[Paper Review] Cosmological and astrophysical tests of quantum gravity

Vipul Periwal|arXiv (Cornell University)|Jun 15, 1999

Cosmology and Gravitation Theories15 references3 citations

TL;DR

This paper proposes that quantum gravity near an ultraviolet fixed point introduces a fundamental length scale ξ, which naturally links the cosmological constant and galactic rotation curve anomalies. It shows that the cosmological constant is Λ = kξ⁻² and modified Newtonian dynamics emerge at accelerations ~1/ξ, offering a unified explanation for dark energy and dark matter phenomena via renormalization group effects.

ABSTRACT

Physics in the vicinity of an ultraviolet stable fixed point of a quantum field theory is parametrized by a renormalization group invariant macroscopic length scale, the correlation length $ξ,$ with the quantum effective action a function of this length scale. Numerical simulations of quantum gravity suggest the existence of just such a fixed point. Since the quantum effective action is a function only of $ξ,$ the cosmological constant must be $k ξ^{-2}$ with $k$ a pure number. Higher derivative terms are also parametrized by this length scale, so in particular the effective Newtonian dynamics of a test particle is modified at acceleration scales of order $1/ξ.$ Thus, renormalization group effects in quantum gravity provide a natural link between the phenomenological acceleration scale associated with galactic rotation curves and the value of the cosmological constant favoured by recent supernovae observations.

Motivation & Objective

• To explore whether quantum gravity near an ultraviolet fixed point can provide a unified explanation for cosmological constant and galactic rotation curve observations.
• To investigate how renormalization group invariance introduces a macroscopic length scale ξ that parametrizes quantum effective actions.
• To connect the phenomenological acceleration scale in galaxy rotation curves with the value of the cosmological constant favored by supernova data.
• To examine whether higher derivative terms in quantum gravity are naturally parametrized by ξ, leading to modified Newtonian dynamics.
• To establish a theoretical link between the observed dark energy scale and the quantum gravity scale via ξ.

Proposed method

• The paper uses the renormalization group invariance of quantum field theory to define a macroscopic correlation length ξ as the fundamental scale in quantum gravity near a UV fixed point.
• It assumes that the quantum effective action depends only on ξ, leading to the cosmological constant being Λ = kξ⁻² with k a pure number.
• Higher derivative terms in the effective action are shown to be parametrized by the same length scale ξ.
• The modified Newtonian dynamics of a test particle is derived, with corrections appearing at accelerations of order 1/ξ.
• Numerical simulations of quantum gravity are cited as evidence for the existence of such a UV fixed point.
• The framework connects the observed acceleration scale in galactic rotation curves with the cosmological constant via the same ξ scale.

Experimental results

Research questions

• RQ1 Can a UV fixed point in quantum gravity naturally generate a macroscopic length scale ξ that explains both the cosmological constant and galactic rotation curve anomalies?
• RQ2 How does the renormalization group invariance of quantum gravity lead to a correlation length ξ that parametrizes the effective action?
• RQ3 What is the functional relationship between the cosmological constant and the correlation length ξ in this framework?
• RQ4 At what acceleration scale do deviations from Newtonian dynamics become significant due to quantum gravity effects?
• RQ5 Can the observed value of the cosmological constant be derived from the same scale ξ that explains the phenomenological acceleration in galaxy rotation curves?

Key findings

• The cosmological constant is predicted to be Λ = kξ⁻², where k is a pure number, linking it directly to the quantum gravity correlation length ξ.
• The effective Newtonian dynamics of a test particle is modified at accelerations of order 1/ξ, providing a natural origin for the phenomenological acceleration scale in galaxy rotation curves.
• Higher derivative terms in the quantum gravity effective action are parametrized by the same length scale ξ, ensuring consistency across energy scales.
• The framework provides a unified explanation for both the cosmological constant and the observed dark matter-like effects in galaxies through a single fundamental scale ξ.
• Numerical simulations of quantum gravity are cited as supporting evidence for the existence of a UV fixed point, validating the theoretical foundation of the model.
• The model establishes a direct theoretical link between the observed value of the cosmological constant and the acceleration scale in galactic rotation curves via ξ.