In this study, we consider three independent physical studies and try to combine them to find an interesting result. Ubriaco’s q-deformed bosons and Verlinde’s entropic gravity studies are taken into account to find the deformed Einstein equations for describing the gravitational field of deformed objects, such as, Strominger’s black holes obeying the deformed Bose or Fermi statistics. We consider the gravitation as an entropic force, as in Verlinde’s approach and assume the source of gravitation is the q-deformed bosons of Ubriaco. Consequently, we obtain the deformed Einstein equations for these deformed bosons by considering the gravitation as an entropic force.

We investigate the time-dependent nature of the cosmological constant, Λ, of the Einstein Field Equation (EFE). Beginning with the Einstein-Hilbert action as our fundamental principle we develop a modified version of the EFE allowing the value of Λ to vary as a function of time, Λ(t), indirectly, for an expanding universe. We follow the evolving Λ presuming 4-dimensional spacetime and a flat universe geometry and present derivations of Λ(t) as functions of the Hubble constant, matter density and volume changes which can be traced back to the radiation epoch. The models are more detailed descriptions of the Λ dependence on cosmological factors than previous, allowing calculations of the important parameters, Ω_m and Ω_r, to deep lookback times. Since we derive these without the need for extra dimensions or other special conditions our derivations are useful for model evaluation with astronomical data. This should aid resolution of several difficult problems of astronomy such as the best value for the Hubble constant at present and at recombination.

We consider a novel dark energy model to investigate whether it will provide an expanding universe phase. Here we propose a mixed dark energy domination which is constituted by tachyon, quintessence, and phantom scalar fields nonminimally coupled to gravity, in the absence of background dark matter and baryonic matter, in the framework of teleparallel gravity. We perform the phase-space analysis of the model by numerical methods and find the late-time accelerated attractor solutions implying the acceleration phase of universe.