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In this paper, we study an isotropic flat FLRW-model in scale-covariant theory of gravity f γ δ (ϕ) 1 which is explained in terms of ordinary and covariant differentiation of scalar field ϕ. As we know, the deceleration parameter (DP) is time-dependent, so we consider the DP q as the function of t. Using this methodology, we find all the important cosmological factors in terms of a hyperbolic function of the cosmic time t. In turn, we create the model having the behavior of the late-time universe, which is ever accelerated expanding and faces a Big Freeze at the end. The model shows the quintessence dark energy model from early to late times. We compute the constrained values of Hubble parameter H 0 = 7 0. 9 7 9 − 0. 0 0 4 3 + 0. 0 2 1 and the model parameter n = 1. 2 4 0 7 9 − 0. 0 0 0 7 9 + 0. 0 0 0 1 5 using joint analysis of the OHD data of 77-points and Pantheon bin data. The model exhibits point-type singularity as it begins with a point of zero volume, infinite energy density and temperature. Furthermore, we obtain the present value of DP (q 0) ≈ − 0. 5 4. Also, we examine the ultimate behavior of our model by the proper analysis of energy conditions (ECs), cosmographical parameters and Statefinder diagnostic. Finally, the proposed model behaves like a quintessence dark energy model. [ABSTRACT FROM AUTHOR]

In this paper, we study a flat homogeneous FLRW model in Lyra geometry which is described by a time-dependent displacement vector. We consider an appropriate parametrization of the energy density of scalar field ρ ϕ in terms of the cosmic scale factor. The result shows two transitions from deceleration to acceleration. Furthermore, we constrain the model parameter α and the displacement field vector β using the recent supernovae data, Hubble dataset of 77 points and their joint data which predict the accelerated expanding phase of the universe in late times. The effective equation of state parameter ω eff speculates Λ CDM in late times. Finally, we use the statefinder diagnostic to differentiate our model from the various dark energy models. [ABSTRACT FROM AUTHOR]

An intriguing solution that appears in General Relativity (GR) but has not been observed so far is the wormhole. This exotic solution describes a topological bridge connecting two distinct universes or two different points in the same universe. It is known that the traversable wormhole solutions violate all the energy conditions in GR, resulting in their instability. In this work, we are going to unveil new wormhole solutions for f (Q) gravity where Q is the nonmetricity scalar, which is responsible for the gravitational interaction. The energy conditions to constraint these wormhole solutions were derived using the embedding procedure. This procedure consists in rewriting the density and the pressures of the solutions as those presented by General Relativity. Then, the nontrivial contributions coming from new theories of gravity are embedded into the effective equations for density and pressures. Along with our approach, we carefully analyze two families of f (Q) models and we use two different shape functions to build the wormholes solutions for each of these f (Q) models. We are going to present new scenarios with the possibility of traversable wormholes satisfying SEC or DEC energy conditions in the presence of exotic matter. [ABSTRACT FROM AUTHOR]