Geometric and Statistical Thermo Field Dynamics in de Sitter Spacetime

Abstract

The dynamics of a massive scalar field non-minimally coupled to gravity in an expanding de Sitter universe are investigated. It is shown that a comoving observer identifies the Bunch--Davies state as the vacuum, whereas a static observer perceives the same state as a thermal bath at the Gibbons--Hawking temperature. Motivated by this observer dependence, a thermal formulation based on Thermo Field Dynamics is developed by combining the geometric doubling associated with the cosmological horizon with the statistical doubling induced by a intrinsec thermal bath. The resulting construction reveals that the doubling procedure is not merely a mathematical artifact, but rather a manifestation of the global causal structure of spacetime together with finite-temperature effects. The temporal evolution of the Bogoliubov angle is analyzed and the corresponding particle number densities are evaluated in both comoving and static frames. In the radiation limit, the comoving number density remains conserved, providing a thermodynamic evolution consistent with that of the Cosmic Microwave Background, whereas in the static frame finite-temperature effects sti\-mulate Parker particle creation. For massive and non-minimally coupled fields, the interplay between geometric and statistical temperatures gives rise to a characteristic thermal scale and a nontrivial dependence on the initial conditions. These results provide a unified framework for describing quantum fields in de Sitter spacetime in the presence of both apparent horizon-induced and intrinsec thermal effects.