Cosmology with Logarithmic Corrected Horizon Entropy According to the Generalized Entropy and Variable-G Correspondence

Abstract

According to the GEVAG (Generalized Entropy Varying-G) framework, any modification to the Bekenstein-Hawking area law would also lead to a varying-$G$ gravity theory in which the effective gravitational constant $G_{\text{eff}}$ becomes area-dependent. Among a myriad of generalized entropy functions explored in the literature, of special interest is the logarithmic correction of quantum gravity. In this work, we apply GEVAG to investigate the effect of logarithmic correction on very early-time cosmology, including the conditions for inflation. We found that if the coefficient of the logarithmic correction term is negative, $G_{\text{eff}}$ becomes twice that of the current value; whereas, a positive coefficient leads to a very small value of $G_{\text{eff}}$, which may ameliorate the "arrow of time" problem. In fact, slow-roll inflation becomes more natural in the latter case. We make some comparisons with the constant-$G$ approach and reveal the advantages of the GEVAG approach. For example, it can evade the sudden singularity that could otherwise arise when the coefficient of the logarithmic correction term is negative. We also check the validity of the generalized second law and comment on the range of the various parameters.

References in corpus (41)

• Thermodynamics of Spacetime: The Einstein Equation of State
• Properties of singularities in (phantom) dark energy universe
• Quantum Nature of the Big Bang: Improved dynamics
• Nonperturbative Evolution Equation for Quantum Gravity
• First Law of Thermodynamics and Friedmann Equations of Friedmann-Robertson-Walker Universe
• Absence of Singularity in Loop Quantum Cosmology
• Black hole entropy in Loop Quantum Gravity
• Spectral Dimension of the Universe
• Sudden Future Singularities
• Robustness of key features of loop quantum cosmology
• Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe
• Quantum Einstein Gravity
• A Short Review of Loop Quantum Gravity
• Fractal Spacetime Structure in Asymptotically Safe Gravity
• Cosmology of the Planck Era from a Renormalization Group for Quantum Gravity
• Corrected Entropy-Area Relation and Modified Friedmann Equations
• On Effective Degrees of Freedom in the Early Universe
• Entropic Corrections to Friedmann Equations
• Asymptotically safe cosmology - a status report
• Generalized Uncertainty Principle, Black Holes, and White Dwarfs: A Tale of Two Infinities
• Entropy signature of the running cosmological constant
• Constraining the generalized uncertainty principle with the gravitational wave event GW150914
• Improved BBN Constraints on the Variation of the Gravitational Constant
• Quantum Gravitational Corrections to the Entropy of a Schwarzschild Black Hole
• Running boundary actions, Asymptotic Safety, and black hole thermodynamics
• The deformation parameter of the generalized uncertainty principle
• Singularities in loop quantum cosmology
• Apparent horizon and gravitational thermodynamics of the Universe: Solutions to the temperature and entropy confusions, and extensions to modified gravity
• From Asymptotic Safety to Dark Energy
• Time-dependent $G$ in Einstein's equations as an alternative to the cosmological constant
• Smooth Initial Conditions from Weak Gravity
• Quantum thermodynamics of de Sitter space
• Variance of Newtonian constant from local gravitational acceleration measurements
• Negative Corrections to Black Hole Entropy from String Theory
• Generalized Entropy Implies Varying-G: Horizon Area Dependent Field Equations and Black Hole-Cosmology Coupling
• Gravitational Collapse in Scale-Dependent Gravity
• Solving the Cosmological Entropy Issue with a Higgs Dilaton
• The irreversible relaxation of inflation
• GUP Effective Metric Without GUP: Implications for the Sign of GUP Parameter and Quantum Bounce
• Do Black Holes With Generalized Entropy Violate Bekenstein Bound?
• High-Frequency Thermal Graviton Remnant from the End of Inflation