New non-conserved gravity theory and alleviate current acceleration epoch without dark energy field

Abstract

Recently, the new modified theory of gravity is introduced in which Rastall’s idea Tμ;νν=α,μ is reinvestigated. Although Rastall’s idea may open a new window to explore field equations of gravity in high levels of energy, his proposal α=γR is questionable. As discussed in Fazlollahi (2023), one may attempt to find the viable form for α by reconsidering the first law of thermodynamics in a relativistic system. In this context, Israel and his colleagues have proposed a covariant form equation between the flux of the energy–momentum tensor and the 4-vector of entropy of the system, satisfies the Gibbs-Duhem relation in flat spacetime (Israel, 1981, Israel, and Stewart, 1980). Generalizing this idea for curved spacetime gives the theoretical form of α which supports Rastall’s idea Tμ;νν=α,μ. However, this modified theory of gravity called ‘non-conserved gravity’ cannot present dark energy in FRW spacetime for comoving observer in the absence of the cosmological constant. In this study and in the following of considering the application of such gravity theory in cosmology, we have shown that the model can illustrate the current acceleration epoch in the absence of extra fluid as dark energy. As a result, the non-conserved theory of gravity gives matter field as the source of current accelerated expansion. This model also satisfies matter structure formations and thus it is not in conflict with observations in the past (high redshift) Universe.