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This article explores wormhole solutions within the framework of Finsler geometry and the modified gravity theory. Modifications in gravitational theories, such as f (R , T) gravity, propose alternatives that potentially avoid the exotic requirements. We derive the field equations from examining the conditions for Finslerian wormhole existence and investigate geometrical and material characteristics of static wormholes using a polynomial shape function in Finslerian space–time. Furthermore, we address energy condition violations for different Finsler parameters graphically. We conclude that the proposed models, which assume a constant redshift function, satisfy the necessary geometric constraints and energy condition violations indicating the presence of exotic matter at the wormhole throat. We also discuss the anisotropy factors of the wormhole models. The results are validated through analytical solutions and 3-D visualizations, contributing to the broader understanding of wormholes in Finsler-modified gravity contexts. [ABSTRACT FROM AUTHOR]

In this study, we explore the enigma of late-time cosmic acceleration in the framework of a general scalar field playing the role of dark energy. Our investigation yields an exact solution to Einstein's field equations, achieved through a parametrization of the deceleration parameter q (a) in quadratic form in the homogeneous and isotropic background geometry represented by Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. This parametrization unveils a seamless transition from a decelerated to an accelerated phase in the cosmic evolution. Furthermore, we leverage this parametrization to reconstruct cosmological parameters with respect to redshift z, elucidating their dependency on certain model parameters that govern the universe's evolutionary trajectory. The model parameters are subsequently constrained using diverse observational datasets. We provide a comprehensive analysis of the evolution of geometrical and physical parameters, complete with the numerically constrained values. To gain deeper insights into the nature of dark energy, we employ Statefinder diagnostics, conducting a thorough examination. Our findings shed light on the intricate interplay between cosmic acceleration, quintessential dark energy and the parametrization of deceleration parameter, offering valuable insights into the fundamental dynamics of the universe. [ABSTRACT FROM AUTHOR]

In this paper, we consider an inflation scenario in which the inflation roll rate, defined by ϕ ̈ H ϕ ̇ is supposed to be constant and study constant-roll inflation by a scalar field with minimal coupling to gravity in the presence of non-commutative (NC) parameters. For this purpose, we use the deformation approach and obtain the corresponding Lagrangian to the model by employing new variables. Then, we find exact solutions for the inflation potential, which include power-law, quadratic hilltop, and natural inflation. Further, we discuss the effect of parameters on the inflation model in NC space. [ABSTRACT FROM AUTHOR]

The goal of this paper is to study SdS space-time and its gravitational field with consideration of the canonical form and invariants of the curvature tensor. The characteristic of λ -tensor identifies the type of gravitational field. Gaussian curvature quantities enunciated in terms of curvature invariants. [ABSTRACT FROM AUTHOR]

We use deformation approach and obtain Lagrangian of charged test particle. We show the effect of non-commutative parameters Θ and β on the Lagrangian of a test particle in Horava-Lifshitz background with charge and without charge and see in the case of β = Θ and without charge, the deformed and non-deformed Lagrangian will be the same. In the case of β = Θ and with charge will be the same but the charge or field need some scaling. Finally, results in the case of β ≠ Θ with charge are completely different. It means that we have other components in addition to having a time component of the field. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effects of noncommutative phase-space on the quintom cosmological model. In that case, we discuss about some cosmological parameters and show that they depend on the deformation parameters. We find that the noncommutative parameter plays important role which helps to re-arrange the divergency of cosmological constant. We draw time-dependent scale factor and investigate the effect of noncommutative parameters. Finally, we take advantage from noncommutative phase-space and obtain the deformed Lagrangian for the quintom model. In order to discuss some cosmological phenomena as dark energy and inflation, we employ Noether symmetry. [ABSTRACT FROM AUTHOR]