We calculate the logarithmic temperature corrections to the thermodynamic entropy of four-dimensional near-extremal Reissner-Nordström de Sitter (dS) black hole by computing a one-loop contribution within the path integral framework in the near-horizon limit. Due to the presence of three horizons, the extremal limit of a charged dS black hole is fundamentally different from its flat and AdS counterparts. In the near-horizon limit, there are three distinct extremal limits known as cold, Nariai, and ultracold configurations. We compute the tensor zero modes of the Lichnerowicz operator acting on linearized metric perturbations for the cold and Nariai extremal limits which are associated with near-horizon AdS₂ and dS₂ asymptotic symmetries. In particular in the near-Nariai limit we compute the quantum corrections to the Hartle-Hawking wavefunction at late times. Our computation establishes the result that at leading order, the small temperature corrections to the extremal entropy is universal in the cold and Nariai limit, paving the way for similar such computations and tests in higher dimensional dS black hole spacetimes, including rotating dS black holes.
Maulik et al. (Tue,) studied this question.