Nash theory of gravity as an alternative for general relativity

Regarding the late-time cosmic expansion, there are several possible explanations, to date. Intuitively, the first one is the introduction of the dark energy component in the universe . Unfortunately, the dark energy sector of the universe still remains an open question. In addition, the second scenario is to interpret this unknown phenomenon by utilizing a purely geometrical picture. The latter is well known as the modified theory of gravity. Interestingly, modified theories of gravity have received more attraction lately due to numerous motivations ranging from high-energy physics, cosmology and astrophysics . Among numerous alternatives, Nash developed a modified theory of gravity for empty space by employing higher-derivatives instead of the usual Einstein-Hilbert action. In this work, we anticipate to generalize the Nash theory by adding the matter fields in the original action. We specify a proper form of the field equations on more general footings for space with matter contents.

Regarding the late-time cosmic expansion, there are several possible explanations, to date. Intuitively, the first one is the introduction of the dark energy component in the universe . Unfortunately, the dark energy sector of the universe still remains an open question. In addition, the second scenario is to interpret this unknown phenomenon by utilizing a purely geometrical picture. The latter is well known as the modified theory of gravity. Interestingly, modified theories of gravity have received more attraction lately due to numerous motivations ranging from high-energy physics, cosmology and astrophysics . Among numerous alternatives, Nash developed a modified theory of gravity for empty space by employing higher-derivatives instead of the usual Einstein-Hilbert action. In this work, we anticipate to generalize the Nash theory by adding the matter fields in the original action. We specify a proper form of the field equations on more general footings for space with matter contents.

D. Momeni et al., Eur.Phys.J. C78 (2018) no.7, 588 D. Momeni et al., arXiv:1808.06483 [gr-qc] D. Momeni et al., arXiv:1812.01990 [gr-qc]