arXiv subjects

Prabir Rudra

Publications and source records attributed to Prabir Rudra.

At least 37 records · Page 2Linked to original sources

arXiv2023

Reconstruction of $f(T,\mathcal{T})$ Lagrangian for various cosmological scenarios

In this paper, we explore a reconstruction scheme in the background of the $f(T,\mathcal{T})$ gravity theory for different cosmological scenarios, where $T$ is the scalar torsion and $\mathcal{T}$ is the trace of the energy-momentum tensor. Using the reconstruction technique $f(T, \mathcal{T})$ Lagrangian is constructed for different cosmological eras such as dust, $ΛCDM$, perfect fluid, etc. Both minimal and non-minimal matter-coupled models are considered for this purpose. Different cosmological scenarios such as power law expansion, de-Sitter expansion, etc. have been considered, and using them Lagrangian functionals are constructed. Mathematical viabilities of all the constructed functionals have been investigated. The physical implications of the obtained solutions are discussed in detail. To check the cosmological compatibility of the constructed $f(T,\mathcal{T})$ functionals we have generated plots of important parameters like the equation of state parameter and deceleration parameter. It is seen that the reconstructed models are perfectly compatible with the late-time accelerated expansion of the universe.

gr-qc↗

arXiv2023

Rotational and inverse square potential effects on harmonic oscillator confined by flux field in a space-time with screw dislocation

This research paper delves into the study of a non-relativistic quantum system, considering the interplay of non-inertial effects induced by a rotating frame and confinement by the Aharonov-Bohm (AB) flux field with potential in the backdrop of topological defects, specifically a screw dislocation. We first focus on the harmonic oscillator problem, incorporating an inverse-square repulsive potential. Notably, it becomes evident that the energy eigenvalues and wave functions are intricately influenced by multiple factors: the topological defect parameter $β$ (representing the screw dislocation), the presence of a rotating frame engaged in constant angular motion with speed $Ω$, and the external potential. Then we study the quantum behavior of non-relativistic particles, engaging in interactions governed by an inverse square potential, all while taking into account the effects of the rotating frame. In both scenarios, a significant observation is made: the quantum flux field's existence brings about a shift in the energy spectrum. This phenomenon bears a resemblance to the electromagnetic Aharonov-Bohm effect.

quant-ph↗

arXiv2023

Ricci-cubic holographic dark energy

In this work, we propose the Ricci-cubic holographic dark energy model. The model is inspired by the cubic curvature invariant formed by the contraction of three Riemann tensors. A combination of Ricci scalar and the cubic invariant is used to describe the infrared cutoff of the holographic dark energy. Such a construction is extremely useful since the evolution does not depend on the past or future features of the universe, but completely on its present features. Moreover, the use of invariants makes the theory more fundamental in nature. We have constructed the model and studied its cosmological features. The analytical solutions of various cosmological parameters such as the density parameter, equation of state parameter, and deceleration parameter are extracted and their behaviour is studied. It is seen that the holographic dark energy model can exhibit the entire thermal history of the universe, sequentially starting from radiation in the early universe, followed by matter, and finally the dark energy dominated epoch at late times. The equation of state parameter shows that the model can exhibit quintessence nature, phantom-divide crossing, and even phantom nature depending on the choice of parameter spaces.

gr-qc↗

arXiv2023

Lorentz and gauge invariance of quantum space

Motivated by generalized uncertainty principle, we derive a discrete picture of the space that respects Lorentz symmetry as well as gauge symmetry through setting an equivalency between linear GUP correction term and electromagnetic interaction term in Dirac equation. We derived a wavefunction solution that satisfies this equivalency. This discreteness may explain the crystal and quasicrystal structures observed in nature at different energy scales.

physics.gen-ph↗

arXiv2022

Klein-Gordon Oscillator with Scalar and Vector Potentials in Topologically Charged Ellis-Bronnikov type Wormhole

In this work, we study the Klein-Gordon oscillator with equal scalar and vector potentials in a topologically charged Ellis-Bronnikov wormhole space-time background. The behaviour of a relativistic oscillator field is studied with a position-dependent mass via transformation $M^{2}\rightarrow (M+S(x))^{2}$ and vector potential through a minimal substitution in the wave equation. Simplifying the Klein-Gordon oscillator equation for three different types of potential, such as linear confining, Coulomb-type, and Cornell-type potential and we arrive at a second-order differential equation known as the biconfluent Heun (BCH) equation and the corresponding confluent Heun function. Finally, we solve the wave equation by the Frobenius method as a power series expansion around the origin and obtain the energy levels and the wave function.

physics.gen-ph↗

arXiv2022

Energy-momentum squared symmetric Teleparallel gravity: $f(Q,T_{μν}T^{μν})$ gravity

In this work we propose the $f(Q,T_{μν}T^{μν})$ gravity as a further extension of the $f(Q)$ and $f(Q,T)$ gravity theories. The action involves an arbitrary function of the non-metricity $Q$ and $T_{μν}T^{μν}$ in the gravity Lagrangian. The field equations for the theory are derived in the metric-affine formalism by varying the action with respect to the metric. The theory involves a non-minimal coupling between the geometric and the matter sectors, and hence the covariant divergence of the energy-momentum tensor is non-zero, thus implying the non-conservation of the same. The vacuum solutions of the theory are investigated and it is found that the theory perfectly admits a de-Sitter-like evolution of the universe. The cosmological equations are derived and it is found that there are two correction terms arising as modification of the gravity. Two specific toy models of the form $Q+η\left(\textbf{T}^2\right)^{n}$ and $f_{0}Q^{m} \left(\textbf{T}^2\right)^{n}$ are explored to gain further insights into the dynamics of the theory. It is seen that the field equations of both the models have terms similar to those arising from the quantum gravity effects and are thus responsible for the avoidance of singularity. One striking feature of the model is that the non-linear correction terms dominate in the early universe and gradually fade away at later times giving the standard FLRW universe. Solutions for the FLRW equations are found wherever possible and the evolution of the scale factor and the matter-energy density are plotted. Finally, the energy conditions are explored in the background of the theory. Using these conditions and some observational data the theory is considerably constrained.

gr-qc↗

arXiv2022

Constraints on Cubic and $f(P)$ Gravity from the Cosmic Chronometers, BAO & CMB datasets : Use of Machine Learning Algorithms

In this work, we perform observational data analysis on Einsteinian cubic gravity and $f(P)$ gravity to constrain the parameter space of the theories. We use the 30-point $z-H(z)$ cosmic chronometer data as the observational tool for our analysis along with the BAO and the CMB peak parameters. The $χ^2$ statistic is used for the fitting analysis and it is minimized to obtain the best fit values for the free model parameters. We have used the Markov chain Monte Carlo algorithm to obtain bounds for the free parameters. To achieve this we used the publicly available CosmoMC code to put parameter bounds and subsequently generate contour plots for them with different confidence intervals. Besides finding the Hubble parameter $H$ in terms of the redshift $z$ theoretically from our gravity models, we have exercised correlation coefficients and two machine learning models, namely the linear regression (LR) and artificial neural network (ANN), for the estimation of $H(z)$. For this purpose, we have developed a Python package for finding the parameter space and performing the subsequent statistical analysis and prediction analysis using machine learning. We compared both our theoretical and estimated values of $H(z)$ with the observations. It is seen that our theoretical and estimated models from machine learning performed significantly well when compared with the observations.

astro-ph.CO↗

arXiv2022

Inflation driven by Barrow Holographic dark energy

In this work we have investigated the inflation mechanism driven by the Barrow Holographic dark energy (BHDE) in the early universe. BHDE is based on the Barrow relation for horizon entropy, which in turn is inspired from the shape of the COVID-19 virus. It was shown by Barrow that the quantum gravitational effects may instigate complex fractal features in the structure of a black hole. Since the length scale during the inflation is expected to be small, the energy density obtained from the application of the holographic principle in the early universe will be large enough to support the inflationary scenario. Using the Granda-Oliveros IR cut-off we have studied the inflationary scenario with the universe filled with BHDE. Various analytic solutions for the model were found out including the slow-roll parameters, scalar spectral index and tensor-to-scalar ratio. Since inflation is generally attributed to the presence of scalar fields, we have explored a correspondence between BHDE and scalar field models. Both canonical scalar field and the Tachyonic scalar field have been considered for this purpose. The evolution of the potential generated from the fields are plotted and found to be consistent with the observations. From the work we see that BHDE can be a model of dark energy that can successfully drive the early time inflation.

gr-qc↗

arXiv2022

Higher order GUP black hole based on COW experiment and Einstein-Bohr's photon box

In this work we have explored the effects of higher order generalized uncertainty principle (GUP), inspired from the quantum gravity COW experiment and the Einstein-Bohr's photon box thought experiment, on the properties of a black hole. Two different GUP models, namely, GUP to all orders in the Planck length model, and GUP with minimal length uncertainty and maximal momentum model are considered for our study. For each model, we have investigated the modified de Broglie formula, modification in gravitational phase shift, Einstein-Bohr's photon box, and the modified Hawking temperature and the tidal force of the GUP modified black hole.

gr-qc↗

arXiv2021

Thermodynamics of the apparent horizon in the generalized energy-momentum-squared cosmology

In this note, we explore the thermodynamic properties of the universe in the background of the generalized energy-momentum-squared gravity. We derive the energy density of matter from the non-standard continuity equation and use it in our analysis. We consider two types of models depending on the nature of coupling between curvature and matter and perform thermodynamic analysis on them using the cosmic apparent horizon. The models are kept as generic as possible from the mathematical point of view in order to gain a wide applicability of the work. In this work we have considered power law and exponential form of models. All the thermodynamic parameters are expressed in terms of the cosmic apparent horizon radius and its time derivatives and their time evolution are studied. By using temperature, heat capacity analysis and the evolution trend of Helmholtz free energy the conditions for thermodynamic stability of the models are derived. It is seen that our stability analysis considerably constrain the parameter space of the model.

gr-qc↗

arXiv2021

Observational Constraint in $f(R,T)$ gravity from the cosmic chronometers and some standard distance measurement parameters

In this work we perform an observational data analysis on the $f(R,T)$ gravity with the aim of constraining the parameter space of the model. Five different models are considered and the 30 point $z-H(z)$ cosmic chronometer data is used in our analysis. The $χ^2$ statistic is formulated as a difference between the theoretical and the observed values of $H(z)$ for different values of redshift $z$. Efforts have been made to minimize the statistic in order to get the best fit values for the free parameters models. We have also used some standard distance measurement parameters like BAO and CMB peaks along with the data for achieving better constraints on the parameter space. We have used the publicly available \textit{CosmoMC} code for obtaining the bounds for the free parameters of the models in different confidence intervals like $68\%$, $95\%$, $99\%$. 1D distributions and 2D joint confidence contours for various confidence levels mentioned above are generated for the free parameters using the \textit{CosmoMC} code. Finally our models have been compared with the standard $ΛCDM$ model by some statistical techniques using the observational data and the support for the models from the data is probed.

gr-qc↗

arXiv2021

Constraints on Energy Momentum Squared Gravity from cosmic chronometers and Supernovae Type Ia data

In this work we perform an observational data analysis on the energy momentum squared gravity model. Possible solutions for matter density are obtained from the model and their cosmological implications are studied. Some recent observational data is used to constrain model parameters using statistical techniques. We have used the cosmic chronometer and SNe Type-Ia Riess (292) $H(z)-z$ data-sets in our study. Along with the data-sets we have also used baryon acoustic oscillation (BAO) peak parameter and cosmic microwave background (CMB) peak parameter to obtain bounds on the model parameters. Joint analysis of the data with the above mentioned parameters have been performed to obtain better results. For the statistical analysis we have used the minimization technique of the $χ^{2}$ statistic. Using this tool we have constrained the free parameters of the model. Confidence contours have been generated for the predicted values of the free parameters at the $66\%$, $90\%$ and $99\%$ confidence levels. Finally we have compared our analysis with the union2 data sample presented by Amanullah et al.,2010 and the recently published Pantheon data sample. Finally a multi-component model is investigated by adding dust to a general cosmological fluid with equation of state $w=-1/3$. The density parameters were studied and their values were found to comply with the observational results.

gr-qc↗

arXiv2021

Note on the thermodynamic stability of a black ring at quantum scales

In this paper, the thermodynamic properties of a thin black ring in AdS space-time is explored when the size of the ring is comparable to quantum scales. The angular momentum to mass ratio of this system has an upper limit, which is the cosmological radius of the black ring. It is found that the small black ring will be thermodynamically stable due to the effects introduced by thermal fluctuations. However, we find that the black ring is less stable than thermal AdS. Thermodynamic analysis indicates that there is no critical point, but there is Hawking-Page transition to radiation, which is confirmed by the Gibbs free energy analysis.

gr-qc↗

arXiv2020

String-inspired Teleparallel Cosmology

The present paper represents an attempt for a very generic string inspired theory of gravitation, based on a stringy action in the teleparallel gravity which includes a specific functional which depends on the scalar field and its kinetic energy, as well as the torsion and boundary terms, embedding also possible effects from the teleparallel Gauss--Bonnet invariants. We focus our study on FLRW cosmology. After we deduce the cosmological equations for the associated generic theory of gravitation, we focus on string inspired couplings which are studied by considering different analytical techniques. The first analytical technique is based on the linear stability theory, by introducing proper dimensionless variables which enables us to study the structure of the phase space and the associated physical effects. In this case, we have obtained different cosmological solutions which correspond to matter and dark energy dominated solutions, achieving a possible transition between matter and dark energy dominated epochs. For each type of cosmological solutions, we have discussed the corresponding physical features, attaining viable constraints for the coupling constants due to dynamical effects. The dynamical study of the physical features included also a numerical analysis by fine--tuning the initial conditions deep into the matter era, obtaining possible trajectories for the effective equation of state for specific coupling functions.

gr-qc↗

arXiv2020

A Time Dependent Spacetime in $f(R,T)$ Gravity: Gravitational Collapse

In this note a time dependent spacetime is explored in the background of $f(R,T)$ gravity via the gravitational collapse of a massive star. The star is modelled by the Vaidya spacetime which is time dependent in nature. The coupling of matter with curvature is the key feature of $f(R,T)$ theory and here we have investigated its effects on a collapsing scenario. Two different types of models, one involving minimal and the other involving non-minimal coupling between matter and curvature are considered for our study. Power law and exponential functionalities are considered as examples to check the outcome of the gravitational collapse. Our prime objective is to explore the nature of singularities (black hole or naked singularity) that form as an end state of the collapse. Existence of outgoing radial null geodesics from the central singularity was probed and such existence implied the formation of naked singularities thus defying the cosmic censorship hypothesis. The absence of such outgoing null geodesics would imply the formation of an event horizon and the singularity formed becomes a black hole. Conditions under which such possibilities occur are derived for all the models and sub-models. Gravitational strength of the singularity is also investigated and the conditions under which we can get a strong or a weak singularity is derived. The results obtained are very interesting and may be attributed to the coupling between curvature and matter. It is seen that for non-minimal coupling there is a possibility of a globally naked singularity, whereas for a minimal coupling scenario local nakedness is the only option. It is also found that the singularity formed can be sufficiently weak in nature, which is cosmologically desirable.

gr-qc↗

arXiv2020

Thermodynamics in $f(R,\mathcal{L})$ theories: Apparent horizon in the FLRW spacetime

In this paper we study the recently proposed $f(R,\mathcal{L})$ theories from a thermodynamic point of view. The uniqueness of these theories lies in the fact that the space-time curvature is coupled to the baryonic matter instead of exotic matter (in the form of scalar field). We investigate the viability of these theories from the point of view of the thermodynamic stability of the models. To be more precise here we are concerned with the thermodynamics of the apparent horizon of Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime in the background of the $f(R,\mathcal{L})$ theory. We consider several models of $f(R,\mathcal{L})$ theories where both minimal and non-minimal coupling has been considered. Various thermodynamic quantities like entropy, enthalpy, internal energy, Gibbs free energy, etc. are computed and using their allowed ranges various model parameters are constrained.

physics.gen-ph↗

arXiv2020

A Non-static Quantum inspired Spacetime in $f(R)$ Gravity: Gravity's Rainbow

In this note we explore a non-static spacetime in quantum regime in the background of $f(R)$ gravity. The time dependent Vaidya metric which represents the spacetime of a radiating body like star is studied in an energy dependent gravity's rainbow, which is a UV completion of General Relativity. In our quest we have used gravitational collapse as the main tool. The focus is to probe the nature of singularity (black hole or naked singularity) formed out of the collapsing procedure. This is achieved via a geodesic study. For our investigation we have considered two different models of $f(R)$ gravity, namely the inflationary Starobinsky's model and the power law model. Our study reveals the fact that naked singularity is as good a possibility as black hole as far as the central singularity is concerned. Via a proper fine tuning of the initial data, we may realize both black hole or naked singularity as the end state of the collapse. Thus this study is extremely important and relevant in the light of the Cosmic Censorship hypothesis. The most important result derived from the study is that gravity's rainbow increases the tendency of formation of naked singularities. We have also deduced the conditions under which the singularity will be a strong or weak curvature singularity. Finally in our quest to know more about the model we have performed a thermodynamical study. Throughout the study we have obtained results which involve deviation from the classical set-up. Such deviations are expected in a quantum evolution and can be attributed to the quantum fluctuations that our model suffers from. It is expected that this study will enhance our knowledge about quantization of gravity and subsequently about the illusive theory of quantum gravity.

gr-qc↗

arXiv2019

Dynamical system analysis of generalized energy-momentum-squared gravity

In this work we have investigated the dynamics of a recent modification to the general theory of relativity, the energy-momentum squared gravity model $f(R,\mathbf{T^2})$, where $R$ represents the scalar curvature and $\mathbf{T^2}$ the square of the energy-momentum tensor. By using dynamical system analysis for various types of gravity functions $f(R,\mathbf{T^2})$, we have studied the structure of the phase space and the physical implications of the energy-momentum squared coupling. In the first case of functional where $f(R,\mathbf{T^2})=f_0 R^n(\mathbf{T^2})^m$, with $f_0$ constant, we have shown that the phase space structure has a reduced complexity, with a high sensitivity to the values of the $m$ and $n$ parameters. Depending on the values of the $m$ and $n$ parameters, the model exhibits various cosmological epochs, corresponding to matter eras, solutions associated with an accelerated expansion, or decelerated periods. The second model studied corresponds to the $f(R,\mathbf{T^2})=αR^n+β\mathbf{(T^2)}^m$ form with $α, β$ constant parameters. In this case, a richer phase space structure is obtained which can recover different cosmological scenarios, associated to matter eras, de--Sitter solutions, and dark energy epochs. Hence, this model represents an interesting cosmological model which can explain the current evolution of the Universe and the emergence of the accelerated expansion as a geometrical consequence.

gr-qc↗