Is Action Complexity better for de Sitter space in Jackiw-Teitelboim gravity?

Abstract

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 ≥ 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 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.