f(R,φ,X) theory, combination of scalar-tensor and f(R)-class gravity, is examined for perfect fluid in Bianchi Type-I space-time. Hybrid model of Starobinsky-like and kessence is used. Two different forms of solution are obtained and discussed in Bianchi Type-I cosmology. Effective energy densities, effective pressures and necessary statements of energy conditions for both solutions are analyzed. It is discussed whether f(R,φ,X) theory allows expanding or contracting cosmologies for obtained two forms of Bianchi Type-I space-time.

Observational viability of fractional holographic dark energy in LRS Bianchi type-I cosmological model

This study performs a comparative cosmological analysis of Brans–Dicke theory (BDT) and [Formula: see text] gravity in the anisotropic Bianchi type-I spacetime. By using a hyperbolic sine form of the scale factor, we constrain the free parameters [Formula: see text] and [Formula: see text] against 77 [Formula: see text] data points via [Formula: see text] minimization, obtaining [Formula: see text] and [Formula: see text], with a reduced chi-square [Formula: see text]. The model predicts the present Hubble and deceleration parameters as [Formula: see text] and [Formula: see text], respectively. We derive and examine the dynamical evolution of energy density, pressure, and the equation of state (EoS) parameter. A key outcome is the marked difference in late-time behavior: the [Formula: see text] model exhibits stronger acceleration with an EoS parameter trending toward phantom regimes, whereas the BDT model shows a distinctive late-time re-acceleration phase driven by the scalar field dynamics. These results highlight how geometric and scalar-field modifications of gravity lead to observationally distinguishable cosmic evolution.

In this work, we investigate a cosmological model within the context of [Formula: see text] gravity by considering a bulk viscous fluid as the cosmic source and adopting a Bianchi type [Formula: see text] anisotropic spacetime. To derive an exact solution of the field equations, we assume a specific time-dependent deceleration parameter expressed in terms of the Hubble parameter. This choice facilitates the derivation of analytical expressions for the scale factor and Hubble parameter as functions of cosmic time t and redshift z. Additionally, we conduct a cosmographic analysis by computing higher-order kinematic parameters — jerk, snap, and lerk — which are found to asymptotically approach unity, thereby indicating consistency with the standard [Formula: see text]CDM cosmological model in the late-time limit. To further constrain the model and solve the field equations, we impose a relation between the directional scale factors as [Formula: see text]. This condition plays a crucial role in reducing the complexity of the anisotropic field equations and enables the derivation of exact expressions for key physical quantities. As a result, we obtain the temporal and redshift evolution of the energy density [Formula: see text], effective pressure [Formula: see text], and the equation of state (EoS) parameter w. The dynamical behavior of these quantities suggests a transition from a decelerated to an accelerated phase of cosmic expansion, compatible with current observational evidence.

In the present work, the Bianchi Type III spacetime is taken into account in the presence of a cosmic string and a domain wall within the framework of f(R,T) theory of gravitation. A specific form of the f(R,T), theory, namely f(R,T) = R + 2f(T), is taken into account in this work. The modified field equations for cosmic string and domain wall models are solved using a particular form of the deceleration parameter, and their physical behaviors are analyzed. In addition, the EoS parameter, jerk parameter, statefinder pair, and Om(z) diagnostic are utilized to analyze the evolutionary behavior of the Universe under the considered modified gravity model, indicating a quintessence-type nature of the cosmic expansion.This research offers significant insights into the anisotropic behaviour of the Universe and effectively describes the cosmic acceleration observed during late times. Our findings are then compared to recent observational data and are found to be in agreement with the ΛCDM model.

The present research aims at investigating the LRS Bianchi type I dark energy cosmological model within the framework of f(G) gravity. To obtain solutions for the field equations, a parametrization of the deceleration parameter is employed. The approximate best-fit values of the model parameters are obtained using the least squares method, incorporating observational constraints from available datasets such as the Hubble dataset and the Pantheon dataset by applying the Root Mean Square Error (RMSE) formula. The related cosmological parameters are graphed against redshift, and the universe's accelerated expansion is subsequently examined. Various physical parameters, including pressure, energy density, and energy conditions, are also discussed.

The gauge problem and polarization modes of gravitational waves in anisotropic Bianchi type I cosmological models

In this paper, we discuss the Bianchi type-I barrow holographic dark energy cosmological model in the framework of [Formula: see text] theory of gravity. We consider the model of pressure-less dark matter and barrow holographic dark energy by solving [Formula: see text] theory field equations. Here, we find the exact solution of the field equations, we assume that the time redshift relation follows a Lambert function distribution as [Formula: see text], where [Formula: see text], where [Formula: see text] and [Formula: see text] are positive constants and [Formula: see text] is the present age of the Universe. We discuss the cosmological parameters such as energy densities ([Formula: see text] and [Formula: see text]), skewness parameter ([Formula: see text]), equation of state parameter [Formula: see text] and deceleration parameter ([Formula: see text]). Also, we study the statefinder parameters such as [Formula: see text] and [Formula: see text]. We found the present values of the deceleration parameter, which are consistent with recent observational data for the Lambert function distribution. We investigate the thermodynamic quantities and the generalized energy conditions in order to test the viability of our model. Finally, the deceleration parameter evolves with cosmic time from initial deceleration to late-time acceleration.

In this work, we analyze the dynamical evolution of locally rotationally symmetric anisotropic cosmological models of Bianchi type I (flat curvature) and Bianchi type III (open curvature) within a noncommutative phase space framework characterized by a deformation parameter γ. Using a Hamiltonian formulation based on Schutz’s formalism for a perfect radiation fluid, we introduce noncommutative Poisson brackets that allow for geometric corrections to commutative dynamics. The resulting equations are solved numerically, which allows for the study of the impact of γ and the energy density C on the expansion of the universe and the evolution of anisotropy. The results show that γ<0 improves expansion and favors isotropization, while γ>0 tends to slow expansion and preserve residual anisotropy, especially in the open curvature model. It is estimated that the influence of noncommutativity was significant during the early stages of the universe, decreasing toward the present time, suggesting that this approach could serve as an effective alternative to the cosmological constant in describing the evolution of the early universe.

In this study, we investigate anisotropic Bianchi Type VI cosmological model within the framework of fractal universe. By utilizing the energy–momentum tensor for a perfect fluid, we solve the corresponding field equations. In this study, we derive leading cosmological parameters, including the hubble parameter H and deceleration parameter q in terms of cosmic time and redshift also. To determine the model parameters such as k, [Formula: see text] and the hubble constant [Formula: see text], the hubble dataset was analyzed using the [Formula: see text] test. This analysis reveals the best-fit values of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] match with the [Formula: see text]CDM model. We carry blow-by-blow analysis of the model’s characteristics via energy density [Formula: see text], pressure p and EoS parameter. We examine whether the energy conditions — null energy condition (NEC), strong energy condition (SEC), weak energy condition (WEC) and dominant energy condition (DEC) — are satisfied. Furthermore, the diagnostic parameters are analyzed to evaluate the deviation of the obtained model from the [Formula: see text]CDM model and to classify various dark energy models during the universe’s expansion. The om diagnostic is depicted as a function of redshift for [Formula: see text] and [Formula: see text] revealing that [Formula: see text] settles around [Formula: see text] with slight deviation in the range [Formula: see text]. The model closely aligns with [Formula: see text]CDM at higher redshifts. The pair of statefinder diagnostics r versus s is also discussed, and our model for [Formula: see text] represents the [Formula: see text]CDM model.

In this paper, we investigated the Locally Rotationally Symmetric (LRS) Bianchi Type-I cosmological model with dark energy in the framework of f (R, Lm) gravity theory, where R is the Ricci scalar and Lm is the matter Lagrangian. Using the functional form f (R, Lm) = R/2 + Lαm + β with Lm = ρ, and applying the special law of variation for the Hubble parameter, we derived exact solutions to the field equations and analyzed the physical and dynamical properties of the universe. Our results show that the model exhibits accelerated expansion consistent with the observational data, with the energy density decreasing and the deceleration parameter transitioning from positive to negative values. The anisotropy parameter initially approaches zero but increases with time for n > 0.5, indicating the evolution from isotropy to anisotropy. These findings provide insights into dark energy behavior within modified gravity frameworks and offer testable predictions for cosmological observations.

This work investigates a spatially homogeneous and anisotropic Bianchi type-I universe within the framework of [Formula: see text] gravity, where [Formula: see text] is the Ricci scalar and [Formula: see text] represents the trace of the energy–momentum tensor, specifically for the case [Formula: see text]2[Formula: see text], with [Formula: see text] bT. The model employs a specific gravitational function that incorporates bulk viscous matter. A novel, time-dependent deceleration parameter is introduced, extending the form proposed by Tiwari and Sofuoglu (Quadratically varying deceleration parameter in [Formula: see text]([Formula: see text])gravity, Int. J. Geom. Methods Mod. Phys.17 (2020) 2030003). The research focuses on a locally rotationally symmetric (LRS) Bianchi type-I bulk viscous fluid model, which describes the evolution of the universe from an early decelerating phase to its present accelerated expansion. Exact solutions of the field equations are derived using the proposed deceleration parameter, and both the physical and kinematic properties are analyzed in detail and presented graphically. Furthermore, the validity of the weak, dominant, and strong energy conditions, along with the evolution of energy density, is examined. The results indicate that bulk viscosity plays a crucial role in driving the current accelerated expansion of the universe.

This study investigates self-similar vector fields of locally rotationally symmetric Bianchi type–I spacetimes within the framework of f(T) gravity, incorporating a perfect fluid as the matter source. The analysis demonstrates that certain spacetimes with a perfect fluid admit self-similar vector fields of infinite, first, zeroth, and second kinds. To address this problem, the Rif tree approach has been employed. In this method, the symmetry and field equations are transformed using Maple, which generates a set of constraints on the spacetime functions. These constraints are then applied to solve the symmetry equations, ultimately yielding the exact form of the self-similar vector field. Furthermore, the physical quantities—energy density ρ, pressure p, torsion scalar T, and torsion-based function f(T)—are calculated for each solution, providing a comprehensive understanding of the physical and geometric properties of the spacetime. In addition, the kinematic variables associated with the derived metrics have also been calculated. The findings of this study have significant applications in cosmology, astrophysics, and modified gravity theories, particularly in modeling cosmic evolution, black hole formation, and anisotropic spacetime structures. The classified self-similar solutions in f(T) gravity contribute to understanding gravitational collapse, the dynamics of the early universe, and the stability of astrophysical objects.

The Bianchi type III (BIII) metric is a useful geometry to study cosmic anisotropies. It includes an extra exponential term multiplied by a directional scale factor and recasts the cosmological model as a dynamical system to provide various significant information regarding the evolution, stability of the system, etc. In this study, we have constructed a dynamical system for the BIII metric using [Formula: see text] gravity theory and performed fixed point analysis in three different [Formula: see text] models. Here, we have found that the first two models i.e. [Formula: see text] and [Formula: see text] are agreed with standard [Formula: see text]CDM cosmology but the third one i.e. [Formula: see text] has the issue of unbounded energy density. Thus, we can remark that some [Formula: see text] models may not be suitable for studying the evolution of the Universe with an anisotropic background, like using BIII metric, etc. However, all three models agree with the heteroclinic path of radiation-dominated, matter-dominated, and dark energy-dominated phases of the Universe as predicted by standard cosmology.

Bianchi type I model cannot explain the observed CMB angular acoustic scale directional variation

A bstract We consider the 3-form theory with non-minimal coupling to gravity in an expanding Universe. First, we assume that the background is homogeneous and isotropic, and that the three-form is coupled to both the Ricci scalar and the Ricci tensor. We show that in this case, it propagates three degrees of freedom: a scalar mode and two tensor ones. Then, we consider an anisotropic background that corresponds to a Bianchi Type I Universe, and set the coupling with the Ricci tensor to zero. We show that, similarly to the Proca theory with non-minimal coupling to gravity, this case leads to two branches for the background solutions — depending on the values of the 3-form. However, in contrast to the Proca case, we show that no extra modes appear. We explore the no-ghost conditions and speed of propagation for all three modes in both branches. Finally, we show that one of the branches can be written as a theory of a constrained scalar, coupled to a cuscuton field.

This article presents a complete classification of Ricci solitons and their associated vector fields in the context of locally rotationally symmetric (LRS) Bianchi type I spacetime, a crucial model in cosmological studies. To systematically address the complexities inherent in the Ricci soliton equations, we adopt the Rif tree technique. The equations defining the Riccisoliton and its vector field are transformed into a reduced involutive form using a computational algorithm, which assists in dividing the integration process into a collection of cases organized in a tree-like structure. Each of these cases is governed by specific constraints on the metric functions, which facilitates the solution process. Definite expressions for the metric functions and the corresponding vector field of the Ricci soliton are obtained by efficiently solving the system of equations characterizing the soliton vector field through the application of these constraints. This powerful approach enables us to derive novel and exact solutions that previous methods have overlooked. Our results demonstrate that this spacetime admits Ricci solitons of shrinking, steady, and expanding natures, characterized by vector fields with up to 11 free parameters. Crucially, we conduct a thorough physical analysis of the resulting models, determining their matter content through the equation of state and testing their physical viability via the standard energy conditions. We find specific families of solutions that correspond to physically significant scenarios, such as a spacetime filled with vacuum energy (a cosmological constant). This work not only provides a comprehensive mathematical classification but also establishes a direct link between these geometric structures and potentially realistic cosmological models.

In recent years, modified theories of gravity, particularly f (R) gravity, have garnered much attention. This study investigates the exact vacuum field solutions for Bianchi type I, Bianchi type-III, and Kantowski-Sachs spacetimes within the f (R) gravity metric theory. We assume a proportional relationship between the expansion scalar θ and shear scalar σ2 and hence derive solutions of the form X = Y m, where X and Y are the metric coefficients. The physical implications of these solutions are examined using relevant physical quantities. Further, we evaluate the functional Ricci scalar for each case. We observe that the average Hubble parameter H(T ) for the Bianchi type-I and type-III models decreases sharply with the progression of cosmic time, T , starting from a high initial value and then approaching a stable equilibrium. In the Kantowski-Sachs model, H(T ) shows a smoother and more uniform decline over time. This behavior aligns with the standard cosmological models, where the expansion rate of the universe slows down due to the gradual decrease in energy density. More-over, the extremely high initial values of the expansion scalar, θ(T ) as T → 0 in all three models Bianchi type-I, type-III, and Kantowski-Sachs correspond well with the expansion phases of the early universe, such as inflation or the radiation-dominated era. The shear scalar σ(T )2 consistently decreases with increasing cosmic time, indicating a trend toward isotropy as the universe expands. The volume scale factor V (T ) increases with time, capturing the continuous expansion which is a fundamental feature of the Big Bang cosmology. Additionally, the function f (R) is well-behaved at low curvatures where R → 0 but for large R in the limit of high curvature, f (R) → R, in all of the three models.

In this paper, we have investigated the LRS Bianchi type-I cosmological model containing anisotropic fluid in Bimetric theory of gravitation. The Rosen’s filed equations are solved with the help of special law of variation for Hubble parameter proposed by Berman (1983). We have deduced Zeldovich universe in this theory which is accelerating in nature. Some geometrical and physical aspects of the derived model are also studied.

Abstract This work considers the dynamics of the gauge vector and inflaton (dilaton) fields inspired by Kaluza–Klein theory in an inflationary universe with Bianchi type-I spacetime. The inverse power-law potential of the inflaton field is used to study dynamical system analysis. As a result, all fixed points in the autonomous system are non-hyperbolic fixed points, and one cannot determine their stability. Therefore, a center manifold theory is required to analyze the stability of the dynamical system properly. Interestingly, we found an isotropic attractor point which means that the universe undergoes accelerated expansion (inflation) from an anisotropic phase to an isotropic phase of the universe. According to the dynamical system analysis of the anisotropic Bianchi type-I universe with the inspired Kaluza–Klein model, our results supported the isotropization of the observed universe.