JT Gravity in de Sitter Space and Its Extensions

Abstract: We discuss and extend some aspects pertaining to the canonical quantisation of JT gravity in de Sitter space, including the problem of time and the construction of a Hilbert space. We then extend this discussion to other two dimensional models obtained by changing the dilaton potential and show that the canonical quantisation procedure can be carried out for a large class of such models. Some discussion leading towards a path integral understanding for states, other than the Hartle Hawking state, is also included here, along with comments pertaining to Holography and the entropy of de Sitter space.