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

Abstract

Volume complexity in dS2 remains O(1) up to a critical time, after which it suddenly diverges. On the other hand, for the dS2 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 dSd (d ≥ 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 dS2 JT gravity. We show that this expectation is met by the complexity = action (CA) conjecture. For this purpose, we obtain an appropriate action for dS2 in JT gravity, by dimensional reduction from dS3. 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.