Emergence of the cosmic space inspired by mass-to-horizon entropy

Abstract

The conception of gravity as an emergent phenomenon, rooted in the thermodynamics of spacetime, offers a radical departure from its geometric description. This paper investigates the emergence of cosmic space by synthesizing two key thermodynamic approaches: the equilibrium perspective, where the first law of thermodynamics is applied to the apparent horizon, and the dynamic perspective of Padmanabhan, where the cosmic space emerges as cosmic time progresses. The central element of our study is the incorporation of a mass-to-horizon entropy relation, $M=\gamma c^2{L}^n/G$, where $M$ denotes the effective mass associated with the system, $L$ corresponds to the cosmological horizon, and $\gamma$ is a constant with dimensions $[L{]}^{1-n}$. We first use this relation within the Clausius relation and apply the first law of thermodynamics, $dE=T_{h}d{S}_h+WdV$, on the apparent horizon to derive the modified Friedmann equations. Subsequently, we embed the mass-to-horizon entropy relation into Padmanabhan's cosmic emergence proposal, the dependence of the volume change on the degrees of freedom in the bulk and on the boundary, and show its consistency with the thermodynamically derived equations. The successful reconstruction of the modified Friedmann equations through these independent yet convergent thermodynamic routes strongly suggests that the mass-to-horizon entropy is a fundamental bridge between the information-theoretic microstructure of spacetime and its effective cosmological description. Finally, we show that the generalized second law of thermodynamics is fulfilled for the universe enveloped by the apparent horizon.

9 pages, Phys. Lett. B, in press

References in corpus (19)

• Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
• The Area of a Rough Black Hole
• Thermodynamic route to Field equations in Lanczos-Lovelock Gravity
• Thermodynamical Properties of Apparent Horizon in Warped DGP Braneworld
• Corrected Entropy-Area Relation and Modified Friedmann Equations
• Friedmann Equations and Thermodynamics of Apparent Horizons
• Deep Connection Between Thermodynamics and Gravity in Gauss-Bonnet Braneworld
• Thermodynamics of apparent horizon and modified Friedman equations
• Entropic Corrections to Friedmann Equations
• The generalized second law of thermodynamics in the accelerating universe
• Barrow Entropy Corrections to Friedmann Equations
• Area-law versus Rényi and Tsallis black hole entropies
• Friedmann equations from emergence of cosmic space
• Emergence of Cosmic Space and the Generalized Holographic Equipartition
• Modified cosmology through Barrow entropy
• Equilibrium Temperature for Black Holes with Nonextensive Entropy
• Thermodynamically consistent entropic late-time cosmological acceleration
• A generalized mass-to-horizon relation: a new global approach to entropic cosmologies and its connection to $\Lambda$CDM
• Modified cosmology through generalized mass-to-horizon entropy: observational constraints from DESI DR2 BAO data