The price of curiosity: information recovery in de Sitter space

Abstract

Recent works have revealed that quantum extremal islands can contribute to the fine-grained entropy of black hole radiation reproducing the unitary Page curve. In this paper, we use these results to assess if an observer in de Sitter space can decode information hidden behind their cosmological horizon. By computing the fine-grained entropy of the Gibbons-Hawking radiation in a region where gravity is weak we find that this is possible, but the observer’s curiosity comes at a price. At the same time the island appears, which happens much earlier than the Page time, a singularity forms which the observer will eventually hit. We arrive at this conclusion by studying de Sitter space in Jackiw-Teitelboim gravity. We emphasize the role of the observer collecting radiation, breaking the thermal equilibrium studied so far in the literature. By analytically solving for the backreacted geometry we show how an island appears in this out-of-equilibrium state.

Shocks and information exchange in de Sitter space

“…which is the stress tensor of a two-dimensional boson gas at inverse temperature β = 2π [18]. Note that although the stress tensor expressed in this coordinate system is not proportional to the metric, this does not imply backreaction as normal ordering breaks general covariance [42].…”

“…Although it should be mentioned that various proposals exist, see for example[1][2][3][4][5][6][7][8] 2. Related questions in the context of lower[12][13][14][15][16][17][18] and higher-dimensional[19] models of gravity in de Sitter space have been studied.…”

“…This assumes the observer at has full access to and can manipulate the large ∼ e S dS number of states, which in practice might be difficult.8 And importantly, one would have to collect all the radiated Hawking quanta for at least the Page time.Note that[18] considered a different setup in de Sitter space where one does have to wait for a Page time to recover information.…”

The FL bound and its phenomenological implications

“…How is FL modified in the presence of other non-trivial interactions? Can the conjecture be related to general properties of entanglement entropy in quasi-dS space [107][108][109] and black holes, just like the WGC can [110]? Is it possible to come up with complementary evidence in string theory that can support or disprove the conjecture?…”

Replica wormholes and capacity of entanglement

“…The island formula has been applied to a wide range of black holes with and without evaporation and shown to yield the Page curves consistent with their unitary evolution in various backgrounds such as asymptotic flat spaces [22][23][24][25][26][27][28], de-Sitter spaces [29][30][31][32][33], two disjoint universes [34][35][36], gravitating thermal baths [36][37][38], shock-wave excited geometries [19,39,40] and extended theories of gravity [41]. By considering holographic matter, the formula has been justified from the doubly holographic models [5,[42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61] combining the AdS/BCFT models [62,63] and the brane world holography [64]…”