Cosmology and gravitational waves in consistent D → 4 Einstein-Gauss-Bonnet gravity

In a very recent paper [1], we have proposed a novel 4-dimensional gravitational theory with two dynamical degrees of freedom, which serves as a consistent realization of D 4 Einstein-Gauss-Bonnet gravity with the rescaled Gauss-Bonnet coupling constant ˜α. This has been made possible by breaking a part of diffeomorphism invariance, and thus is consistent with the Lovelock theorem. In the present paper, we study cosmological implications of the theory in the presence of a perfect fluid and clarify the similarities and differences between the results obtained from the consistent 4-dimensional theory and those from the previously considered, naive (and inconsistent) D→4 limit. Studying the linear perturbations, we explicitly show that the theory only has tensorial gravitational degrees of freedom (besides the matter degree) and that for 0˜α> and 0