# Ricci Flow Approach to The Cosmological Constant Problem

## TL;DR

This paper proposes a quantum geometric framework using Ricci flow to address the cosmological constant problem, linking quantum spacetime fluctuations to cosmic acceleration and matching observational data.

## Contribution

It introduces a quantum spacetime reference frame with a new geometry based on higher moments, and connects Ricci flow dynamics to cosmological acceleration.

## Key findings

- Spacetime stabilized against quantum fluctuations.
- Accelerating universe modeled by Ricci flow with observed deceleration parameter.
- Effective gravity theory derived within the new geometric framework.

## Abstract

In order to resolve the cosmological constant problem, the notion of reference frame is re-examined at the quantum level. By using a quantum non-linear sigma model (Q-NLSM), a theory of quantum spacetime reference frame (QSRF) is proposed. The underlying mathematical structure is a new geometry endowed with intrinsic 2nd central moment (variance) or even higher moments of its coordinates, which generalizes the classical Riemannian geometry based on only 1st moment (mean) of its coordinates. The 2nd central moment of the coordinates directly modifies the quadratic form distance which is the foundation of the Riemannian geometry. At semi-classical level, the 2nd central moment introduces a flow which continuously deforms the Riemannian geometry driven by its classical Ricci curvature, which is known as the Ricci flow. A generalized equivalence principle of quantum version is also proposed to interpret the new geometry endowed with at least 2nd moment. As a consequence, the spacetime is stabilized against quantum fluctuation, and the cosmological constant problem is resolved within the framework. With an isotropic positive curvature initial condition, the long flow time solution of the Ricci flow exists, the accelerating expansion universe at cosmic scale is an observable effect of the spacetime deformation of the normalized Ricci flow. A deceleration parameter -0.67 consistent with measurement is obtained by using the reduced volume method introduced by Perelman. Effective theory of gravity within the framework is also discussed.