# Physical Cosmological Constant in Asymptotically Background Free Quantum Gravity

## TL;DR

This paper investigates a background-free quantum gravity model where the cosmological constant is derived as a renormalization group invariant, providing a potential solution to the cosmological constant problem without ultraviolet cutoff dependence.

## Contribution

It introduces a nonperturbative quantization of the conformal-factor field in quantum gravity, leading to a physical cosmological constant that is invariant under RG flow and calculable at one-loop level.

## Key findings

- The physical cosmological constant is a function of renormalized parameters.
- It is invariant under the renormalization group flow.
- The calculated value could match the observed cosmological constant.

## Abstract

We study the effective potential in renormalizable quantum gravity with a single dimensionless conformal coupling without a Landau pole. In order to describe a background-free dynamics at the Planck scale and beyond, the conformal-factor field is quantized exactly in a nonperturbative manner. Since this field does not receive renormalization, the field-independent constant in the effective potential becomes itself invariant under the renormalization group flow. That is to say, it gives the physical cosmological constant. We explicitly calculate the physical cosmological constant at the one-loop level in the Landau gauge. We find that it is given by a function of renormalized quantities of the cosmological constant, the Planck mass and the coupling constant, and it should be the observed value. It will give a new perspective on the cosmological constant problem free from an ultraviolet cutoff.