Abstract

Metric transformation is a tool to find a new theory of gravity beyond general relativity. The gravity action is guaranteed to be free from the dangerous Ostrogradsky mode as long as the metric transformation is regular and invertible. Various degenerate higher-order scalar–tensor theories without extra degrees of freedom have been found through the metric transformation with a scalar field and its derivatives. In this work, we examine how a matter coupling changes the degeneracy for a theory generated from the Horndeski theory through the metric transformation with the second derivative of a scalar field, taking a minimally coupled free scalar field as the matter field. When the transformation is invertible, this theory is equivalent to the Horndeski theory with a higher-order derivative coupling to the matter scalar field. Working in this Horndeski frame and the unitary gauge, we find that the degeneracy conditions are solvable and the matter metric must have a certain structure to remove the Ostrogradsky mode.

Details

Title
Ostrogradsky mode in scalar–tensor theories with higher-order derivative couplings to matter
Author
Naruko, Atsushi 1 ; Saito, Ryo 2 ; Tanahashi, Norihiro 3 ; Yamauchi, Daisuke 4 

 Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics , Kyoto University, Kyoto 606-8502 , Japan 
 Graduate School of Science and Engineering, Yamaguchi University , Yamaguchi 753-8512 , Japan 
 Department of Physics, Chuo University , Kasuga, Bunkyo-ku, Tokyo 112-8551 , Japan 
 Faculty of Engineering, Kanagawa University , Kanagawa 221-8686 , Japan 
Publication year
2023
Publication date
May 2023
Publisher
Oxford University Press
e-ISSN
20503911
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
3171920253
Copyright
© The Author(s) 2023. Published by Oxford University Press on behalf of the Physical Society of Japan. This work is published under https://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.