arXiv subjects

Jibitesh Dutta

Publications and source records attributed to Jibitesh Dutta.

At least 19 recordsLinked to original sources

arXiv2026

Exact Integrable $Λ$CDM-Mimicking $f(Q)$ Cosmology: Background, Stability, and Perturbations in the First Connection Branch

We re-examine the problem of mimicking the standard cosmological model, characterized by $j=1$ (where $j$ is the cosmographic jerk parameter), within the context of the first connection branch of $f(Q)$ gravity. While this problem has previously been addressed via reconstruction techniques$-$yielding the analytic form $f(Q)=-2Λ+αQ + β\sqrt{-Q}$ with $Q=-6H^2$ $-$here we tackle this problem from two distinct perspectives, applying either a cosmographic closure strategy or an auxiliary-variable hierarchy approach to the traditional dynamical systems formulation. Remarkably, the cosmographic closure renders the dynamical system integrable for $Λ$CDM-mimicking $f(Q)$ models. Consequently, we obtain closed-form analytical solutions for all relevant cosmological quantities at both the background and linear perturbation levels, with the perturbative solutions elegantly expressed in terms of generalized Heun functions. Furthermore, we analyze the structural stability of the $Λ$CDM-mimicking phase space against small kinematic deviations from $j=1$, demonstrating the robustness of these solutions. Our approach provides a systematic route to studying $Λ$CDM-mimicking dynamics without requiring a closed-form analytic reconstruction of the underlying action. Finally, we utilize this framework to establish a direct comparison between $Λ$CDM-mimicking dynamics in the first connection branch of $f(Q)$ gravity and those in $f(R)$ gravity.

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arXiv2025

A Unified Dynamical Systems Framework for Cosmology in $f(Q)$ Gravity: Generic Features Beyond the Coincident Gauge

We present a unified dynamical systems framework for spatially flat FLRW cosmology in $f(Q)$ gravity, covering all three connection branches via a single set of Hubble-normalised variables without fixing $f(Q)$ \textit{a priori}. This connection-agnostic, model-independent approach enables direct comparison across branches and reveals generic structural features that are not apparent in model or connection-specific analyses. Beyond fixed points, we identify invariant submanifolds, model-independent trajectories, and viable phase-space regions common to multiple branches. For a broad class of viable $f(Q)$ models, we find generic de Sitter attractors and matter-dominated points in non-coincident branches, ensuring late-time acceleration without fine-tuning. An invariant submanifold is shown to reproduce $Λ$CDM-like backgrounds despite dynamics distinct from GR, offering a geometric origin for cosmic acceleration detectable only at the perturbation level. On this submanifold, a first integral enables analytic reconstruction of the dynamical connection and uncovers hidden conservation laws. While trivial connections display strong parameter dependence, nontrivial branches often exhibit parameter-independent behaviour. We also analyse the variation of the effective gravitational coupling $κ_{\text{eff}}=\frac{1}{f_Q}$ across branches, providing observational constraints that bridge theory and data. Applying the framework to $f(Q)=αQ+β(-Q)^n$, we recover late-time acceleration and $Λ$CDM-like behaviour without vacuum energy. Finally, we propose a general route for extending dynamical systems analysis to broader classes of $f(Q)$ models using the $m_i$-hierarchy method, which enables closure of the autonomous system for models previously inaccessible to standard approaches.

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arXiv2025

Reproducing $Λ$CDM-like Solutions in $f(Q)$ Gravity: A Comprehensive Study Across All Connection Branches

Given the remarkable success of the $Λ$CDM model in fitting various cosmological observations, a pertinent question in assessing the phenomenological viability of modified gravity theories is whether they can reproduce an exactly $Λ$CDM-like cosmic background evolution. In this paper, we address this question in the context of $f(Q)$ gravity, where $Q$ denotes the nonmetricity scalar. It is known that there are three possible symmetric teleparallel connection branches that respect the cosmological principles of spatial homogeneity, isotropy, and global spatial flatness. By enforcing a $Λ$CDM-like background evolution via the cosmographic condition $j(z)=1$, where $j$ is the jerk parameter, we reconstruct the $Λ$CDM-mimicking $f(Q)$ theory for each of the three possible connection branches. For the first connection branch, also known as the ``coincident gauge'' in cosmology, we recover the previously known result that a theory of the form $f(Q)=-2Λ+αQ+β\sqrt{-Q}$ can exactly reproduce a $Λ$CDM-like cosmic evolution. Furthermore, we establish that the stability of the $Λ$CDM-like cosmic solution within this reconstructed $f(Q)$, as well as the robustness of the reconstructed $f(Q)$ form with respect to small errors in the astrophysical measurements of the jerk parameter. For the second connection branch, we analytically reconstruct the $Λ$CDM-mimicking $f(Q)$ to be of the form $f(Q)=-2Λ+αQ-βQ^2$. For the third connection branch, we could decouple the evolution equation for the dynamical connection function, which enabled us to perform a numerical reconstruction. Our analysis proves that, at least at the background level, it is possible to obtain $Λ$CDM-mimicking $f(Q)$ models for all the three possible connection branches.

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arXiv2024

Eccentricity Spectra and Integral Eigenvalues of Zero Divisor Graphs

In this work, we study the eccentricity spectra of zero divisor graphs (ZDGs) associated with the ring $\mathbb{Z}_n.$ While previous studies have examined the Laplacian and distance Laplacian spectra of ZDGs, the eccentricity spectra have remained largely unknown due to the unique features of the eccentricity matrix. More specifically, we prove that for a prime $p$, the ZDG and extended ZDG of $\mathbb{Z}_{p^t}$ have integral eccentricity eigenvalues for $t \geq 3$ and $t \geq 2$, respectively. We also find the eccentricity spectra for specific classes of ZDGs and the relationship between the eccentricity matrix of these ZDGs and their tree structures using matrix analysis tools. In addition, for the usefulness of the energy gap in applications, we have calculated the eccentricity energy gap of ZDGs. These findings reveal interesting behaviours of the eccentricity matrix and may contribute to a more profound understanding of the structural properties of ZDGs.

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arXiv2024

Modelling the Accelerating Universe with $f(Q)$ Gravity: Observational Consistency

In this paper, we present a cosmological model within the framework of symmetric teleparallel gravity, focusing on $f(Q)$ gravity, where $Q$ represents the non-metricity scalar. Utilizing cosmological datasets, we derive an accelerating cosmological model by constraining its free parameters. To achieve this, we determine the parametric form of the Hubble parameter using a well-motivated $f(Q)$ function. Remarkably, all obtained values fall within the range suggested by cosmological observations. By employing the best-fit parameters, we calculate the present geometrical parameters and demonstrate the accelerating behaviour of the Universe. Furthermore, we thoroughly examine the evolutionary behaviours of the Universe, noting that our model converges to the $Λ$CDM model at late times. Finally, we investigate the energy conditions and find a violation of the strong energy condition, which could provide a valuable understanding of the nature of dark energy.

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arXiv2023

Global phase space analysis for a class of single scalar field bouncing solutions in general relativity

We carry out a compact phase space analysis of a non-canonical scalar field theory whose Lagrangian is of the form $F(X)-V(ϕ)$ within general relativity. In particular, we focus on a kinetic term of the form $F(X)=βX^m$ with power law potential $V_0 ϕ^n$ and exponential potential $V_0 e^{-λϕ/M_{Pl}}$ of the scalar field. The main aim of this work is to investigate the genericity of nonsingular bounce in these models and to investigate the cosmic future of the bouncing cosmologies when they are generic. A global dynamical system formulation that is particularly suitable for investigating nonsingular bouncing cosmologies is used to carry out the analysis. We show that when $F(X)=βX^m$ ($β<0$), nonsingular bounce is generic for a power law potential $V(ϕ) = V_0 ϕ^n$ only within the parameter range $\left\lbrace \frac{1}{2}<m<1,\,n<\frac{2m}{m-1}\right\rbrace$ and for an exponential potential $V(ϕ) = V_0 e^{-λϕ/M_{Pl}}$ only within the parameter range $\left\lbrace\frac{1}{2}<m\leq1\right\rbrace$. Except in these cases, nonsingular bounce in these models is not generic due to the non-existence of global past or future attractors. Our analysis serves to show the importance of a global phase space analysis to address important questions about nonsingular bouncing solutions, an idea that may and must be adopted for such solutions even in other theories.

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arXiv2022

Cosmology in $f(Q)$ gravity: A unified dynamical system analysis at background and perturbation levels

Motivated by the fact that cosmological models based on $f(Q)$ gravity are very efficient in fitting observational datasets at both background and perturbation levels, we perform a combined dynamical system analysis of both background and perturbation equations in order to examine the validity of this result through an independent method. We examine two studied $f(Q)$ models of the literature, namely the power-law and the exponential ones. For both cases, we obtain a matter-dominated saddle point characterized by the correct growth rate of matter perturbations, followed by the transition to a stable dark-energy dominated accelerated universe in which matter perturbations remain constant. Furthermore, analyzing the behavior of $f σ_8$, we find that the models fit observational data successfully, obtaining a behavior similar to that of $Λ$CDM scenario, although the exponential model does not possess the latter as a particular limit. Hence, through the independent approach of dynamical systems, we do verify the results of observational confrontation, namely that $f(Q)$ gravity can be considered as a very promising alternative to the $Λ$CDM concordance model.

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arXiv2022

Background evolution and growth of structures in interacting dark energy through dynamical system analysis

We apply the formalism of dynamical system analysis to investigate the evolution of interacting dark energy scenarios at the background and perturbation levels in a unified way. Since the resulting dynamical system contains the extra perturbation variable related to the matter overdensity, the critical points of the background analysis split, corresponding to different behavior of matter perturbations, and hence to stability properties. From the combined analysis, we find critical points that describe the non-accelerating matter-dominated epoch with the correct growth of matter structure, and the fact that they are saddle provides the natural exit from this phase. Furthermore, we find stable attractors at late times corresponding to a dark energy-dominated accelerated solution with constant matter perturbations, as required by observations. Thus, interacting cosmology can describe the matter and dark energy epochs correctly, both at the background and perturbation levels, which reveals the capabilities of the interaction.

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arXiv2021

Cosmological dynamics and bifurcation analysis of the general non-minimally coupled scalar field models

Non-minimally coupled scalar field models are well-known for providing interesting cosmological features. These include a late time dark energy behavior, a phantom dark energy evolution without singularity, an early time inflationary universe, scaling solutions, convergence to the standard $Λ$CDM, etc. While the usual stability analysis helps us determine the evolution of a model geometrically, bifurcation theory allows us to precisely locate the parameters' values describing the global dynamics without a fine-tuning of initial conditions. Using the center manifold theory and bifurcation analysis, we show that the general model undergoes a transcritical bifurcation, which predicts us to tune our models to have certain desired dynamics. We obtained a class of models and a range of parameters capable of describing a cosmic evolution from an early radiation era towards a late time dark energy era over a wide range of initial conditions. There is also a possible scenario of crossing the phantom divide line. We also find a class of models where the late time attractor mechanism is indistinguishable from that of a structurally stable general relativity based model; thus, we can elude the big rip singularity generically. Therefore, bifurcation theory allows us to select models that are viable with cosmological observations.

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arXiv2021

Interacting quintessence in light of Generalized Uncertainty Principle: Cosmological perturbations and dynamics

We consider a cosmological scenario endowed with an interaction between the universe's dark components $-$ dark matter and dark energy. Specifically, we assume the dark matter component to be a pressure-less fluid, while the dark energy component is a quintessence scalar field with Lagrangian function modified by the quadratic Generalized Uncertainty Principle. The latter modification introduces new higher-order terms of fourth-derivative due to quantum corrections in the scalar field's equation of motion. Then we investigate asymptotic dynamics and general behaviour of solutions of the field equations for some interacting models of special interests in the literature. At the background level, the present interacting model exhibits the matter-dominated and de Sitter solutions which are absent in the corresponding quintessence model. Furthermore, to boost the background analysis, we study cosmological linear perturbations in the Newtonian gauge where we show how perturbations are modified by quantum corrected terms from the quadratic Generalized Uncertainty Principle. Depending on the coupling parameters, scalar perturbations show a wide range of behavior.

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arXiv2021

Cosmological solutions and growth index of matter perturbations in $f(Q)$ gravity

The present work studies one of Einstein's alternative formulations based on the non-metricity scalar $Q$ generalized as $f(Q)$ theory. More specifically, we consider the power-law form of $f(Q)$ gravity i.e. $f(Q)=Q+α\, Q^n$. Here, we analyze the behavior of the cosmological model at the background and perturbation level. At the background level, we find the effective evolution of the model is the same as that of the $Λ$CDM for $|n|<1$. Interestingly, the geometric component of the theory solely determined the late-time acceleration of the Universe. We also examine the integrability of the model by employing the method of singularity analysis. In particular, we find the conditions under which field equations pass the Painlevé test and hence possess the Painlevé property. While the equations pass the Painlevé test in the presence of dust for any value of $n$, the test is valid after the addition of radiation fluid only for $n<1$. Finally, at the perturbation level, the behavior of matter growth index signifies a deviation of the model from the $Λ$CDM even for $|n|<1$.

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arXiv2020

From inflation to dark energy in scalar-tensor cosmology

The methods of dynamical systems have found wide applications in cosmology, with focus either upon inflation or upon the passage into dark energy era. In this paper, we endeavor to capture the whole history of the universe into a dynamical system by considering generic scalar tensor gravity with radiation and dust matter fluids in flat Friedmann-Lemaitre-Robertson-Walker spacetime. We construct the dynamical variables in such a way that the main stages of the cosmic evolution, viz. inflation, radiation domination, matter domination, and dark energy domination can be represented by the respective fixed points in the phase space. As the evolution of solutions is ruled by the sequence of these fixed points with appropriate properties, we can determine the conditions that the scalar potential and nonminimal coupling must satisfy for the model to deliver viable cosmic history in a generic manner. We illustrate the construction by a scalar field with quartic potential, with and without quadratic nonminimal coupling to curvature.

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arXiv2019

Thermodynamics of scalar field models with kinetic corrections

In the present work, we compare the thermodynamical viability of two types of non-canonical scalar field models with kinetic corrections: the square kinetic and square root kinetic corrections. In modern cosmology, the generalised second law of thermodynamics (GSLT) plays an important role in deciding thermodynamical compliance of a model as one cannot consider a model to be viable if it fails to respect GSLT. Hence, for comparing thermodynamical viability, we examine the validity of GSLT for these two models. For this purpose, by employing the Unified first law (UFL), we calculate the total entropy of these two models in apparent and event horizons. The validity of GSLT is then examined from the autonomous systems as the original expressions of total entropy are very complicated. Although, at the background level, both models give interesting cosmological dynamics, however, thermodynamically we found that the square kinetic correction is more realistic as compared to the square root kinetic correction. More precisely, the GSLT holds for the square kinetic correction throughout the evolutionary history except only during the radiation epoch where the scalar field may not represent a true description of the matter content. On the other hand, the square root kinetic model fails to satisfy the GSLT in major cosmological eras.

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arXiv2019

Linear growth index of matter perturbations in Rastall gravity

Rastall gravity theory shows notable features consistent with physical observations in comparison to the standard Einstein theory. Recently, there has been a debate about the equivalence of Rastall gravity and general relativity. Motivated by this open issue, in the present work, we attempt to shed some light on this debate by analyzing the evolution of the Rastall based cosmological model at the background as well as perturbation level. Employing the dynamical system techniques, we found that at late times, the dynamics of the model resembles the $Λ$CDM model at the background level irrespective of the choice of Rastall's parameter. However, at the perturbation level, we found that the evolution of the growth index heavily depends on the Rastall's parameter and displays a significant deviation from the $Λ$CDM model.

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arXiv2019

Cosmological dynamics of the general non-canonical scalar field models

We extend the investigation of cosmological dynamics of the general non-canonical scalar field models by dynamical system techniques for a broad class of potentials and coupling functions. In other words, we do not restrict the analysis to exponential or power-law potentials and coupling functions. This type of investigation helps in understanding the general properties of a class of cosmological models. In order to better understand the phase space of the models, we investigate the various special cases and discuss the stability and viability issues. Performing a detailed stability analysis, we show that it is possible to describe the cosmic history of the universe at the background level namely the early radiation dominated era, intermediate matter dominated era and the late time dark energy domination. Moreover, we find that we can identify a broad class of coupling functions for which it is possible to get an appealing unified description of dark matter and dark energy. The results obtained here, therefore, enlarge the previous analyses wherein only a specific potential and coupling functions describes the unification of dark sectors. Further, we also observe that a specific scenario can also possibly explain the phenomenon of slow-roll inflationary exit.

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arXiv2018

Cosmological dynamics of brane gravity: A global dynamical system perspective

The braneworld model of gravity is well-known for several notable cosmological features such as self-acceleration originating from a geometric and not matter source, effective dark energy behavior with phantom characteristics but not leading to a Big-Rip singularity, rough resemblance to the $Λ$CDM evolution, etc. The dynamical system tools usually allow us to obtain generic conclusions on the global dynamics of a system over a wide range of initial conditions. With this motivation, in order to recover the important features of the braneworld model from a more global perspective, here, we investigate the global cosmological dynamics of the braneworld model using dynamical system techniques. We first analyze the case where there is just a normal matter on the brane and then extend the analysis to the case with an extra scalar field also trapped on the brane. In the presence of a scalar field, potentials belonging to different classes are considered. The stability behavior of critical points is examined using linear stability analysis and when necessary center manifold theory as well as numerical perturbation techniques are also used. To understand the global dynamics of a dynamical system, we utilized the Poincaré compactification method to capture the properties of all possible critical points. Applying dynamical system analysis, we found that brane gravity is consistent with observed actions of the Universe. In particular, our analysis shows that important cosmological behaviors like the long-lasting matter-dominated era, late time acceleration as well as the avoidance of Big-Rip singularity can be realized in brane gravity for a wide range of initial conditions.

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arXiv2018

Cosmological dynamics of mimetic gravity

We present a detailed investigation of the dynamical behavior of mimetic gravity with a general potential for the mimetic scalar field. Performing a phase-space and stability analysis, we show that the scenario at hand can successfully describe the thermal history of the universe, namely the successive sequence of radiation, matter, and dark-energy eras. Additionally, at late times the universe can either approach a de Sitter solution, or a scaling accelerated attractor where the dark-matter and dark-energy density parameters are of the same order, thus offering an alleviation of the cosmic coincidence problem. Applying our general analysis to various specific potential choices, including the power-law and the exponential ones, we show that mimetic gravity can be brought into good agreement with the observed behavior of the universe. Moreover, with an inverse square potential we find that mimetic gravity offers an appealing unified cosmological scenario where both dark energy and dark matter are characterized by a single scalar field, and where the cosmic coincidence problem is alleviated.

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arXiv2017

Extended Phase Space Analysis of Interacting Dark Energy Models in Loop Quantum Cosmology

The present work deals with the dynamical system investigation of interacting dark energy models (quintessence and phantom) in the framework of Loop Quantum Cosmology by taking into account a broad class of self-interacting scalar field potentials. The main reason for studying potentials beyond the exponential type is to obtain additional critical points which can yield more interesting cosmological solutions. The stability of critical points and the asymptotic behavior of the phase space are analyzed using dynamical system tools and numerical techniques. We study two class of interacting dark energy models and consider two specific potentials as examples: the hyperbolic potential and the inverse power-law potential. We found a rich and interesting phenomenology including the avoidance of big rip singularities due to loop quantum effects, smooth and non-linear transitions from matter domination to dark energy domination and finite periods of phantom domination with dynamical crossing of the phantom barrier.

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