Generalized nonconservative gravitational field equations from Herglotz action principle

We present an alternative nonconservative gravitational theory based on the Herglotz variational principle in a fully covariant form. The model may be seen as improvement of proposed Ref. [Lazo et al, Phys. Rev. D 95, 101501 (2017)], whose resulting is meaningful just particular coordinate systems. In work, we report new that free from such restriction. It also obtained using and by taking advantage restricted equivalence between Lagrangian functions scope action principle. more class equivalent functions, comparison with Hamilton principle, key point to find furnishes covariant. Once equations govern dynamics field are obtained, few simple cosmological models investigated. found reduces single function that, under certain conditions, plays role constant general relativity, turning unnecessary use dark energy explain accelerated expansion universe. linearized version investigated it verified shows dissipative character regard waves. From observational data, both scenarios, vector estimated.