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Avik De

Publications and source records attributed to Avik De.

At least 37 records · Page 2Linked to original sources
arXiv2023

Cosmology of $f(Q)$ gravity in non-flat Universe

We investigate the cosmological implications of $f(Q)$ gravity, which is a modified theory of gravity based on non-metricity, in non-flat geometry. We perform a detailed dynamical-system analysis keeping the $f(Q)$ function completely arbitrary. As we show, the cosmological scenario admits a dark-matter dominated point, as well as a dark-energy dominated de Sitter solution which can attract the Universe at late times. However, the main result of the present work is that there are additional critical points which exist solely due to curvature. In particular, we find that there are curvature-dominated accelerating points which are unstable and thus can describe the inflationary epoch. Additionally, there is a point in which the dark-matter and dark-energy density parameters are both between zero and one, and thus it can alleviate the coincidence problem. Finally, there is a saddle point which is completely dominated by curvature. In order to provide a specific example, we apply our general analysis to the power-law case, showing that we can obtain the thermal history of the Universe, in which the curvature density parameter may exhibit a peak at intermediate times. These features, alongside possible indications that non-zero curvature could alleviate the cosmological tensions, may serve as advantages for $f(Q)$ gravity in non-flat geometry.

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arXiv2023

Phase-space analysis of a novel cosmological model in $f(Q)$ theory

The vanishing affine connections have been used solely while adopting the modified $f(Q)$ gravity theory to the cosmology. Consequently, researchers could not get beyond what is already known in $f(T)$ theory earlier. To alleviate this problem, in the present manuscript we investigate a recently proposed construction of $f(Q)$ theory using non-vanishing affine connection in the spatially flat FLRW spacetime. We then investigate the cosmological solutions of $f(Q)$ theory for a perfect fluid through the phase space analysis. We introduce few variables and dimensionless parameters to construct the corresponding equations suitable for the dynamical system approach. The conservation of the energy-momentum tensor leads to a constraint equation that relates the dynamical variables. Briefly, both unstable and stable de Sitter solutions appear which correspond to early and late times accelerated expansions. Also, unstable points corresponding to the matter dominated and radiation dominated eras have been found which do exist for every $f(Q)$ function. As a result, the present discussion shows that $f(Q)$ gravity endowed by non-vanishing affine connections is capable of explaining a true sequence of cosmic eras.

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arXiv2023

Energy condition bounds on $f(Q)$ model parameters in a curved FLRW universe

In this exclusive study of the modified $f(Q)$ theory of gravity in the open and closed type Friedmann-Lemaître-Robertson-Walker (FLRW) universe model, we impose some constraints from the classical energy conditions. The viable range of parameter $β$ for two different $f(Q)$ models, $f(Q)=Q+βQ^2$ and $f(Q)=Q+β\sqrt{-Q}$, are analyzed in details and the related cosmological implications are discussed. Violation of effective strong energy condition is resulting into late-time acceleration of the Universe. Present observational values of Hubble parameter and deceleration parameter are used to constrain the parameters.

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arXiv2023

Observational constraints on two cosmological models of $f(Q)$ theory

In the past few years, $f(Q)$ theories have drawn a lot of research attention in replacing Einstein's theory of gravity successfully. The current study examines the novel cosmological possibilities emerging from two specific classes of $f(Q)$ models using the parametrization form of the equation of state (EoS) parameter as $ω\left( z\right) =-\frac{1}{1+3β\left( 1+z\right) ^{3}}$, which displays quintessence behavior with the evolution of the Universe. We do statistical analyses using the Markov chain Monte Carlo (MCMC) method and background datasets like Type Ia Supernovae (SNe Ia) luminosities and direct Hubble datasets (from cosmic clocks), and Baryon Acoustic Oscillations (BAO) datasets. This lets us compare these new ideas about the Universe to the $Λ$CDM model in a number of different possible ways. We have come to the conclusion that, at the current level of accuracy, the values of their specific parameters are the best fits for our $f(Q)$ models. To conclude the accelerating behavior of the Universe, we further study the evolution of energy density, pressure, and deceleration parameter for these $f(Q)$ models.

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arXiv2023

Anisotropic Universe in $f(Q,T)$ gravity, a novel study

$f(Q,T)$ theory of gravity is very recently proposed to incorporate within the action Lagrangian, the trace $T$ of the energy-momentum tensor along with the non-metricity scalar $Q$. The cosmological application of this theory in a spatially flat isotropic and homogeneous Universe is well-studied. However, our Universe is not isotropic since the Planck era and therefore to study a complete evolution of the Universe we must investigate the $f(Q,T)$ theory in a model with a small anisotropy. This motivated us to presume a locally rotationally symmetric (LRS) Bianchi-I spacetime and derive the motion equations. We analyse the model candidate $f(Q,T)=αQ^{n+1}+βT$, and to constrain the parameter $n$, we employ the statistical Markov chain Monte Carlo (MCMC) method with the Bayesian approach using two independent observational datasets, namely, the Hubble datasets, and Type Ia supernovae (SNe Ia) datasets.

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arXiv2023

On the viability of $f(Q)$ gravity models

In general relativity, the contracted Bianchi identity makes the field equation compatible with the energy conservation, likewise in $f(R)$ theories of gravity. We show that this classical phenomenon is not guaranteed in the symmetric teleparallel theory, and rather generally $f(Q)$ model specific. We further prove that the energy conservation criterion is equivalent to the affine connection's field equation of $f(Q)$ theory, and except the $f(Q)=αQ+β$ model, the non-linear $f(Q)$ models do not satisfy the energy conservation or, equivalently the second field equation in every spacetime geometry; unless $Q$ itself is a constant. So the problem is deep-rooted in the theory, several physically motivated examples are provided in the support.

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arXiv2023

How different connections in flat FLRW geometry impact energy conditions in $f(Q)$ theory?

In this study of the modified $f(Q)$ theory of gravity in the spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime, we explore all the affine connections compatible with the symmetric teleparallel structure; three classes of such connections exist, each involving an unknown time-varying parameter $γ(t)$. Assuming ordinary barotropic fluid as the matter source, we first derive the Friedmann-like pressure and energy equations. Next we impose constraints on the parameters of two separate $f(Q)$ models, $f(Q)=Q+βQ^2$ and $f(Q)=Q+β\sqrt{-Q}$ from the traditional energy conditions. Observational values of some prominent cosmological parameters are used for this purpose, yielding an effective equation of state $ω^{eff}=-0.82$.

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arXiv2023

Anisotropic LRS-BI Universe with $f(Q)$ gravity theory

The possible anisotropic nature in the early phases of the Universe is one of the interesting aspects of study in cosmology. We investigate the evolution of the Universe in terms of few cosmological parameters considering an anisotropic locally rotationally symmetric (LRS) Bianchi type-I spacetime (LRS-BI) under the $f(Q)$ gravity of symmetric teleparallel theory equivalent to the GR (STEGR). In this study we consider two $f(Q)$ gravity models, viz., $f(Q) = -\,(Q+2Λ)$, a simple model with the cosmological constant $Λ$ and the power law model, $f(Q) = -\, αQ^n$ with two constant parameters $α$ and $n$. Considering a proportionality relation between the directional Hubble parameters with a proportionality constant parameter $λ$ we find a significant contribution of the anisotropic factor in the evolution of the early Universe for both models. The power law model shows the more dominating effect of anisotropy in comparison to the simple model depending on model parameters, especially on the parameter $n$. The power law model also shows some possible effects of anisotropy on the Universe's evolution in the near future. In addition, both models confirm that the anisotropy does not obtain any appreciable signature in the current stage of the Universe. From our analysis we also set rough constraints on our model parameters as $0.5 \le λ\le 1.25$, $0.75 \le α\le 1.5$ and $0.95 \le n \le 1.05$.

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arXiv2023

$f(Q,T)$ gravity, its covariant formulation, energy conservation and phase-space analysis

In the present article we analyze the matter-geometry coupled $f(Q,T)$ theory of gravity. We offer the fully covariant formulation of the theory, with which we construct the correct energy balance equation and employ it to conduct a dynamical system analysis in a spatially flat Friedmann-Lemaître-Robertson-Walker spacetime. We consider three different functional forms of the $f(Q,T)$ function, specifically, $f(Q,T)=αQ+ βT$, $f(Q,T)=αQ+ βT^2$, and $f(Q,T)=Q+ αQ^2+ βT$ . We attempt to investigate the physical capabilities of these models to describe various cosmological epochs. We calculate Friedmann-like equations in each case and introduce some phase space variables to simplify the equations in more concise forms. We observe that the linear model $f(Q,T)=αQ+ βT$ with $β=0$ is completely equivalent to the GR case without cosmological constant $Λ$. Further, we find that the model $f(Q,T)=αQ+ βT^2$ with $β\neq 0$ successfully depicts the observed transition from decelerated phase to an accelerated phase of the universe. Lastly, we find that the model $f(Q,T)= Q+ αQ^2+ βT$ with $α\neq 0$ represents an accelerated de-Sitter epoch for the constraints $β< -1$ or $ β\geq 0$.

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arXiv2022

Impact of curvature based geometric constraints on $F(R)$ theory

Theories of gravity are fundamentally a relation between matter and the geometric structure of the underlying spacetime. So once we put some additional restrictions on the spacetime geometry, the theory of gravity is bound to get the impact, irrespective of whether it is general relativity or the modified theories of gravity. In the present article, we consider two curvature-based constraints, namely the almost pseudo-Ricci symmetric and weakly Ricci symmetric condition. As a novel result, such spacetimes with non-null associated vectors are entirely classified, and then applying the obtained results, we investigate these spacetimes as solutions of the $F(R)$-gravity theory. The modified Friedmann equations are derived and analysed in a model-independent way first. Finally, two $F(R)$ gravity models are examined for recent observational constrained values of the deceleration, jerk, and Hubble parameters. We further discuss the behavior of energy conditions.

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arXiv2022

Comment on "Energy conditions in $f(Q)$ gravity"

In Phys. Rev. D 102, 024057 (2020), the authors studied energy conditions in $f(Q)$ theory following the same path as researchers handled the energy conditions in the curvature-based modified gravity theories, like $f(R)$ or $f(R,G)$ theories. However, the field equations in the $f(Q)$ theory was not expressed as an effective theory in the literature earlier and in the above mentioned paper [1], the authors claimed that the pressure and energy density follow a set of energy condition criteria without showing how they came to this conclusion. In this comment, we express $f(Q)$ theory as an effective theory in Friedmann-Lemaître-Robertson-Walker (FLRW) universe. And from there, the correct energy conditions are obtained in the traditional (general relativistic) way. Unfortunately, some missing terms in the published work [1] are noticed.

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arXiv2022

Periodic cosmic evolution in $f(Q)$ gravity formalism

We study the periodic cosmic transit behavior of accelerated universe in the framework of symmetric teleparallelism. The exact solution of field equations is obtained by employing a well known deceleration parameter (DP) called periodic varying deceleration parameter (PVDP), $q = m cos kt-1$. The viability and physical reliability of the DP are studied by using the observational constraint. The dynamics of periodicity and singularity are addressed in details with respect to time and redshift parameter. Several ECs are discussed in this setting.

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arXiv2022

Accelerating expansion of the universe in modified symmetric teleparallel gravity

The fundamental nature and origin of dark energy are one of the premier mysteries of theoretical physics. In General Relativity Theory, the cosmological constant $Λ$ is the simplest explanation for dark energy. On the other hand, the cosmological constant $Λ$ suffers from a delicate issue so-called fine-tuning problem. This motivates one to modify the spacetime geometry of Einstein's GR. The $f(Q)$ gravity is a recently proposed modified theory of gravity in which the non-metricity scalar $Q$ drives the gravitational interaction. In this article, we consider a linear $f(Q)$ model, specifically $f(Q)=αQ + β$, where $α$ and $β$ are free parameters. Then we estimate the best fit values of model parameters that would be in agreement with the recent observational data sets. We use 57 points of the updated $H(z)$ data sets, 6 points of the BAO data sets, and 1048 points from the Pantheon supernovae samples. We apply the Bayesian analysis and likelihood function along with the Markov Chain Monte Carlo (MCMC) method. Further, we analyse the physical behaviour of cosmological parameters such as density, deceleration, and the EoS parameters corresponding to the constraint values of the model parameters. The evolution of deceleration parameter predicts a transition from decelerated to accelerated phases of the universe. Further, the evolution of equation of state parameter depicts quintessence type behaviour of the dark energy fluid part. We found that our $f(Q)$ cosmological model can effectively describe the late time cosmic acceleration without invoking any dark energy component in the matter part.

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arXiv2022

Complete dark energy scenario in $f(Q)$ gravity

In theoretical physics, the fundamental nature and evolution mechanism of dark energy is still an open question. In General Relativity Theory, the simplest explanation for dark energy is the cosmological constant $Λ$. However, the cosmological constant $Λ$ facing a sensitive problem called fine-tunning problem. In the present work, we follow a different approach where the gravitational sector is the responsible candidate for the evolution of dark energy instead of the matter source. The modified symmetric teleparallel gravity or $f(Q)$ gravity is a recently proposed theory of gravity where the gravitational interaction ruled by the non-metricity term $Q$. In this manuscript, we assume a $f(Q)$ model that contains a linear and a non-linear form of non-metricity scalar, particularly $f(Q)=αQ + βQ^n$, where $α$, $β$, and $n$ are free model parameters. Then we find the values of our model parameters that would be in agreement with the observed value of cosmographic parameters. We analyze the behavior of different cosmological parameters like deceleration parameter, density, and the equation of state parameter with the energy conditions for our cosmological model. We found that for higher positive values of $n$ specifically $n \geq 1$, dark energy fluid part evolving due to non-metricity behaves like quintessence type dark energy while for higher negative values of $n$ specifically $n \leq -1$ it follows phantom scenario. Further for $n=0$, our cosmological $f(Q)$ model behaves like $Λ$CDM model. Thus, we conclude that the geometrical generalization of GR can be a viable candidate for the description of origin of the dark energy.

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arXiv2022

Isotropization of locally rotationally symmetric Bianchi-I universe in $f(Q)$-gravity

Despite having the somewhat successful description of accelerated cosmology, the early evolution of the universe always challenges mankind. Our promising approach lies in a new class of symmetric teleparallel theory of gravity named $f(Q)$, where the non-metricity scalar $Q$ is responsible for the gravitational interaction, which may resolve some of the issues. To study the early evolution of the universe, we presume an anisotropic locally rotationally symmetric (LRS) Bianchi-I spacetime and derive the motion equations. We discuss the profiles of energy density, equation of state and skewness parameter and observe that our models archive anisotropic spatial geometry in the early phase of the universe with a possible presence of anisotropic fluid and as time goes on, even in the presence of an anisotropic fluid, the universe could approach isotropy due to inflation and the anisotropy of the fluid fades away at the same time.

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arXiv2021

How a projectively flat geometry regulates $F(R)$-gravity theory?

In the present paper we examine a projectively flat spacetime solution of $F(R)$-gravity theory. It is seen that once we deploy projective flatness in the geometry of the spacetime, the matter field has constant energy density and isotropic pressure. We then make the condition weaker and discuss the effects of projectively harmonic spacetime geometry in $F(R)$-gravity theory and show that the spacetime in this case reduces to a generalised Robertson-Walker spacetime with a shear, vorticity, acceleration free perfect fluid with a specific form of expansion scalar presented in terms of the scale factor. Role of conharmonic curvature tensor in the spacetime geometry is also briefly discussed. Some analysis of the obtained results are conducted in terms of couple of $F(R)$-gravity models.

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arXiv2021

A complete study of conformally flat pseudo-symmetric spacetimes in the theory of F(R)-gravity

We investigate the geometrical and physical structures of a pseudo-symmetric spacetime $(PS)_4$ with timelike vector under the condition of conformal flatness. We classify it into two possible types: constant Ricci scalar and closed velocity vector. We further study this spacetime as a solution of $F(R)$-gravity theory and show that the pressure and energy density of the effective cosmological perfect fluid separately possess certain typical relations with the geometry and the gravity sector of the theory. Based on this result, some observational and cosmological analyses are done for the $F(R)$-gravity model and the energy conditions are investigated, supporting the accelerated expansion of the universe.

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arXiv2021

How a conformally flat (GR)4 impacts Gauss-Bonnet gravity?

First and foremost, we show that a 4-dimensional conformally flat generalized Ricci recurrent spacetime $(GR)_4$ is an Einstein manifold. We examine such a spacetime as a solution of $f(R, G)$-gravity theory and it is shown that the additional terms from the modification of the gravitational sector can be expressed as a perfect fluid. Several energy conditions are investigated with $f(R, G) = R +\sqrt{G}$ and $f(R, G) = R^2+GlnG$. For both the models, weak, null and dominant energy conditions are satisfied while strong energy condition is violated, which is a good agreement with the recent observational studies which reveals that the current universe is in accelerating phase.

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