Modified Tsallis Holographic Dark Energy

In this work we propose Modified Tsallis Holographic Dark Energy (MTHDE) in General Relativity (GR) in the framework of Bianchi type III space-time. Einstein's field equations are solved by using a special law of variation of Hubble parameter H proposed by Berman which yields constant deceleration parameter (DP). Interestingly, for the two different constant values of deceleration parameter, we have obtained two different cosmological models. The model 1 behaves like a quintessence dark energy model whereas model 2 behaves like a cosmological constant model. A correspondence between model 1 and quintessence scalar field is established. The quintessence dynamics of the potential and scalar field are reconstructed which illustrates the accelerating phase of the Universe. Various parameters like deceleration parameter, Hubble parameter, anisotropy parameter, equation of state (EOS) parameter, etc. for both the cosmological models are thoroughly discussed. The results obtained are found to be consistent with the recent observations on the present-day Universe.