https://doi.org/10.1140/epjc/s10052-023-11861-9
Regular Article - Theoretical Physics
Constraining Palatini–Horndeski theory with gravitational waves after GW170817
1
Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, School of Physical Science and Technology, Lanzhou University, 730000, Lanzhou, China
2
Institute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, 730000, Lanzhou, China
Received:
17
April
2023
Accepted:
23
July
2023
Published online:
7
August
2023
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 ![$$S = \int d^4x \sqrt{-g} \big [K(\phi ,X)-G_{3}(\phi ,X){{\tilde{\Box }}}\phi +G_{4}(\phi ){\tilde{R}}\big ]$$](/articles/epjc/abs/2023/08/10052_2023_Article_11861/10052_2023_Article_11861_tex_eq1.png)
is left as the possible action in Palatini–Horndeski theory. We also find that when 
, the tensor part of the connection will propagate and there are two different tensor gravitational wave speeds.
© The Author(s) 2023
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