Narrow Results

This research focuses on formulating a physical model for spherically symmetric system incorporating electromagnetic fields within the framework of $f(Q)$ gravity. To accomplish this, we investigate $f(Q)$ gravity’s field equations in the setting of anisotropic matter and solve these equations by choosing viable solution, i.e. Tolman-IV model. Matching conditions help us calculate the constants in terms of physical parameters. For this, we choose exterior geometry as Reissner–Nordström corresponding to charged anisotropic matter in the interior of spherically symmetric metric. To ensure that the obtained solution is physical viable and well-behaved, we rigorously examine the accessibility conditions (casualty conditions, TOV equations, adiabatic index, Harrison–Zeldovich–Novikov criterion and energy conditions) through graphically with software like Mathematica. Next, we implement this model to investigate various well-known compact objects, including LMC X-4 having mass $(1.04\pm 0.09)$ and a radius of $(8.301\pm 0.2)$ kilometers.

Using the FLRW cosmological model, this paper explores the dynamics of perfect fluid as a source in the context of modified gravity, where the non-metricity $Q$, which causes the gravitational interaction, is represented by the arbitrary function Lagrangian as the trace of the non-metricity tensor $Q$, say $f(Q)$ gravity. We govern the features of the derived cosmological model in view of the parameterization of Hubble’s parameter of the form, $H(z)=\frac{H_0}{(\gamma +1)}(\gamma +{(1+z)}^{\xi })$. We have spoken about how the energy density, pressure, equation of state parameter, and skewness parameter in our model represent the physical behavior of the cosmos. In addition, we have looked at the kinematic parameters in our model that describe the cosmos, including the jerk, deceleration, and Hubble parameters. The universe’s phase transition from deceleration to acceleration is indicated by our model’s deceleration parameter, $q(z)$. Furthermore, the deceleration parameter’s present value, $q_0$ clearly aligns with the essential $\mathrm{\Lambda }$CDM model. In order to determine the nature of the dark energy model, we also examined geometrical diagnostics such as the Statefinder pairs and $O_m(z)$ diagnostic. Additionally, we used the squared speed of sound test to examine the stability of the cosmos in our model. In the end, at present, the universe in our model is expanding, accelerating, and behaving in a manner consistent with a quintessential dark energy concept while at late the cosmos is dominated by $\mathrm{\Lambda }$CDM.

In this paper, we have studied the reconstruction formalism of the Dirac–Born–Infeld (DBI)-essence scalar field model in the background of non-metric gravity or $f(Q)$ gravity which is controlled by the deformation or non-metricity scale $Q$. The deformation is caused by the fifth dimension of wrapped compact spaces in brane cosmology. The fifth dimension of that wrapped space is controlled by the D-Brane tension $T(\varphi )$. Hence, we have reconstructed the formalism of DBI scalar field energy densities and pressures using the coupling of deformation geometry and brane scalar fields, i.e. $f(Q)$ and DBI-Scalar fields. The accretion of dark energy onto black holes and wormholes and its critical analysis had been studied with this reconstructed model. The validity of energy conditions has been studied. We have assumed four types of singularity resolutions of the scale factor to investigate the nature of the black hole and wormhole masses due to accretion. Graphically, the physical quantities like mass, kinetic and potential energies have been analyzed for DBI-essence model in the background of $f(Q)$ gravity.

This study investigates the dynamics of a spatially homogeneous and anisotropic LRS Bianchi type-I Universe with viscous fluid in the framework of $f(Q)$ symmetric teleparallel gravity. We assume a linear form for $f(Q)$ and introduce hypotheses regarding the relationship between the expansion and shear scalars, as well as the Hubble parameter and bulk viscous coefficient. The model is constrained using three observational datasets: the Hubble dataset (31 data points), the Pantheon SN dataset (1048 data points), and the BAO dataset (6 data points). The calculated cosmological parameters indicate expected behavior for matter-energy density and bulk viscous pressure, supporting the universe’s accelerating expansion. Diagnostic tests suggest that the model aligns with a $\mathrm{\Lambda }$CDM model in the far future and resides in the quintessence region. These findings are consistent with recent observational data and contribute to our understanding of cosmic evolution within the context of modified gravity and bulk viscosity.

In order to solve the mystery of the accelerating and expanding universe model first, various dark energy candidates, such as Quintessence, Tachyon, k-essence, Phantom and DBI-essence, were investigated in detail in the $f(Q)$ modified symmetric teleparallel gravitation theory for homogeneous and isotropic FRLW universe model. The $f(Q)=a{Q}^n+b$ model is used to obtain solutions in $f(Q)$ theory. Also, the physical behaviors of some cosmological parameters such as pressure and density were studied. Dark energy candidates were analyzed for different values of n with various graphs.

In this work, we have discussed a spatially homogeneous and anisotropic Bianchi type-I space–time in the presence of Barrow holographic dark energy (infrared cut-off is the Hubble’s horizon) proposed by Barrow recently [J. D. Barrow, Phys. Lett. B 808, 135643 (2020).] and matter in the framework of $f(Q)$ gravity where the nonmetricity $Q$ is responsible for the gravitational interaction for the specific choice of $f(Q)=\lambda Q^2$ (where $\lambda <0$ is a constant). To find the exact solutions to the field equations, we consider the deceleration parameter $q$, which is a function of the Hubble’s parameter $H$ i.e. $q=b-\frac{n}{H}$ (where $b$ and $n$ are constants). We have studied the physical behavior of important cosmological parameters such as the EoS parameter, BHDE and matter density, skewness parameter, squared sound speed and ${\omega }_B-{\omega }_B^{\prime }$ plane. Also, we constrain the values of the model parameters $b$ and $n$ using 57 Hubble’s parameter measurements.

In this work, we have examined the metric affine-based geometric model $f(Q)=Q+m{Q}^n$ to investigate inflationary cosmology and bouncing cosmology. The four bouncing models we have examined are the exponential, matter, symmetric and super-bounce models. Furthermore, in the inflationary situation, we have employed a scalar field to test whether or not kinetic energy is dominated and whether or not all of the bouncing models are consistent with inflationary conditions. We have investigated various energy conditions for various scale factors and verified whether or not these scale factors are consistent with inflationary scenarios within the framework of inflationary cosmology under $f(Q)\text{gravity}$. In the end, we have shown that the bouncing scale factor under the polynomial model ($Q+m{Q}^n$) of $f(Q)$ gravity in a single scalar field is compatible with the inflationary scenario.

The work presented in this paper aims to study the inflationary cosmology of $f(Q)$ gravity where $Q=6H^2$ by two models of Dark Energy (DE), namely Variable Generalized Chaplygin Gas (VGCG) and the Nojiri–Odintsov Holographic Dark Energy. The reconstruction has been carried out in the absence as well as presence of viscosity. The viscous pressure is considered to be $\mathrm{\Pi }=-3H\xi$, where $\xi ={\xi }_0+{\xi }_{1}H+{\xi }_2(Ḣ+H^2)$ and $H$ is the Hubble parameter. In viscous and nonviscous scenarios, the reconstruction has been carried out for power law scale factor and bounce scale factor. For the specific range of cosmic time $t$, the quintessence and quintom behavior are observed for the equation of state parameters. The slow roll parameters have been studied for both the cases in nonviscous scenario and for the case, namely bounce scale factor for VGCG of nonviscous scenario, we have found that there is a scope of exit from inflation. Furthermore, constraints have been deduced to study the presence of singularity. Finally, the $f(Q)$ gravity is reconstructed as a function of cosmic time $t$ and is found to stay at positive level for a range of cosmic time $t$.

In this paper, we examine the homogeneous and isotropic flat Universe in the frame of symmetric teleparallel gravity say $f(Q)$ gravity (where $Q$ is the nonmetricity scalar). In this work, we parametrized the field equations with the help of Hubble’s parameter defined as $H(z)=\eta [1+{(z+1)}^{-\gamma }]$, where $\eta$ and $\gamma$ are model/free parameters which are constrained with updated 57 data points of the Hubble data set within the redshift range $0.07<z<2.36$. For this, we have used a Markov Chain Monte Carlo Technique (MCMCT). Some physical parameters of the model are discussed. In addition, we analyze the jerk parameter and the statefinder parameters and we also study the energy conditions to assess the compatibility of our model with dark energy models; we determine that the Strong Energy Condition (SEC) is violated due to the fact that the Universe is currently accelerating.

Inspired by an exponential $f(R)$ gravity model studied in the literature, in this work we introduce a new and viable $f(Q)$ gravity model, which can be represented as a perturbation of $\mathrm{\Lambda }$CDM. Typically, within the realm of $f(Q)$ gravity, the customary approach to investigate cosmological evolution involves employing a parametrization of the Hubble expansion rate in terms of the redshift, $H(z)$, among other strategies. In this work, we have implemented a different strategy, deriving an analytical approximation for $H(z)$, from which we deduce approximated analytical expressions for the parameters $w_{\mathrm{\text{DE}}}$, $w_{\mathrm{\text{eff}}}$ and ${\mathrm{\Omega }}_{\mathrm{\text{DE}}}$, as well as the deceleration parameter q. In order to verify the viability of this approximate analytical solution, we examined the behavior of these parameters in the late-time regime, in terms of the free parameter of the model, b. We find that for $b>0$, $w_{\mathrm{\text{DE}}}$ shows a quintessence-like behavior, while for $b<0$, it shows a phantom-like behavior. However, regardless of the sign of b, $w_{\mathrm{\text{eff}}}$ exhibits a quintessence-like behavior. Furthermore, it has been deduced that as the magnitude of the parameter b increases, the present model deviates progressively from $\mathrm{\Lambda }$CDM. We have also performed a Markov Chain Monte Carlo statistical analysis to test the model predictions with the Hubble parameter, the Pantheon supernova (SN) observational data and the combination of those samples, obtaining constraints on the parameters of the model and the current values of the Hubble parameter and the matter density. Our findings indicate that this $f(Q)$ gravity model is indeed a viable candidate for describing the late-time evolution of the Universe at the background level.

In this work, we have proposed a simple parametrization for the pressure component $p(z)$ of the dark energy model and have studied the cosmological implications of this model in the framework of $f(Q)$ modified gravity theory, aka, the symmetric teleparallel gravity theory, where Q is known as the nonmetricity scalar. By considering a particular parametric form of $p(z)$, we obtained the Hubble solution for the $f(Q)$ modified gravity model. In order to see whether this model is consistent with or challenges the $\mathrm{\Lambda }$CDM limits, we tried to put constraints on the model parameters using the recent observational datasets like Hubble data, Cosmic Chronometer data, Type Ia Supernovae (SNIa) data, baryonic acoustic oscillations (BAO) data. We have employed the ${\chi }^2$ minimization technique and have carried out the Markov Chain Monte Carlo (MCMC) analysis using emcee package. We have found that the deceleration parameter shows a smooth transition from positive to negative value in recent past which is essential for the structure formation of the Universe. It has been found that the parametric form of the dark energy pressure parameter is consistent with current cosmological scenario.

There is ongoing interest in the nonmetricity formulation of gravity. The nonlinear extension of the theory, called $f(Q)$ gravity, has recently been proposed and offers a promising avenue for addressing some of the long-standing challenges in cosmology and fundamental physics. A number of solutions have already been found that have confirmed the usefulness of the theory for astrophysics and cosmology. Motivated by earlier work on Gödel-type spacetimes, we investigate whether $f(Q)$ gravity admits such cosmological solutions, which entail causality violation. In the coincident gauge, which is shown to be a legitimate gauge because the connection field equations are satisfied, we find that Gödel-type metrics are allowed by this modified gravity theory for any function $f(Q)$. Noncausal and causal solutions exist depending on the matter content. For a perfect fluid, out of all Gödel-type metrics only Gödel’s original model is allowed in $f(Q)$ gravity, implying violation of causality. The requirement that energy conditions be obeyed by the fluid leads to mild restrictions on $f(Q)$. For a massless scalar field in the presence of a cosmological constant, there are causal solutions for any reasonable function $f(Q)$.

In this research, we delve into the localization patterns of fermionic fields within a braneworld setting, employing a modified gravity model denoted as $f(Q)$. Our investigation revolves around two specific models, $f_1(Q)=Q+k{Q}^n$ and $f_2(Q)=Q+k_1{Q}^2+k_2{Q}^3$, where we systematically vary the parameters n and $k_{1,2}$. Through an in-depth analysis encompassing the effective potential, massless, and massive modes, we elucidate how deviations from the conventional Symmetric Teleparallel Equivalent of General Relativity (STEGR) gravity impact the localization of fermionic fields. To ensure greater precision, our methodology integrates probabilistic measures such as Shannon entropy and relative probability. Moreover, we gauge the stability of these models employing Differential Configurational Entropy (DCE), revealing a compelling correlation between the most stable configurations and the emergence of novel structures within the background scalar field. This work significantly contributes to our understanding of the gravitational modifications’ intricate influence on fermionic field localization within braneworld scenarios. By shedding light on these dynamics, it advances the broader comprehension of the interplay between gravity modifications and fermionic field behaviors in these theoretical frameworks.

The presence of exotic matter for the existence of the wormhole geometry has been an unavoidable problem in GR. In recent studies, researchers have tried to deal with this issue using modified gravity theories where the WH geometry is explained by the extra curvature terms and NEC’s are not violated signifying the standard matter in the WH geometry. In this paper, we investigate the solutions of traversable wormholes with normal matter in the throat within the framework of symmetric teleparallel gravity $f(Q)$, where $Q$ is the non-metricity scalar that defines the gravitational interaction. We analyze the wormhole geometries for three forms of function $f(Q)$. First is the linear form $f(Q)=\alpha Q$, second a nonlinear form $f(Q)=\alpha Q^2+\beta$ and third one a more general quadratic form $f(Q)=\alpha Q^2+\beta Q+\gamma$ with $\alpha$, $\beta$ and $\gamma$ being the constants. For all the three cases, the shape function is taken as $b(r)=\frac{r_{0}ln(r+1)}{ln(r_0+1)}$ where $r_0$ is the throat radius. A special variable redshift function is considered for the discussion. All the energy conditions are then examined for the existence and stability of the wormhole geometry.

The paper presents Barrow holographic dark energy (infrared cut-off is the Hubble horizon) suggested by Barrow [The area of a rough black hole, Phys. Lett. B 808 (2020) 135643] recently in an anisotropic Bianchi type-I Universe within the framework of $f(Q)$ symmetric teleparallel gravity, where the non-metricity scalar $Q$ is responsible for the gravitational interaction. We consider two cases: Interacting and non-interacting models of pressureless dark matter and Barrow holographic dark energy by solving $f(Q)$ symmetric teleparallel field equations. To find the exact solutions of the field equations, we assume that the time-redshift relation follows a Lambert function distribution as $t(z)=\frac{m{t}_0}{l}g(z)$, where $g(z)=\mathrm{\text{Lambert}}W\left[\right.\frac{l}{m}{e}^{\frac{l-ln(1+z)}{m}}\left]\right.$, $m$ and $l$ are non-negative constants and $t_0$ represents the age of the Universe. Moreover, we discuss several cosmological parameters such as energy density, equation of state (EoS) and skewness parameters, squared sound speed, and $({\omega }_B-{\omega }_B^{{}^{\prime }})$ plane. Finally, we found the values of the deceleration parameter (DP) for the Lambert function distribution as $q_{(z=0)}=-0.45$ and $q_{(z=-1)}=-1$ which are consistent with recent observational data, i.e. DP evolves with cosmic time from initial deceleration to late-time acceleration.

This study investigates a bulk viscous fluid anisotropic cosmological model with $f(Q)$ gravity. Here, $Q$ stands for the nonmetricity factor that drives gravitational interaction. We reconstructed the associated parameters with Tsallis holographic dark energy (THDE). We have solved the modified Einstein’s field equations by considering the bulk viscosity factor $\xi ={\xi }_0+{\xi }_{1}H+{\xi }_2(Ḣ+H^2)$. Under the viscous and nonviscous THDE frameworks, we have obtained the expressions of $f(Q)$ using the power-law form of expansion. We have investigated the nature of various energy conditions for the stability analysis. The positive behavior of DEC and WEC indicates the model’s validation; on the other hand, SEC is violating, indicating the universe’s accelerated expansion. We have also investigated the reconstructed EoS parameter ${\omega }_{\mathrm{\text{rec}},T}$ for bulk viscosity and obtained the one that lies in both quintessence and phantom regions. We also discussed the correspondence of the tachyon scalar field with THDE energy density in $f(Q)$ gravity. This correspondence permits the reconstruction of potentials and dynamics for scalar field models describing accelerated expansion.

This paper is focused on the investigation of wormhole solutions in $f(Q)$ gravity, where $Q$ denotes the non-metricity scalar. To obtain these solutions, three specific forms of $f(Q)$ gravity models are considered and the shape function, which is responsible for the shape of the wormhole, has been obtained numerically for each model. Further, the energy conditions are checked and the stability of solutions is obtained by determining the adiabatic sound speed in each case.

In this paper, we investigate the accelerated expansion of the Universe in the context of $f(Q)$ modified theory of gravity, where $Q$ is a non-metricity scalar which characterizes the gravitational interaction by using parametrization of the deceleration parameter $q=\alpha -\frac{\beta }{H}$ with $f(Q)=\xi +\lambda Q$, where $\xi$ and $\lambda$ are free parameters constrained by the 57 points of $H(z)$ datasets, 1048 points of Pantheon, 10 points from Baryon Acoustic Oscillations (BAO) datasets and the shift parameters from Planck 2018 of Cosmic Microwave Background (CMB). In the purpose of validating our model, we proceed by the Om diagnostic and the energy conditions. Later we discussed how our model statistically supports $\mathrm{\Lambda }$CDM using ${\mathrm{\text{AIC}}}_c$ criterion analysis.

In Einstein’s General Relativity (GR), the gravitational interactions are described by the spacetime curvature. Recently, other alternative geometric formulations and representations of GR have emerged in which the gravitational interactions are described by the so-called torsion or non-metricity. Here, we consider the recently proposed modified symmetric teleparallel theory of gravity or $f(Q)$ gravity, where $Q$ represents the non-metricity scalar. In this paper, motivated by several papers in the literature, we assume the power-law form of the function $f(Q)$ as $f(Q)=\alpha Q^{n+1}+\beta ,$ (where $\alpha$, $\beta$, and $n$ are free model parameters) that contains two models: Linear ($n=0$) and nonlinear ($n\ne 0$). Further, to add constraints to the field equations we assume the deceleration parameter form as a divergence-free parametrization. Then, we discuss the behavior of various cosmographic and cosmological parameters such as the jerk, snap, lerk, $Om$ diagnostic, cosmic energy density, isotropic pressure, and equation of state (EoS) parameter with a check of the violation of the strong energy condition (SEC) to obtain the acceleration phase of the Universe. Hence, we conclude that our cosmological $f(Q)$ models behave like quintessence dark energy (DE).

In this study, the bouncing cosmological models have been presented in the non-metricity-based gravitational theory, the $f(Q)$ gravity, where $Q$ be the non-metricity scalar. The two bouncing cosmological models, one in which the Lagrangian $f(Q)$ is assumed to have a linear dependence on $Q$ and the other in which it has a polynomial functional form have been shown. It has been obtained that the parameters of the models largely depend on the behavior of the models. The equation of state (EoS) parameter shows the bouncing behavior of the Universe. It should be highlighted that the built-in cosmological models go against the energy requirements. The kinematical and physical characteristics of the models are also analyzed.