Comprehensive Solution to the Cosmological Constant, Zero-Point Energy, and Quantum Gravity Problems

TL;DR

This paper proposes a unified quantum gravity framework where the cosmological constant and zero-point energy cancel each other, solving longstanding problems without the need for regulation or classical fields, using conformal invariance in two and four dimensions.

Contribution

It introduces a quantum gravity approach with mutual cancellation of cosmological constant and zero-point energy, avoiding trace anomalies and classical fields, based on conformal invariance.

Findings

Mutual cancellation of cosmological constant and zero-point energy in quantum gravity.

No need for matter field zero-point energy regulation, avoiding trace anomalies.

Demonstrated in conformal invariant theories in 2D and 4D, with ghost-free, unitary properties.

Abstract

We present a solution to the cosmological constant, the zero-point energy, and the quantum gravity problems within a single comprehensive framework. We show that in quantum theories of gravity in which the zero-point energy density of the gravitational field is well-defined, the cosmological constant and zero-point energy problems solve each other by mutual cancellation between the cosmological constant and the matter and gravitational field zero-point energy densities. Because of this cancellation, regulation of the matter field zero-point energy density is not needed, and thus does not cause any trace anomaly to arise. We exhibit our results in two theories of gravity that are well-defined quantum-mechanically. Both of these theories are locally conformal invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based quantum conformal gravity in four dimensions (a fourth-order derivative quantum theory of the type that Bender and Mannheim have recently shown to be ghost-free and unitary). Central to our approach is the requirement that any and all departures of the geometry from Minkowski are to be brought about by quantum mechanics alone. Consequently, there have to be no fundamental classical fields, and all mass scales have to be generated by dynamical condensates. In such a situation the trace of the matter field energy-momentum tensor is zero, a constraint that obliges its cosmological constant and zero-point contributions to cancel each other identically, no matter how large they might be. Quantization of the gravitational field is caused by its coupling to quantized matter fields, with the gravitational field not needing any independent quantization of its own. With there being no a priori classical curvature, one does not have to make it compatible with quantization.