Apparent horizon and gravitational thermodynamics of the Universe: Solutions to the temperature and entropy confusions, and extensions to modified gravity

Abstract

The thermodynamics of the Universe is restudied by requiring its compatibility with the holographic-style gravitational equations which govern the dynamics of both the cosmological apparent horizon and the entire Universe, and possible solutions are proposed to the existent confusions regarding the apparent-horizon temperature and the cosmic entropy evolution. We start from the generic Lambda Cold Dark Matter ($\Lambda$CDM) cosmology of general relativity (GR) to establish a framework for the gravitational thermodynamics. The Cai-Kim Clausius equation for the isochoric process of an instantaneous apparent horizon indicates that, the Universe and its horizon entropies encode the \emph{positive heat out} thermodynamic sign convention, which encourages us to adjust the traditional positive-heat-in Gibbs equation into the positive-heat-out version $d{E}_m=-T_{m}d{S}_m-P_{m}dV$. It turns out that the standard and the generalized second laws (GSLs) of nondecreasing entropies are always respected by the event-horizon system as long as the expanding Universe is dominated by nonexotic matter $-1\le w_m\le 1$, while for the apparent-horizon simple open system the two second laws hold if $-1\le w_m<-1/3$; also, the artificial local equilibrium assumption is abandoned in the GSL. All constraints regarding entropy evolution are expressed by the equation of state parameter, which show that from a thermodynamic perspective the phantom dark energy is less favored than the cosmological constant and the quintessence. Finally, the whole framework is extended from GR and $\Lambda$CDM to modified gravities with field equations $R_{\mu \nu }-R{g}_{\mu \nu }/2=8\pi G_{\text{eff}}{T}_{\mu \nu }^{\text{(eff)}}$. Furthermore, this paper argues that the Cai-Kim temperature is more suitable than Hayward, and the Bekenstein-Hawking and Wald entropies cannot unconditionally apply to the event and particle horizons.

23 pages, 1 table. Event-horizon systems recalculated, non-universality of Bekenstein-Hawking & Wald entropies proved, and several interpretative paragraphs added. Matching the published version

References in corpus (29)

• Dynamics of dark energy
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Reconstructing Dark Energy
• Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
• Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe
• Hawking Radiation of Apparent Horizon in a FRW Universe
• Thermodynamic interpretation of the generalized gravity models with geometry - matter coupling
• Thermodynamical Properties of Apparent Horizon in Warped DGP Braneworld
• Deep Connection Between Thermodynamics and Gravity in Gauss-Bonnet Braneworld
• Thermodynamics of Apparent Horizon in Brane World Scenario
• Generalized Second Law of Thermodynamics in Quintom Dominated Universe
• The generalized second law of thermodynamics in generalized gravity theories
• Isolated, slowly evolving, and dynamical trapping horizons: geometry and mechanics from surface deformations
• The generalized second law of thermodynamics in Horava-Lifshitz cosmology
• Cosmological apparent and trapping horizons
• Generalized second law in modified theory of gravity
• Validity of the Generalized Second Law of Thermodynamics of the Universe Bounded by the Event Horizon in Holographic Dark Energy Model
• The generalized second law of thermodynamics and the nature of the Entropy Function
• Cosmological entropy and generalized second law of thermodynamics in $F(R,G)$ theory of gravity
• Generalized Second Law of Thermodynamics in Extended Theories of Gravity
• Interpretation of the Cosmological Metric
• The generalized second law of thermodynamics for interacting $f(R)$ gravity
• Friedmann equations from nonequilibrium thermodynamics of the Universe: A unified formulation for modified gravity
• Lessons from $f(R,R_c^2,R_m^2,L_m)$ gravity: Smooth Gauss-Bonnet limit, energy-momentum conservation and nonminimal coupling
• Generalized second law of thermodynamics in QCD ghost f(G) gravity
• Scalar-Tensor Theory of Gravity and Generalized Second Law of Thermodynamics on the Event Horizon
• Generalized second law of thermodynamics in presence of interacting DBI essence and other dark energies
• Interacting Three Fluid System and Thermodynamics of the Universe Bounded by the Event Horizon

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• Implications, consequences and interpretations of generalized entropy in the cosmological setups
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• A note on the relations between thermodynamics, energy definitions and Friedmann equations
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• Emergence of cosmic space and its connection with thermodynamic principles
• Thermodynamics of the R_h=ct Universe: A Simplification of Cosmic Entropy
• A statistical representation of the cosmological constant from finite size effects at the apparent horizon
• First law of thermodynamics and entropy of FLRW universe in modified gravity
• The Logotropic Dark Fluid: Observational and Thermodynamic Constraints
• Entropy, energy and temperature-length inequality for Friedmann universes
• Fluctuations of the flux of energy on the apparent horizon
• Thermodynamics of FRW Universe With Chaplygin Gas Models
• Planckian corrections to the Friedmann flat equations from thermodynamics at the apparent horizon
• Energy definition and dark energy: a thermodynamic analysis
• Quasilocal energy and thermodynamic equilibrium conditions
• Thermodynamical study of FRW universe in Quasi-Topological Theory
• A comprehensive analysis of Barrow holographic Chaplygin gas model reconstruction and its cosmological consequences
• On the thermodynamics of scale factor dual Universes
• Apparent horizon and gravitational thermodynamics of Universe in the Eddington-Born-Infeld theory
• Entropy Bounds and Holographic Dark Energy: Conflicts and Consensus
• Critical Robertson-Walker universes
• Cosmology with Logarithmic Corrected Horizon Entropy According to the Generalized Entropy and Variable-G Correspondence
• Scalar-Field Reconstruction of Ricci--Gauss--Bonnet Dark Energy in Hořava--Lifshitz Cosmology
• Modified Cosmology from Mass-to-Horizon Relation: Background Evolution
• A Combined Barrow Entropy and QCD Ghost Mechanism for Late-Time Cosmic Acceleration
• First-order phase transitions and cosmic evolution: thermodynamic approach to generalized holographic dark energy