[Paper Review] Quantum gravitational anomaly as a dark matter

P. O. Kazinski|arXiv (Cornell University)|Jan 23, 2015

Cosmology and Gravitation Theories57 references3 citations

TL;DR

This paper proposes that quantum gravitational anomalies give rise to a perfect relativistic fluid with a polytropic equation of state, which can account for a significant portion of cold dark matter. Using the background field method, the authors derive Ward identities for entropy and vorticity conservation, identify leading gradient corrections to pressure, and show these corrections avoid ghosts while enabling a dynamical solution to the problem of time in quantum gravity.

ABSTRACT

The general properties of a perfect relativistic fluid resulting from the quantum gravitational anomaly are investigated. It is found that, in the limit of a weak gravitational field, this fluid possesses a polytropic equation of state characterized by two universal constants: the polytropic constant and the natural polytropic index. Based on the astrophysical data, the estimates for the polytropic constant are given. It is shown that this fluid can describe a considerable part of the cold dark matter. The quantum theory of such a fluid is constructed in the framework of the background field method. The Ward identities associated with the entropy and vorticity conservation laws are derived. The leading gradient corrections to the pressure of the perfect fluid are found and the restrictions on their form are obtained. These restrictions guarantee, in particular, the absence of ghosts in the model. The second order nonlinear corrections to the equations of motion of a perfect relativistic fluid are analyzed and the explicit expressions for the transverse and longitudinal perturbations induced by a sufficiently strong sound wave are obtained. A dynamical solution to the problem of time in quantum gravity is proposed.

Motivation & Objective

• To investigate the general properties of a perfect relativistic fluid arising from quantum gravitational anomalies.
• To determine whether such a fluid can account for a substantial fraction of cold dark matter based on astrophysical data.
• To construct a consistent quantum theory of the fluid using the background field method.
• To resolve the problem of time in quantum gravity by dynamically determining the vacuum state via the field ξμ.
• To derive and analyze higher-order corrections to the fluid's equations of motion, including nonlinear perturbations from strong sound waves.

Proposed method

• Employ the background field method to formulate a quantum theory of the fluid, ensuring background independence and resolving vacuum-state dependence.
• Derive Ward identities associated with entropy and vorticity conservation laws in the effective action.
• Compute leading gradient corrections to the pressure of the perfect fluid, imposing constraints to prevent ghost states.
• Analyze second-order nonlinear corrections to the fluid equations of motion, deriving explicit expressions for transverse and longitudinal perturbations induced by strong sound waves.
• Use the Gelfand-Naimark-Segal (GNS) construction to relate the vector field ξμ to the vacuum state and representation of observables.
• Demonstrate that finite, non-covariant contributions in the effective action—unremovable by counterterms—arise from quantum gravitational anomalies, leading to a dynamical ξμ field.

Experimental results

Research questions

• RQ1 Can a fluid emerging from quantum gravitational anomalies reproduce the observed properties of cold dark matter?
• RQ2 How do gradient and nonlinear corrections to the fluid's equations of motion affect its stability and physical consistency?
• RQ3 What is the role of the vector field ξμ in dynamically resolving the problem of time in quantum gravity?
• RQ4 How do Ward identities for entropy and vorticity constrain the form of the effective action and its corrections?
• RQ5 Can the quantum gravitational anomaly lead to a finite, non-covariant contribution in the effective action that cannot be canceled by counterterms?

Key findings

• The fluid resulting from the quantum gravitational anomaly exhibits a polytropic equation of state with a universal polytropic index and a polytropic constant estimated from astrophysical data.
• The fluid can describe a considerable fraction of cold dark matter, consistent with cosmological observations.
• Leading gradient corrections to the pressure are derived and constrained to avoid ghost states, ensuring the model's unitarity and stability.
• Second-order nonlinear corrections to the fluid equations yield explicit expressions for transverse and longitudinal perturbations induced by strong sound waves.
• The vector field ξμ, which determines the vacuum state, is dynamically determined by Ward identities, leading to a solution of the problem of time in quantum gravity.
• Finite, non-covariant contributions in the effective action—unremovable by counterterms—arise from the anomaly, confirming its physical significance beyond perturbative corrections.