Reconstructing f(R), f(G), f(T), and Einstein-Aether gravities from entropy-corrected (m,n) type pilgrim dark energy

Abstract

First, we describe the ordinary holographic dark energy (HDE), (m,n) type holographic dark energy, entropy-corrected holographic dark energy (ECHDE) for logarithmic and power-law versions and pilgrim dark energy (PDE) models. Next, we introduce the (m,n) type pilgrim dark energy and its entropy-corrected versions of logarithmic and power-law forms i.e., (m,n) type LECPDE and PLECPDE models. The main motivation of the work is to have reconstructions of f(R), f(G), f(T), and Einstein-Aether gravities from (m,n) type entropy-corrected pilgrim dark energy (ECPDE). Briefly the idea of our proposed entropy-corrected (m,n) type pilgrim dark energy model is discussed. We also discuss the modified Friedmann equations for f(R), f(G), f(T), and Einstein-Aether gravities and then from the equations we find the effective density and pressure for the f(R), f(G), f(T), and Einstein-Aether gravities sectors, respectively. These can be treated as an effective dark energy. Assuming the power-law solution of the scale factor, a∼t ^δ, we can reconstruct the unknown functions of f(R), f(G), f(T), and F(K) of Einstein-Aether gravities from logarithmic and power-law corrected versions of ECPDE. Finally, we give some cosmological implications of the reconstructed models.