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

TL;DR

This paper investigates how quantum properties of spacetime at the Planck scale interact with curvature effects in astrophysics and cosmology, challenging previous assumptions of their independence and highlighting potential significance in the early universe.

Contribution

It demonstrates, through a quantum de Sitter model, that Planck-scale and curvature effects can significantly interplay, affecting astrophysical and cosmological observations.

Findings

Quantum de Sitter spacetime shows interplay between Planck-scale and curvature effects.

In the Minkowski limit, deformation parameters relate solely to the Planck scale.

In curved spacetime, quantization depends on both Planck scale and curvature.

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.