Cosmological scenario based on the first and second laws of thermodynamics: thermodynamic constraints on a generalized cosmological model - Nobuyoshi Komatsu (European Physical Journal C: Particles and Fields)
Abstract The first and second laws of thermodynamics should lead to a consistent scenario for discussing the cosmological constant problem. In the present study, to establish such a thermodynamic scenario, cosmological equations in a flat Friedmann–Lemaître–Robertson–Walker universe were derived from the first law, using an arbitrary entropy $$S_{H}$$ S H on a cosmological horizon. Then, the cosmological equations were formulated based on a general formulation that includes two extra driving terms, $$f_{Λ }(t)$$ f Λ ( t ) and $$h_{\text {B}}(t)$$ h B ( t ) , which are usually used for, e.g., time-varying $$Λ (t)$$ Λ ( t ) cosmology and bulk viscous cosmology, respectively. In addition, thermodynamic constraints on the two terms are examined using the second law of thermodynamics, extending a previous analysis (Komatsu in Phys. Rev. D 99:043523, 2019). It is found that a deviation $$S_{Δ }$$ S Δ of $$S_{H}$$ S H from the Bekenstein–Hawking entropy plays important roles in the two terms. The second law should constrain the upper limits of $$f_{Λ }(t)$$ f Λ ( t ) and $$h_{\text {B}}(t)$$ h B ( t ) in our late Universe. The orders of the two terms are likely consistent with the order of the cosmological constant $$Λ _{\text {obs}}$$ Λ obs measured by observations. In particular, when the deviation $$S_{Δ }$$ S Δ is close to zero, $$h_{\text {B}}(t)$$ h B ( t ) and $$f_{Λ }(t)$$ f Λ ( t ) should reduce to zero and a constant value (consistent with the order of $$Λ _{\text {obs}}$$ Λ obs ), respectively, as if a consistent and viable scenario could be obtained from thermodynamics.