Duality between k-essence and Rastall gravity

摘要: The k-essence theory with a power-law function of $(\partial\phi)^2$ and Rastall's non-conservative gravity scalar field are shown to have the same solutions for metric under assumption that both fields depend on single coordinate. This equivalence (called k-R duality) holds static configurations various symmetries (spherical, plane, cylindrical, etc.) all homogeneous cosmologies. In presence matter, requires additional assumptions how stress-energy tensor non-conservation is distributed between different contributions. Two versions such considered in case isotropic spatially flat cosmological models perfect fluid: one (R1) which there no coupling fluid, another (R2) fluid separately obeys usual conservation law. version R1 it duality not only themselves but also their adiabatic perturbations. R2, among other results, particular model singled out reproduces expansion history as standard $\Lambda$CDM predicts behaviors small fluctuations Rastall frameworks.