Quantum Gravity Corrections and Entropy at the Planck time

Abstract

We investigate the effects of Quantum Gravity on the Planck era of the universe. In particular, using different versions of the Generalized Uncertainty Principle and under specific conditions we find that the main Planck quantities such as the Planck time, length, mass and energy become larger by a factor of order 10-10^{4} compared to those quantities which result from the Heisenberg Uncertainty Principle. However, we prove that the dimensionless entropy enclosed in the cosmological horizon at the Planck time remains unchanged. These results, though preliminary, indicate that we should anticipate modifications in the set-up of cosmology since changes in the Planck era will be inherited even to the late universe through the framework of Quantum Gravity (or Quantum Field Theory) which utilizes the Planck scale as a fundamental one. More importantly, these corrections will not affect the entropic content of the universe at the Planck time which is a crucial element for one of the basic principles of Quantum Gravity named Holographic Principle.

7 pages, REVTeX 4, 1 figure, accepted for publication in JCAP; v2: one reference added and various cosmetic (but no physics) changes to match published version

References in corpus (21)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Quantum gravity and minimum length
• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• A Generalized Uncertainty Principle in Quantum Gravity
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• Generalized Lorentz invariance with an invariant energy scale
• Universality of Quantum Gravity Corrections
• Discreteness of Space from the Generalized Uncertainty Principle
• The algebraic structure of the generalized uncertainty principle
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• Nonpointlike Particles in Harmonic Oscillators
• Minimal Length Uncertainty Relation and Hydrogen Atom
• Signatures in the Planck Regime
• Phenomenological Implications of the Generalized Uncertainty Principle
• Quantum Uncertainty in Doubly Special Relativity
• Natural extension of the Generalised Uncertainty Principle
• Limits on the Measurability of Space-time Distances in (the Semi-classical Approximation of) Quantum Gravity
• Generalised Uncertainty Principle, Remnant Mass and Singularity Problem in Black Hole Thermodynamics
• Primordial Gravitational Waves and Cosmology

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• 30 years in: Quo vadis generalized uncertainty principle?
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• Position and Momentum Uncertainties of the Normal and Inverted Harmonic Oscillators under the Minimal Length Uncertainty Relation
• Geodesic Structure of the Quantum-Corrected Schwarzschild Black Hole Surrounded by Quintessence
• Remnant mass and entropy of black holes and modified uncertainty principle
• Primordial Power Spectra of Cosmological Fluctuations with Generalized Uncertainty Principle and Maximum Length Quantum Mechanics
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• Entropy Bound with Generalized Uncertainty Principle in General Dimensions
• Lorentz Force and Ponderomotive Force in the Presence of a Minimal Length
• A Note on Coherent States with Quantum Gravity Effects
• Uncertainty Principles and Maximum Entropic Force