arXiv subjects

Avik De

Publications and source records attributed to Avik De.

At least 19 recordsLinked to original sources

arXiv2026

The role of anisotropy in $f(Q)$ gravity: insights from cosmological observations

We investigate the cosmological dynamics of Bianchi-I spacetime in symmetric teleparallel $f(Q)$ gravity through a dynamical system approach to analyse observational constraints. By reformulating the modified field equations into an autonomous system, we analyse two representative $f(Q)$ models and constrain their parameters using Pantheon Plus, DES Y5, DESI DR2, and compressed CMB data. The observational analysis yields consistent constraints across all dataset combinations and tightly bounds the anisotropic contribution, indicating that deviations from isotropy remain small. Both models reproduce the standard matter-dominated evolution and the observed late-time accelerated expansion while exhibiting distinct dark-energy dynamics. Model I undergoes a smooth phantom-divide crossing and approaches a de Sitter phase in the asymptotic future, whereas Model II evolves from an early phantom regime toward a cosmological-constant-like state around the present epoch, closely mimicking the late-time evolution of the $\Lambda$CDM model. These results indicate that anisotropic $f(Q)$ cosmology remains consistent with current background observations while admitting characteristic dark-energy evolution that may be testable with future cosmological surveys.

physics.gen-ph↗

arXiv2026

Perturbation Dynamics and Structure Formation in Extended Proca-Nuevo Gravity

A comprehensive analysis of cosmological perturbations and structure formation is presented for the Extended Proca-Nuevo (EPN) framework, a vector-tensor extension of General Relativity with a massive spin-1 field. In this scenario, the vector field modifies the background expansion through an algebraic constraint, leading to a characteristic Hubble evolution that interpolates between $\Lambda$CDM limits while introducing deviations at intermediate redshifts. Assuming minimal matter coupling, the linear perturbation equations are derived in gauge-invariant form and the resulting growth of matter inhomogeneities is analyzed. The EPN sector induces effective anisotropic stress and couples a single propagating scalar mode to the metric potentials, leaving the matter growth equation in its GR form but with a modified expansion history. The full scalar perturbation system is presented, stability conditions are discussed, and the results provide a foundation for testing the EPN framework against current and future cosmological observations.

gr-qc↗

arXiv2026

Scalar field coupled to boundary in non-metricity: a new avenue towards dark energy

While conformal transformations in metric scalar-tensor theories recover General Relativity, this feature is notably absent in standard non-metricity-based theories. We demonstrate that by introducing the boundary term C, a non-metricity scalar-tensor theory can recover Symmetric Teleparallel Equivalent of General Relativity (STEGR) in the Einstein frame. Motivated by this, we propose a novel gravity model where a scalar field couples nonminimally to both the non-metricity scalar Q and the boundary term C. We focus in the cosmological scenario where we present the covariant formulation and a unified autonomous system framework that treats generic affine-connection choices, including coincident and non-coincident gauges, on an equal footing. Our dynamical analysis across three connection branches reveals standard thermal histories and stable de Sitter attractors. These results show that boundary-term couplings provide a well-posed, geometrically flexible route to addressing late-time cosmic acceleration.

gr-qc↗

arXiv2025

Density contrast in the scalar-tensor extension of non-metricity gravity

We present a novel derivation of scalar cosmological perturbations in the scalar-tensor extension of non-metricity gravity, where the non-metricity scalar $Q$ is non-minimally coupled to a dynamical scalar field. While previous investigations of symmetric teleparallel gravity focused primarily on background evolution or specialised gauge choices, a complete treatment of scalar perturbations in this non-minimally coupled framework has remained unexplored. In this work, we derive the full set of perturbed field equations, impose the quasi-static approximation, and obtain the effective Poisson equation together with the corresponding modified gravitational constant $G_{\rm eff}$. These ingredients allow us to construct the density contrast evolution equation and analyse the matter growth rate and growth index. Through numerical analysis, we showed that the scalar non-metricity theory is comparable to the well-known $\Lambda CDM$ model to some extent. The results provide a foundation for testing scalar non-metricity theories against large-scale structure observations and open new avenues for constraining non-minimally coupled non-metricity cosmologies.

gr-qc↗

arXiv2025

Scalar-Tensor Symmetric Teleparallel Gravity: Reconstruct the Cosmological History with a Steep Potential

Within the framework of scalar-non-metricity gravity, we introduce a steep potential together with a power-law coupling function and investigate whether the acceleration phases of the universe can be consistently described by this model. In the symmetric teleparallel formulation, and under a Friedmann--Lema\^itre--Robertson--Walker background, three distinct branches of the connection arise, leading to three different cosmological scenarios. We perform a detailed dynamical analysis of these models by examining the phase space and determining the asymptotic cosmological solutions. The analysis reveals a rich hierarchy of critical points, including matter-dominated epochs, kinetic-dominated stiff-fluid regimes, and steep potential-dominated de Sitter solutions, along with asymptotic trajectories that approach Big Crunch or Big Rip singularities, as well as transient, unstable matter-dominated eras. The stability of the steep potential-dominated de Sitter points is further studied using Center Manifold Theory, showing that, under specific parametric conditions, the model can provide a unified description of both the early and late-time acceleration phases of the universe.

gr-qc↗

arXiv2025

Cosmological Scenarios in $f(Q,C)$ gravity with a dynamical degree of freedom

The $f(Q,C)$ theory, which extends symmetric teleparallel gravity by including the boundary term $C$ in addition to the non-metricity scalar $Q$, provides a unifying framework that encompasses both $f(Q)$ and $f(\mathring{R})$ gravities. In this work, we develop a comprehensive dynamical system analysis of $f(Q,C)$ cosmology formulated within the non-coincident affine connection branches. Unlike the coincident case, these branches introduce a dynamical degree of freedom that significantly enriches the cosmological phase space. We show that even for simple power-law forms of the Lagrangian, the theory accommodates a broad spectrum of cosmic scenarios, including successive pressureless matter eras, stiff-matter phases between early inflation and dark matter domination, and late-time acceleration. Our analysis demonstrates that the Universe can naturally evolve from an initial de Sitter phase to a matter-dominated epoch and subsequently to a final de Sitter attractor, consistent with the observed thermal history. These results highlight the role of the dynamical connection in shaping cosmic evolution and underline the potential of $f(Q,C)$ gravity as a viable alternative framework for addressing outstanding issues in modern cosmology.

gr-qc↗

arXiv2025

Exact cosmological solutions in non-coincidence $f(Q)$-theory

We study exact cosmological solutions in $f(Q)$ gravity formulated beyond the coincident gauge, focusing on the non-coincident connection branch $\Gamma_B$. Using a minisuperspace approach, the field equations are recast into an equivalent scalar-tensor form, enabling analytic reconstruction of cosmological models. We obtain exact solutions of particular interest, including de Sitter, scaling, $\Lambda$CDM, Chaplygin gas, generalized Chaplygin gas, and CPL parameterizations. The corresponding scalar potentials and $f(Q)$ functions are derived in closed or parametric form. Our analysis shows that non-coincident $f(Q)$ gravity admits a richer solution space than the coincident case and can describe both early-time inflationary dynamics and late-time acceleration within a unified framework. These results open new directions for testing $f(Q)$ cosmology against observations and exploring its role as a viable alternative to $\Lambda$CDM.

gr-qc↗

arXiv2025

Role of the Dynamic Degree of Freedom in Scalar-Tensor Non-Metricity Gravity with Curved FLRW Geometry

We investigate a non-minimally coupled scalar field theory within the framework of scalar-tensor non-metricity gravity, focusing on spatially curved FLRW spacetimes. Employing the dynamical systems approach with Hubble-normalized variables, we reformulate the field equations into an autonomous system and analyze the resulting critical points. Four distinct cases, determined by the scalar coupling and potential functions, are studied in detail. For each case, we identify the existence and stability of equilibrium points, classify their cosmological behavior, and compute key observables such as the deceleration parameter and effective equation of state. Our results reveal that the theory admits matter-dominated eras, parameter-dependent saddle solutions, and stable de Sitter attractors capable of driving late-time cosmic acceleration. The additional scalar degree of freedom introduced by the non-coincident gauge plays a crucial role in determining the system's dynamics and viability. These findings emphasize the potential of scalar-tensor non-metricity gravity as a robust extension of general relativity and motivate further confrontation of the model with observational data.

gr-qc↗

arXiv2025

Can an Extra Degree of Freedom in Scalar-Tensor Non-Metricity Gravity Account for the Evolution of the Universe?

We investigate whether the extra scalar degree of freedom that arises in the second connection class of scalar-tensor non-metricity gravity can accurately replicate and potentially enrich the cosmic expansion history. Focusing on a spatially flat FLRW background, we introduce Hubble-normalized variables and recast the field equations into an autonomous dynamical system. Four representative scenarios are analyzed comprehensively. Phase-space research reveals a rich hierarchy of critical points: matter-dominated, stiff-fluid, and de Sitter solutions, together with asymptotic trajectories leading to Big-Crunch/Rip singularities and transient, unstable matter epochs. With suitable parameter choices, the standard $\Lambda$CDM sequence is reinstated; however, novel late-time and high-curvature regimes arise exclusively from the non-metricity sector. A systematic comparison of metric scalar-tensor and teleparallel scalar-torsion theories reveals unique stability characteristics and potential observational discriminants. Our findings indicate that the additional time-dependent function inherent to scalar-tensor non-metricity gravity can effectively explain the Universe's evolution while providing new phenomenology that can be tested by upcoming surveys.

gr-qc↗

arXiv2025

Phase-space analysis of an anisotropic universe in $f(Q,C)$ gravity

In this study, we analyze the anisotropic universe in $f(Q,C)$ gravity theory. To achieve this, we consider three specific models of $f(Q,C)$ gravity and rewrite the equations of motion of each model as an autonomous system. We identify and analyze the critical points, examine their stability, and plot phase portraits to illustrate the behavior of each critical point. The evolution of key parameters, including the equation of state (EoS) parameter $w_{eff}$, the deceleration parameter $q$, and the standard density parameters $\Omega_{m}$ and $\Omega_{DE}$, is thoroughly investigated. The anisotropic dynamical variable exhibits decelerated behavior, consistent with the early universe, while the others demonstrate accelerated behavior, aligned with late-time observations across all models.

gr-qc↗

arXiv2025

A generic dynamical system formulation for Bianchi-I cosmology with isotropic fluid in $f(Q)$ gravity

In this article, we present a generic dynamical system formulation for Bianchi-I cosmology in the presence of an isotropic fluid within the coincident gauge connection branch and one of the non-coincident gauge connection branches of $f(Q)$ gravity theory. For both the connection branches under consideration, we start from the generic Bianchi-I cosmological field equations in $f(Q)$ and present a prescription of how one can construct an autonomous dynamical system in terms of the standard Hubble-normalized dimensionless dynamical variables once an $f(Q)$ theory is provided. Particular care has been taken to single out the physically viable regions in the phase space for each of the models under consideration. This results in the finding that, for both of the connection branches under consideration, the Kasner solution marginally violates the key physical viability condition of positive effective gravitational coupling ($f_Q>0$) for all the models considered, whereas a physically viable de-Sitter future attractor appears in all the models, except for the very special case of the monomial model within the coincident gauge connection. In the context of the early universe cosmology, we find that isotropization of a homogeneously perturbed inflating FLRW universe is a generic model-independent feature in the coincident gauge, whereas the isotropization of a homogeneously perturbed pre-bounce ekpyrotically contracting FLRW universe is, although not completely generic, but a likely scenario.

gr-qc↗

arXiv2024

Emergent Universe in f(Q) gravity theories

One resolution of the ancient cosmic singularity, i.e., the Big Bang Singularity (BBS), is to assume an inflationary stage preceded by a long enough static state in which the universe and its physical properties would oscillate around certain equilibrium points. The early period is referred to as the Einstein Static (ES) Universe phase, which characterizes a static phase with positive spatial curvature. A stable Einstein static state can serve as a substitute for BBS, followed by an inflationary period known as the Emergent Scenario. The initial need has not been fulfilled within the context of General Relativity, prompting the investigation of modified theories of gravity. The current research aims to find such a solution within the framework of symmetric teleparallel gravity, specifically in the trendy $f(Q)$ theories. An analysis has been conducted to investigate stable solutions for both positively and negatively curved spatial FRW universes, in the presence of a perfect fluid, by utilizing various torsion-free and curvature-free affine connections. Additionally, we propose a method to facilitate an exit from a stable ES to a subsequent inflationary phase. We demonstrate that $f(Q)$ gravity theories have the ability to accurately depict the emergence of the universe.

gr-qc↗

arXiv2024

Scalar perturbation and density contrast evolution in $f(Q,C)$ gravity

The symmetric teleparallel theory offers an alternative gravitational formulation which can elucidate events in the early and late universe without requiring the physical existence of dark matter or dark energy. In this formalism, $f(Q, C)$ gravity has been recently introduced by incorporating the boundary term $C$ with the non-metricity scalar $Q$. In this paper, we develop the theory of cosmological scalar perturbation for $f(Q, C)$ gravity, and retrieve that of $f(\mathring{R})$ and $f(Q)$ gravity from our result. The analysis assumes a model-independent approach within these theories that adheres to the conventional continuity equation at the background level. We derive the density contrast equation by employing some standard cosmological approximations, where the $f(Q,C)$ theory is encoded in the effective Newtonian constant $G_{eff}$. Finally, we derive the evolution equation of density growth $f_g$.

gr-qc↗

arXiv2024

The cosmological significance of boundary term in non-metricity gravity

Within the context of metric-affine gravity, we examine the significance of the boundary term in symmetric teleparallel gravity by employing the cosmological dynamical system analysis method. We focus on the novel gravity models characterized by the functions $f(Q,C)$, where $f$ is a smooth function of the non-metricity scalar $Q$ and the associated boundary term $C$. In a cosmological setting adopting three different classes of symmetric teleparallel affine connections, we investigate a model $f(Q,C)=Q^{s}+eC^{r}$, and some special cases of this model. We show that the boundary term which is added to the Einsteinian field equations (or equivalently to $f(Q)=Q$ ones) are capable of bringing forward solutions corresponding to the early accelerated expansion. This alludes the physics behind the boundary terms which usually are discarded in the most gravitational theories.

gr-qc↗

arXiv2023

Cosmological reconstruction and $\Lambda$CDM universe in $f(Q,C)$ gravity

Symmetric Teleparallel Gravity allows for the reformulation of gravity in the form of nonmetricity by vanishing the contorsion term in the generic affine connection. Our focus is on investigating a recently proposed extension of this theory in which the Lagrangian has the form $f(Q,C)$ by incorporating the boundary term $C$. In this work, we first use a reconstruction approach in $f(Q,C)$ gravity that might admit the $\Lambda$CDM expansion history. Furthermore, we perform a novel approach for cosmological reconstruction of $f(Q,C)$ gravity in terms of e-folding, and it shows how any FLRW cosmology can arise from a specific $f(Q,C)$ gravity. A variety of instances are provided using this approach in which $f(Q, C)$ gravity is reconstructed to yield the well-known cosmic evolution: $\Lambda$CDM era, acceleration/deceleration era which is equivalent to the presence of phantom and non-phantom matter, late-time acceleration with the crossing of phantom-divide line and transient phantom era.

gr-qc↗

arXiv2023

How to Model Brushless Electric Motors for the Design of Lightweight Robotic Systems

A key step in the development of lightweight, high performance robotic systems is the modeling and selection of permanent magnet brushless direct current (BLDC) electric motors. Typical modeling analyses are completed a priori, and provide insight for properly sizing a motor for an application, specifying the required operating voltage and current, as well as assessing the thermal response and other design attributes (e.g.transmission ratio). However, to perform these modeling analyses, proper information about the motor's characteristics are needed, which are often obtained from manufacturer datasheets. Through our own experience and communications with manufacturers, we have noticed a lack of clarity and standardization in modeling BLDC motors, compounded by vague or inconsistent terminology used in motor datasheets. The purpose of this tutorial is to concisely describe the governing equations for BLDC motor analyses used in the design process, as well as highlight potential errors that can arise from incorrect usage. We present a power-invariant conversion from phase and line-to-line reference frames to a familiar q-axis DC motor representation, which provides a ``brushed'' analogue of a three phase BLDC motor that is convenient for analysis and design. We highlight potential errors including incorrect calculations of winding resistive heat loss, improper estimation of motor torque via the motor's torque constant, and incorrect estimation of the required bus voltage or resulting angular velocity limitations. A unified and condensed set of governing equations is available for designers in the Appendix. The intent of this work is to provide a consolidated mathematical foundation for modeling BLDC motors that addresses existing confusion and fosters high performance designs of future robotic systems.

cs.RO↗

arXiv2023

Non-metricity with bounday terms: $f(Q,C)$ gravity and cosmology

We formulate $f(Q,C)$ gravity and cosmology. Such a construction is based on the symmetric teleparallel geometry, but apart form the non-metricity scalar $Q$ we incorporate in the Lagrangian the boundary term $C$ of its difference form the standard Levi-Civita Ricci scalar $\mathring R$. We extract the general metric and affine connection field equations, we apply them at a cosmological framework, and adopting three different types of symmetric teleparallel affine connections we obtain the modified Friedmann equations. As we show, we acquire an effective dark-energy sector of geometrical origin, which can lead to interesting cosmological phenomenology. Additionally, we may obtain an effective interaction between matter and dark energy. Finally, examining a specific model, we show that we can obtain the usual thermal history of the universe, with the sequence of matter and dark-energy epochs, while the effective dark-energy equation-of-state parameter can be quintessence-like, phantom-like, or cross the phantom-divide during evolution.

gr-qc↗

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.

gr-qc↗