Abstract
The objective of the present paper is to investigate an almost-pseudo-Ricci symmetric FRW spacetime with a constant Ricci scalar in a dynamic cosmological term Λ(t) and equation of state (EoS) ω(t) scenario. Several cosmological parameters are calculated in this setting and thoroughly studied, which shows that the model satisfies the late-time accelerating expansion of the universe. We also examine all of the energy conditions to check our model’s self-stability.
Highlights
Ricci calculus in semi-Riemannian manifolds has a very rich history in the literature, which might have started from the concept of local symmetry, where the curvature tensor is parallel in the sense that ∇r Rijkl = 0, and later extended to conformally symmetric manifolds [1], recurrent manifolds [2], conformally recurrent manifolds [3], pseudo-symmetric manifolds [4], weakly symmetric manifolds [5], weakly Ricci symmetric manifolds [6], pseudo-Ricci symmetric manifolds [7], etc., as well as their interactions with general relativity
It should be noted that the standard theory of gravity governed by Einstein’s field equations (EFEs), which were introduced in 1915, is a very complicated system of partial differential equations and that different types of symmetries are commonly used to find the exact solutions; these kinds of restrictions on Riemannian or Ricci curvature tensors or on their covariant derivatives are very popular for such uses
We will consider an almost-pseudo-Ricci symmetric manifold (APRS)n, which was defined by Chaki and Kawaguchi [8] as a non-flat semi-Riemannian manifold whose Ricci curvature tensor Rij is not identically zero and satisfies the condition
Summary
We will consider an almost-pseudo-Ricci symmetric manifold (APRS)n, which was defined by Chaki and Kawaguchi [8] as a non-flat semi-Riemannian manifold whose Ricci curvature tensor Rij is not identically zero and satisfies the condition. The geometrical aspects of (APRS)n can be found in [9,10] and the references therein This concept was introduced as a more generalized version of the pseudo-Ricci symmetric (PRS)n manifold [7], which is defined as a non-flat semi-Riemannian manifold whose Ricci curvature tensor Rij is not identically zero and satisfies the condition. The authors of [13] showed that a conformally flat (APRS) reduced to a Robertson–Walker spacetime, and in Einstein’s field equations with a cosmological constant, the stress–energy tensor was a perfect fluid with non-constant pressure and energy density when the underlying metric was (APRS). One can explore the evolution of the cosmological models by fixing the forms of ω(t), calculating the Hubble parameter from (10), and continuing from there
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