Abstract
In this paper, we investigate the possible parameter space of Palatini–Horndeski theory with gravitational waves in a spatially flat Universe. We develop a general method for obtaining the speed of gravitational waves in the Palatini formalism in the cosmological background and we find that if the theory satisfies the following condition: in any spatially flat cosmological background, the tensor gravitational wave speed is the speed of light c, then only S = int d^4x sqrt{-g} big [K(phi ,X)-G_{3}(phi ,X){{tilde{Box }}}phi +G_{4}(phi ){tilde{R}}big ] is left as the possible action in Palatini–Horndeski theory. We also find that when G_{5}(phi ,X)ne 0, the tensor part of the connection will propagate and there are two different tensor gravitational wave speeds.
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