Abstract
We analyze the response and thermal behavior of an Unruh-DeWitt detector as it travels through cosmological spacetimes, with special reference to the question of how to define surface gravity and temperature in dynamical spacetimes. Working within the quantum field theory on curved spacetime approximation, we consider a detector as it travels along geodesic and accelerated Kodama trajectories in de Sitter and asymptotically de Sitter FLRW spacetimes.
By modelling the temperature of the detector using the detailed-balance form of the Kubo-Martin-Schwinger (KMS) conditions as it thermalizes, we can better understand the thermal behavior of the detector as it interacts with the quantum field, and use this to compare competing definitions of surface gravity and temperature that persist in the literature. These include the approaches of Kodama [Prog.
Theor. Phys. 63, 1217 (1980).], Ashtekar and Krishnan [Living Rev.
Relativity 7, 10 (2004).], Fodor et al. [Phys. Rev.
D 54, 3882 (1996).], and Nielsen [Classical Quantum Gravity 23, 4637 (2006).]. While these are most often examined within the context of a dynamical black hole, here we shift focus to surface gravity on the evolving cosmological horizon.