Spacetime singularity resolution in Snyder noncommutative space

Abstract

Inspired by quantum gravity proposal, we construct a deformed phase space which supports the UV and IR cutoffs. We show that the Liouville theorem is satisfied in the deformed phase space which allows us to formulate the thermodynamics of the early Universe in the semiclassical regime. Applying the proposed method to the Snyder noncommutative space, we find a temperature dependent equation of state which opens a new window for natural realization of inflation as a phase transition from quantum gravity regime to the standard radiation dominated era. Also we obtain finite energy and entropy densities for the Universe, when at least the Weak Energy Condition is satisfied. We show that there is a minimum size for the Universe which is proportional to the Planck length and consequently the Big Bang singularity is removed.

11 pages, 4 figures, Revised for PRD, title changed

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Cited by in corpus (19)

• Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole
• Cosmological Constant from a Deformation of the Wheeler-DeWitt Equation
• High temperature dimensional reduction in Snyder space
• Natural Cutoffs via Compact Symplectic Manifolds
• Polymeric Quantization and Black Hole Thermodynamics
• Seiberg-Witten map and quantum phase effects for neutral Dirac particle on noncommutatiave plane
• Thermostatistics of the Polymeric Ideal Gas
• Motion of spinning particles around a polymer black hole in loop quantum gravity
• Viscous Cosmologies
• Noncommutative spaces and covariant formulation of statistical mechanics
• Entropy bound for the photon gas in noncommutative spacetime
• Early universe thermostatistics in curved momentum spaces
• Lifshitz field theories, Snyder noncomutative space-time and momentum dependent metric
• Black hole thermodynamics in Snyder phase space
• Effects of the generalized uncertainty principle on the thermal properties of Kemmer oscillator
• Photon gas thermodynamics in dS and AdS momentum spaces
• Nonsingular universe from generalized thermostatistics
• Quantum Spacetimes from General Relativity?
• Snyder and their representation with creation and annihilation operators