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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]

This study extends two phenomenological models of dark energy within the framework of Finsler–Randers space–time, accommodating anisotropies. The models consider the cosmological constant Λ in two scenarios: one where Λ is proportional to the second time derivative of the scale factor a ̈ , and another where it varies with the matter-energy density ρ. Earlier, such Λ -decaying cosmologies were proposed to address long-standing cosmological constant problems. However, following the discovery of late-time cosmic acceleration, the focus shifted to modeling dark energy. Since Λ is widely viewed as the most significant and suitable candidate for driving cosmic acceleration, it is worthwhile to revisit the phenomenological approach in this context. This work uses this approach to find solutions for the scale factor a (t) and other geometrical and physical parameters. Additionally, we analyze the evolution of density parameters Ω m , Ω Λ , and Ω κ , representing matter, dark energy, and curvature, from early to late times. The phenomenological approach is employed to solve the field equations, with model parameters constrained using recent observational data, yielding ranges consistent with observations. The solutions converge to the Λ CDM cosmology at early and late times. The added complexity introduced by Finsler–Randers geometry enhances accuracy compared to analogous solutions in Riemannian space–time. [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]

This research aims to shed light on how the quintessential dark energy influences the shadows cast by black holes by considering different kinds of surrounding accretion profiles within the framework of Finsler-Hayward geometry. We explore the impact of the Finsler parameter (η) and the quintessence parameter (ω) on fundamental properties of the black hole, such as its horizons, photon sphere, and impact parameter. By examining the observed characteristics of the black hole's shadow, including the photon ring and shadow intensities, we analyze how the quintessence affects these features under varying scenarios of matter accretion. Leveraging observational data from the Event Horizon Telescope, exclusively focusing on celestial bodies such as Sgr A* and M87*, we narrow down the range of the Finsler parameter (η) within our model of quintessence-infused Finsler Hayward black holes. By comparing our findings with models such as Finsler Schwarzschild, with and without the quintessence Finsler Hayward black holes, we observe that the quintessence's influence on the black hole's shadow surpasses the effects attributed to regularity. This study contributes to our insight into how the Finsler parameter and the quintessence of dark energy shape the shadows of black holes in diverse accretion environments, shedding light on their intricate nature and behavior, particularly in the context of Finsler Hayward geometry. [ABSTRACT FROM AUTHOR]