Is action complexity better for de Sitter space in Jackiw-Teitelboim gravity?

Volume complexity in dS(2) remains O(1) up to a critical time, after which it suddenly diverges. On the other hand, for the dS(2) solution in JT gravity, there is a linear dilaton which smoothly grows towards the future infinity. From the dimensional reduction viewpoint, the growth of the dilaton is due to the expansion of the orthogonal sphere in higher-dimensional dS(d) (d & GE; 3). Since in higher dimensions complexity becomes very large even before the critical time, by properly taking into account the dilaton, the same behavior is expected for complexity in dS(2) JT gravity. We show that this expectation is met by the complexity = action (CA) conjecture. For this purpose, we obtain an appropriate action for dS(2) in JT gravity, by dimensional reduction from dS(3). In addition, we discuss complexity = refined volume where we choose an appropriate Weyl field-redefinition such that refined volume avoids the discontinuous jump in time evolution.

Automated summary

In dS(2), the volume complexity remains O(1) until a critical time, after which it suddenly diverges. However, in the dS(2) solution in JT gravity, there is a linear dilaton that smoothly grows towards future infinity. By considering the expansion of the orthogonal sphere in higher-dimensional dS(d) and properly accounting for the dilaton, it is expected that the complexity in dS(2) JT gravity exhibits the same behavior, as the complexity becomes very large before the critical time in higher dimensions. This expectation is confirmed by the complexity = action (CA) conjecture, where an appropriate action for dS(2) in JT gravity is obtained by dimensional reduction from dS(3). Additionally, the complexity = refined volume is discussed, with the introduction of an appropriate Weyl field-redefinition to avoid discontinuous jumps in time evolution.