R+RG gravity with maximal Noether symmetry

Abstract

A Noether symmetric, 3rd order polynomial in the Riemann curvature tensor R αβμν extension of the General Relativity (GR) without cosmological constant (R+RG gravity) is suggested and discussed as a possible fundamental theory of gravity in 4-dimensional space-time with the geometric part of the Lagrangian to be . Here is the Einstein constant, - the metric tensor, GN - the Newton constant, c - the speed of light, - the Ricci scalar, - the Gauss-Bonnet topological invariant, and GP - a new constant of the gravitational self-interaction to model the cosmological bounce, inflation, accelerated expansion of the Universe, etc. The best fit to the Baryon Acoustic Oscillations data for the Hubble parameter H (z) at the redshifts z<2.36 leads to with the mean square weighted deviation from the data about 3 times smaller than for the standard cosmological (ΛCDM) model. Due to the self-gravitating term ∼RG the respective Einstein equation in the R+RG gravity contains the additional (tachyonic in the past and now) scalar (spin = 0) graviton and the perfect geometric fluid tensor with pressure-and matter-like terms equal to the respective terms in the ΛCDM model at |z| 1. Some predictions of this R+RG gravity for the Universe are also done.