Horizon thermodynamics and cosmological equations: A holographic-like connection between thermostatistical quantities on a cosmological horizon and in the bulk

Abstract

Horizon thermodynamics is expected to be related to the effective energy based on the energy density calculated from the Friedmann equation for a Friedmann--Robertson--Walker (FRW) universe. In the present study, the effective energy and thermostatistical quantities on a cosmological horizon are examined to clarify the holographic-like connection between them, with a focus on a de Sitter universe. To this end, the Helmholtz free energy on the horizon is derived from horizon thermodynamics. The free energy is found to be equivalent to the effective energy calculated from the Friedmann equation. This consistency is interpreted as a kind of holographic-like connection. To examine this connection, Padmanabhan's holographic equipartition law, which is related to the origin of spacetime dynamics, is applied to a de Sitter universe. It is found that the law should lead to a holographic-like connection. The holographic-like connection is considered to be a bridge between thermostatistical quantities on the horizon and in the bulk. For example, cosmological equations for a flat FRW universe can be derived from horizon thermodynamics by accepting the connection as a viable scenario. In addition, a thermal entropy equivalent to the Bekenstein--Hawking entropy is obtained from the Friedmann equation using the concept of a canonical ensemble in statistical physics. The present study provides new insight into the discussion of horizon thermodynamics and cosmological equations.

Final version accepted for publication in EPJC. Several paragraphs and references are added. [10 pages]

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• Cosmological model based on both holographic-like connection and Padmanabhan's holographic equipartition law
• Holographic thermodynamic relation for dissipative and non-dissipative universes in a flat FLRW cosmology
• Cosmological scenario based on the first and second laws of thermodynamics: Thermodynamic constraints on a generalized cosmological model