Interplay between curvature and Planck-scale effects in astrophysics and cosmology

Abstract

Several recent studies have considered the implications for astrophysics and cosmology of some possible nonclassical properties of spacetime at the Planck scale. The new effects, such as a Planck-scale-modified energy-momentum (dispersion) relation, are often inferred from the analysis of some quantum versions of Minkowski spacetime, and therefore the relevant estimates depend heavily on the assumption that there could not be significant interplay between Planck-scale and curvature effects. We here scrutinize this assumption, using as guidance a quantum version of de Sitter spacetime with known Inonu-Wigner contraction to a quantum Minkowski spacetime. And we show that, contrary to common (but unsupported) beliefs, the interplay between Planck-scale and curvature effects can be significant. Within our illustrative example, in the Minkowski limit the quantum-geometry deformation parameter is indeed given by the Planck scale, while in the de Sitter picture the parameter of quantization of geometry depends both on the Planck scale and the curvature scalar. For the much-studied case of Planck-scale effects that intervene in the observation of gamma-ray bursts we can estimate the implications of "quantum spacetime curvature" within robust simplifying assumptions. For cosmology at the present stage of the development of the relevant mathematics one cannot go beyond semiheuristic reasoning, and we here propose a candidate approximate description of a quantum FRW geometry, obtained by patching together pieces (with different spacetime curvature) of our quantum de Sitter. This semiheuristic picture, in spite of its limitations, provides rather robust evidence that in the early Universe the interplay between Planck-scale and curvature effects could have been particularly significant.

26 pages.

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Cited by in corpus (21)

• Hamilton geometry: Phase space geometry from modified dispersion relations
• Planck-scale-modified dispersion relations in FRW spacetime
• Particle propagation and effective space-time in Gravity's Rainbow
• Investigation on Finsler geometry as a generalization to curved spacetime of Planck-scale-deformed relativity in the de Sitter case
• Deformed relativity symmetries and the local structure of spacetime
• Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes
• On the initial singularity problem in rainbow cosmology
• Deformed Lorentz symmetry and relative locality in a curved/expanding spacetime
• Curved momentum spaces from quantum (Anti-)de Sitter groups in (3+1) dimensions
• Kinematics of particles with quantum de Sitter symmetries
• Testing Noncommutative Spacetimes and Violations of the Pauli Exclusion Principle with underground experiments
• A (2+1) non-commutative Drinfel'd double spacetime with cosmological constant
• Exploring Special Relative Locality with deSitter momentum-space
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Towards (3+1) gravity through Drinfel'd doubles with cosmological constant
• AdS Poisson homogeneous spaces and Drinfel'd doubles
• Extending general covariance: Moyal-type noncommutative manifolds
• $\kappa$-de Sitter and $\kappa$-Poincaré symmetries emerging from Chern-Simons (2+1)D gravity with a cosmological constant
• Conformal Bootstrap in dS/CFT and Topological Quantum Gravity
• A Short Essay on Quantum Black Holes and Underlying Noncommutative Quantized Space-Time
• Quantum groups and noncommutative spacetimes with cosmological constant