Ostrogradsky mode in scalar-tensor theories with higher-order derivative couplings to matter
Ostrogradsky mode in scalar-tensor theories with higher-order derivative couplings to matter
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DOI：
10.1093/ptep/ptad049
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发表时间：
2022-09
影响因子：
3.5
通讯作者：
A. Naruko;R. Saito;Norihiro Tanahashi;Daisuke Yamauchi
中科院分区：
文献类型：
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作者：
A. Naruko;R. Saito;Norihiro Tanahashi;Daisuke Yamauchi
度规变换是超越广义相对论找到新引力理论的工具。只要度规变换是正则的和可逆的，就保证引力作用不受危险的Ostrogradsky模的影响。通过标量场及其导数的度规变换，得到了各种不带额外自由度的简并高阶标量张量理论。在这项工作中，我们研究了如何物质耦合的变化从Horndeski理论通过度量变换与标量场的二阶导数产生的理论的简并，采取最小耦合的自由标量场作为物质场。当变换是可逆的，这个理论是等价的Horndeski理论与高阶导数耦合到物质标量场。在这个Horndeski框架和幺正规范下，我们发现简并条件是可解的，并且物质度规必须具有一定的结构才能去除Ostrogradsky模。
A metric transformation is a tool to find a new theory of gravity beyond general relativity. The gravity action is guaranteed to be free from a dangerous Ostrogradsky mode as long as the metric transformation is regular and invertible. Various degenerate higher-order scalar-tensor theories (DHOST) 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.