The existing analysis reports a reconstruction scheme of the newly proposed gravity say f(Q) gravity through the scale factor of the form a(t)=a0tn=11+z by describing the power-law cosmology. The reconstructed f(Q) gravity models disclosed how this modified gravity model is capable to replicate dissimilar epochs of the cosmological history. Also, the reconstructed f(Q) gravity models are castoff to develop the expressions for density and pressure and the equation of state parameter. We reconstruct two cases of interacting fluid scenario ghost and pilgrim dark energy with pressureless dark matter. The physical behavior of the models is talked over the evolution of the Universe is accelerated. Moreover, the well-known cosmological planes i.e., (ωD−ωD′) and (r − s) constructed for our models, also include a comparison of our findings of these dynamical parameters with observational constraints. It is also quite interesting to mention here that the results of the equation of state parameter, (ωD−ωD′) and (r − s)-planes coincide with the modern observational data.

Any new gravitational theories can be built with the help of a gauge theory with local Poincare symmetry. This local Poincare symmetry can set up a space-time with torsion. In the present study, the authors working on the parametrization approach towards Hubble’s parameter in the frame of modified teleparallel Gauss-Bonnet gravity which is established on the torsion invariant T and the teleparallel equivalent of the Gauss-Bonnet term TG, say F(T,TG) gravity. In particular, gravity is responsible for an integrated explanation of the cosmological history from early-time inflation to late-time acceleration expansion, by lacking the addition of a cosmological constant. The domino effect acquired is reliable with recent cosmological outcomes. A transition scenario from a decelerating phase to an accelerating phase of cosmic evolution has been detected. Using the combined datasets (SNe-Ia+BAO+CMB+H(z)), we have constrained the transition redshift zt (at which the universe transit from a decelerating phase to an accelerating) and established the best fit value of zt. Next, we paralleled the renovated results of q(z) and ω(z) and found that the outcomes are well-suited with a ΛCDM universe.

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