# Gravitational Coupling, Dynamical Changes of Units and The Cosmological Constant Problem

## TL;DR

This paper explores a model where units of measurement vary dynamically over cosmic time, potentially addressing the cosmological constant problem by considering different conformal frames and their evolution.

## Contribution

It introduces a gravitational model with epoch-dependent unit conversion factors, linking conformal transformations to dynamical units and addressing the cosmological constant discrepancy.

## Key findings

- Dynamical units can influence the cosmological constant problem.
- Different conformal frames relate to varying fundamental constants.
- Model connects unit evolution with violation of equivalence principle.

## Abstract

A spacetime interval connecting two neighbouring points can be measured in different unit systems. For instance, it can be measured in atomic unit defined in terms of fundamental constants existing in quantum theories. It is also possible to use a gravitational unit which is defined by using of properties of macroscopic objects. These two unit systems are usually regarded as indistinguishable up to a constant conversion factor. Here we consider the possibility that these two units are related by an epoch-dependent conversion factor. This is a dynamical changes of units. Regarding a conformal transformation as a local unit transformation, we use a gravitational model in which the gravitational and the matter sectors are given in different conformal frames (or unit systems). It is relevant to the cosmological constant problem, namely the huge discrepancy between the estimated and the observational values of the cosmological constant in particle physics and cosmology, respectively. We argue that the problem arises when one ignores evolution of the conversion factor relating the two units during expansion of the Universe. Connection of the model with violation of equivalence principle and possible variation of fundamental constants are also discussed.