating Vacuum Energy (NGVE) theory and its implications for various cosmological characteristics. The equation is formulated based on the NGVE framework, in which global scale invariance generates a unique geometry. The newly developed geometry introduces a metric that is conformally connected to the conventional metric, with the conformal factor dependent on scalar field potentials. The cosmological study is carried out under the framework of a flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe. Assuming matter behaves as an ideal fluid in the modified geometry, we formulate models for conditional expansion, collapse, and steady state, governed by the scalar field ($\phi$). In this context, the caustic solution and the focusing theorem are also studied. Scalar field solutions for exponential and power-law scale factors are also derived using NGVE theory's equations of motion. Finally, graphical analysis is used to investigate the behavior of the interaction terms that appear in the modified RE under these scale factors.

gr-qc↗

arXiv2024

Thermodynamics of a Non-canonical $f(\bar{R},\bar{T})$ gravity

This work comprises a study of the thermodynamic behavior of modified $f(\bar{R},\bar{T})$ gravity, which had been developed based on a non-canonical theory known as K-essence theory. In this development, we use the Dirac-Born-Infeld (DBI) type of non-standard Lagrangian. We develop a modified first law and generalized second law of thermodynamics (GSLT) within the modified $f(\bar{R},\bar{T})$ gravity, where we consider the background metric to be the usual Friedmann-Lema$\hat{\text{i}}$tre-Robertson-Walker (FLRW) type. A graphical analysis of surface gravity has been performed for the modified FLRW metric via the $f(\bar{R},\bar{T})$ theory, which is different from the usual FLRW gravity through the usual $f(R,T)$ gravity. Exponential and power law scale factors are used to analyze cosmic surface gravity. Through the investigation of the modified GSLT, using the relation of scale factor with the scalar field, we have seen that during the initial phase of the universe, the entropy's rate of change may be either negative or positive, contingent upon the value of the curvature constant. The negativity of the entropy change indicates that the modified GSLT is not feasible in that particular area for a particular curvature constant. These traits suggest that during the inflationary period, entropy might have been either negative or positive. It has also been seen that entropy saturates every curvature value at different time ranges, which indicates the heat death of the universe.

gr-qc↗

arXiv2024

Form Invariance of Raychaudhuri equation in the presence of Inflaton-type fields

We show that the Raychaudhuri equation remains form invariant for certain solutions of scalar fields $\phi$ whose Lagrangian is non-canonical and of the form $\mathcal{L}(X,\phi)=-V(\phi)F(X)$, with $X=\frac{1}{2} g_{\mu\nu} \nabla^{\mu}\phi \nabla^{\nu} \phi$ and $V(\phi)$ the potential. Solutions exist for both homogeneous and inhomogeneous fields that are like inflatons. Certain recent observations indicate that the cosmos is inhomogeneous and thus our results are in sync with the latest observations. So the Raychaudhuri equation can accommodate primordial inhomogeneities as well as cosmologically relevant scenarios.

gr-qc↗

arXiv2024

NEC violation in $f(\bar{R},\bar{T})$ gravity in the context of a non-canonical theory via modified Raychaudhuri equation

In this work, we develop the Raychaudhuri equation in $f(\bar{R},\bar{T})$ gravity in the setting of a non-canonical theory, namely K-essence theory. We solve the modified Raychaudhuri equation for the additive form of $f(\bar{R},\bar{T})$, which is $f_{1}(\bar{R})+f_{2}(\bar{T})$. For this solution, we employ two different scale factors to give two types of $f(\bar{R},\bar{T})$ solutions. The ongoing debate between Fisher et. al. and Harko et. al. in 2020 regarding the additive form of $f(\bar{R},\bar{T})$ may provide a resolution within the modified $f(\bar{R},\bar{T})$ gravity theory. By conducting a viability test and analyzing energy conditions, we have determined that in the first scenario, the null energy condition (NEC) is violated between two regions where the NEC is satisfied. Additionally, we have observed that this violation of the NEC exhibits a symmetric property during the phase transition. These observations indicate that bouncing events may occur as a result of the symmetrical violation of the NEC during the expansion of the universe. Moreover, this model indicates that resonant-type quantum tunneling may take place during the period when the NEC is violated. The findings of NEC violation through the power law of scale factor may have empirical relevance in contemporary observations. In the second scenario, our model indicates that the strong energy condition is violated, but the NEC and weak energy conditions are satisfied. The effective energy density decreases and is positive, while the effective pressure and equation of state parameters are negative. This suggests that the universe is expanding with acceleration and is dominated by dark energy.

gr-qc↗

arXiv2023

Collapsing scenarios of K-essence generalized Vaidya spacetime under $f(\bar{R},\bar{T})$ gravity

The paper investigates the collapse of the generalized emergent Vaidya spacetime in the setting of $f(\bar{R}, \bar{T})$ gravity, specifically in K-essence theory. In this study, the Dirac-Born-Infeld type non-standard Lagrangian is used to calculate the emergent metric $\bar{G}_{\mu\nu}$, which is not conformally equivalent to the conventional gravitational metric. We use the function $f(\bar{R}, \bar{T})$ to reflect the additive nature of the emergent Ricci scalar ($\bar{R}$) and the trace of the emergent energy-momentum tensor ($\bar{T}$). Our study demonstrates that certain choices of $f(\bar{R}, \bar{T})$ may result in the existence of a naked singularity caused by gravitational collapse. The alternative $f(\bar{R}, \bar{T})$ values resulted in an accelerating universe dominated by dark energy. Moreover, the investigation showed the presence of both positive and negative masses, which might suggest the coexistence of dark matter and dark energy. Furthermore, for a given quantity of kinetic part of the K-essence scalar field, mass is completely changed into energy, meaning that spacetime is Minkowskian. The K-essence theory may also be employed as a dark energy framework and a basic gravitational theory, making it possible for researchers to investigate a wide ranges of cosmic phenomena.

gr-qc↗

arXiv2023

Reconstruction of $f(R,T)$ gravity model via the Raychaudhuri equation

In this work, we investigate for an analytical solution under modified gravity theory, specifically the $f(R,T)$ gravity for two different eras, i.e., matter and dark energy dominated accelerating universe from completely geometrical and mathematical point of view with the help of the Raychaudhuri equation. To construct $f(R,T)$ gravity model, we consider the functional form of $f(R,T)$ as the sum of two independent functions of the Ricci scalar $R$ and the trace of the energy-momentum tensor $T$, respectively. Under the consideration of this type of power law expansion of the Universe we have studied the viability, stability and all the energy conditions. We note that the strong energy condition is not satisfied in our model, which is obvious for the present scenario of the Universe.

gr-qc↗

arXiv2023

Raychaudhuri equation in $k$-essence geometry: conditional singular and non-singular cosmological models

We investigate how the Raychaudhuri equation behaves in the $k$-essence geometry. As far as we are concerned, both the early and current epochs of the universe are relevant to the $k$-essence theory. Here, we have studied the $k$-essence geometry using the Dirac-Born-Infeld (DBI) variety of non-standard action. The corresponding $k$-essence emergent spacetime is not conformally equivalent to the usual gravitational metric. We assume that the background gravitational metric is of the Friedmann-Lemaitre-Robertson-Walker (FLRW) type in this case. We have found that both the conditional singular and non-singular cosmological models of the universe through the modified Raychaudhuri equation are possible where we have used the spacetime as the flat $k$-essence emergent FLRW-type. We have also addressed to the Focusing theorem and conditional caustic universe construction. These conditional effects are caused by the additional interactions that arise as a result of the coupling that exists between the gravity and the $k$-essence scalar field.

gr-qc↗

arXiv2022

Collapsing scenario for the k-essence emergent generalised Vaidya spacetime in the context of massive gravity's rainbow

In this paper, we study the collapsing scenario for the k-essence emergent Vaidya spacetime in the context of massive gravity's rainbow. For this study, we consider that the background metric is Vaidya spacetime in massive gravity's rainbow. We show that the k-essence emergent gravity metric resembles closely to the new type of generalized Vaidya massive gravity metric with the rainbow deformations for null fluid collapse where we consider the k-essence scalar field as a function solely of the advanced or the retarded time. The k-essence emergent Vaidya massive gravity rainbow mass function is also different. This new type k-essence emergent Vaidya massive gravity rainbow metric has satisfied the required energy conditions. The existence of the locally naked central singularity, the strength and the strongness of the singularities for the rainbow deformations of the k-essence emergent Vaidya massive gravity metric are the interesting outcomes of the present work.

gr-qc↗

arXiv2022

Cosmological effects on $f(\bar{R},\bar{T})$ gravity through a non-standard theory

This study aims to investigate the impact of dark energy in cosmological scenarios by exploiting $f(\bar{R},\bar{T})$ gravity within the framework of a {\it non-standard} theory, called {\it {\bf K-}essence} theory, where $\bar{R}$ represents the Ricci scalar and $\bar{T}$ denotes the trace of the energy-momentum tensor associated with the {\bf K-}essence geometry. The Dirac-Born-Infeld (DBI) non-standard Lagrangian has been employed to generate the emergent gravity metric $(\bar{G}_{\mu\nu})$ associated with the {\bf K-}essence. This metric is distinct from the usual gravitational metric $(g_{\mu\nu})$. It has been shown that under a flat FLRW background gravitational metric, the modified field equations and the Friedmann equations of the $f(\bar{R},\bar{T})$ gravity are distinct from the usual ones. In order to get the equation of state (EOS) parameter $\omega$, we have solved the Friedmann equations by taking into account the function $f(\bar{R},\bar{T})\equiv f(\bar{R})+\lambda \bar{T}$, where $\lambda$ represents a parameter within the model. We have found a relationship between $\omega$ and time for different kinds of $f(\bar{R})$ by treating the kinetic energy of the {\bf K-}essence scalar field ($\dot{\phi}^{2}$) as the dark energy density which fluctuates with time. Surprisingly, this result meets the condition of the restriction on $\dot{\phi}^{2}$. By presenting graphical representations of the EOS parameter with time, we show that our model is consistent with the data of $SNIa$+$BAO$+$H(z)$ within a certain temporal interval.

gr-qc↗

arXiv2020

$f(\bar{R}, L(X))$-gravity in the context of dark energy with power law expansion and energy conditions

The motto of this work is to generate a general formalism of $f(\bar{R}, L(X))-$gravity in the context of dark energy under the framework of the {\bf K-}essence emergent geometry with the Dirac-Born-Infeld (DBI) variety of action, where $\bar{R}$ is the familiar Ricci scalar, $L(X)$ is the DBI type non-canonical Lagrangian with $X={1\over 2}g^{\mu\nu}\nabla_{\mu}\phi\nabla_{\nu}\phi$ and $\phi$ is the {\bf K-}essence scalar field. The emergent gravity metric $\bar{G}_{\mu\nu}$ and the well known gravitational metric $g_{\mu\nu}$ are not conformally equivalent. We have constructed a modified field equation using the metric formalism in $f(\bar{R}, L(X))$-gravity incorporating the corresponding Friedmann equations in the framework of the background gravitational metric which is of Friedmann-Lema{\^i}tre-Robertson-Walker (FLRW) type. The solution of modified Friedmann equations have been deduced for the specific choice of $f(\bar{R}, L(X))$, which is of Starobinsky-type, using power law expansion method. The consistency of the model with the accelerating phase of the Universe has been shown, when we restrict ourselves to consider the value of the dark energy density, as $\dot\phi^{2}=\frac{8}{9}=0.888 <1$, which indicates that the present Universe is dark energy dominated. Graphical plots for the energy density ($\rho$), pressure ($p$) and equation of state parameter ($\omega$) w.r.t. time ($t$) based on parametric values are interestingly consistent with the dark energy domination and hence accelerating features. We also put some light on the corresponding energy conditions and constraints of the $f(\bar{R}, L(X))$ theory with one basic example.

gr-qc↗