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Friedmann equations from GUP-modified equipartition law

Özgür Ökcü

TL;DR

The paper couples the quadratic generalized uncertainty principle (GUP) to Verlinde’s entropic gravity by deriving a GUP-adjusted equipartition law and using it to obtain modified Friedmann equations. The analysis reveals a maximum energy density ρ_max and a finite maximum Hubble rate H_max, implying a non-singular early Universe, with a quadratic density correction reminiscent of braneworld cosmology. It extends the framework to compute the deceleration parameter and to revisit gravitational baryogenesis, showing that GUP-induced fluctuations can break thermal equilibrium in the radiation era and constraining the GUP parameter α from observations. These results offer a quantum-gravity-inspired route to non-singular cosmology and potential connections to early-Universe baryogenesis, while suggesting testable bounds on α from cosmological and particle-physics data.

Abstract

In this paper, combining the thermodynamical arguments of the horizon with the quadratic generalised uncertainty principle (GUP), we heuristically obtain the modified equipartition law of energy. Employing this modified equipartition law of energy, we derive the Friedmann equations in Verlinde's entropic gravity. We find a maximum energy density at the beginning of the Universe. Remarkably, this feature emerges not only for positive GUP parameter but also for negative GUP parameter. From the initial acceleration, we deduce that the negative GUP parameter is more preferable. We also obtain maximum Hubble parameter from the first Friedmann equation, indicating a universe without initial singularity. Moreover, we compute the Kretschmann curvature scalar, again indicating a non-singular universe. Interestingly, we find that GUP-modified Friedmann equations share some similarities with braneworld cosmolgy where the quadratic term in energy density appears. We also compute the deceleration parameter. Finally, we revisit the gravitational baryogenesis and show that the GUP-modified equipartition law of energy provides a mechanism for generating baryon asymmetry. Moreover, we constrain the GUP parameter from observations.

Friedmann equations from GUP-modified equipartition law

TL;DR

The paper couples the quadratic generalized uncertainty principle (GUP) to Verlinde’s entropic gravity by deriving a GUP-adjusted equipartition law and using it to obtain modified Friedmann equations. The analysis reveals a maximum energy density ρ_max and a finite maximum Hubble rate H_max, implying a non-singular early Universe, with a quadratic density correction reminiscent of braneworld cosmology. It extends the framework to compute the deceleration parameter and to revisit gravitational baryogenesis, showing that GUP-induced fluctuations can break thermal equilibrium in the radiation era and constraining the GUP parameter α from observations. These results offer a quantum-gravity-inspired route to non-singular cosmology and potential connections to early-Universe baryogenesis, while suggesting testable bounds on α from cosmological and particle-physics data.

Abstract

In this paper, combining the thermodynamical arguments of the horizon with the quadratic generalised uncertainty principle (GUP), we heuristically obtain the modified equipartition law of energy. Employing this modified equipartition law of energy, we derive the Friedmann equations in Verlinde's entropic gravity. We find a maximum energy density at the beginning of the Universe. Remarkably, this feature emerges not only for positive GUP parameter but also for negative GUP parameter. From the initial acceleration, we deduce that the negative GUP parameter is more preferable. We also obtain maximum Hubble parameter from the first Friedmann equation, indicating a universe without initial singularity. Moreover, we compute the Kretschmann curvature scalar, again indicating a non-singular universe. Interestingly, we find that GUP-modified Friedmann equations share some similarities with braneworld cosmolgy where the quadratic term in energy density appears. We also compute the deceleration parameter. Finally, we revisit the gravitational baryogenesis and show that the GUP-modified equipartition law of energy provides a mechanism for generating baryon asymmetry. Moreover, we constrain the GUP parameter from observations.

Paper Structure

This paper contains 6 sections, 63 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. A heuristic derivation of the equipartition law of energy from the uncertainty principle
  3. Friedmann equations from the entropic gravity
  4. Deceleration parameter
  5. Baryogenesis
  6. Conclusions and discussions

Figures (2)

  • Figure 1: (a) Kretschmann curvature scalar at maximum density vs GUP parameter and equation of state parameter. (b) Kretschmann curvature scalar at maximum density vs GUP parameter. Black solid and red dashed lines corresponds to $\omega=1/3$ and $\omega=0$, respectively. We use $G_{N}=\hbar=c=1$.
  • Figure 2: (a) Kretschmann curvature scalar at maximum density vs GUP parameter and equation of state parameter. (b) Kretschmann curvature scalar at maximum density vs GUP parameter. Black solid and red dashed lines corresponds to $\omega=-0.6$ and $\omega=-0.5$, respectively. We use $G_{N}=\hbar=c=1$.