Non-conserved modified gravity theory

AbstractIn the curved spacetime the conservation of stress-energy tensor $${\mathcal {T}}_{\,\,\,\,\, \mu ; u }^{ u }=0$$ T μ ; ν ν = 0 has been questioned by Rastall. However, this idea in which $${\mathcal {T}}_{\,\,\,\,\, \mu ; u }^{ u }=\lambda R_{,\mu }$$ T μ ; ν ν = λ R , μ is own questionable. In this study and in follows the covariant form of thermodynamics law proposed by Israel and his colleagues, the new non-conserved modified gravity is introduced. As its application, we have explored spherically symmetric solutions and evolution of the Universe for very early and late time Universe in the presence of the cosmological constant. As shown, the model gives no new result with respect to Einstein gravity for vacuum solutions, while during inflation only scalar spectra index deviates from standard model. Also, we have considered late-time and constraint model with observations through using MCMC algorithm.