# Emergent scale symmetry: Connecting inflation and dark energy

## TL;DR

This paper proposes a scalar field model connecting inflation and dark energy through emergent scale symmetry, aligning with quantum gravity insights and compatible with cosmological observations.

## Contribution

It introduces a variable gravity model with a Lambert function potential that unifies inflation and dark energy using a single scalar field.

## Key findings

- The model naturally accounts for inflation and dark energy.
- It provides a graceful reheating scenario with observable implications.
- The model fits cosmological data with few parameters.

## Abstract

Quantum gravity computations suggest the existence of an ultraviolet and an infrared fixed point where quantum scale invariance emerges as an exact symmetry. We discuss a particular variable gravity model for the crossover between these fixed points which can naturally account for inflation and dark energy, using a single scalar field. In the Einstein-frame formulation the potential can be expressed in terms of Lambert functions, interpolating between a power-law inflationary potential and a mixed-quintessence potential. For two natural heating scenarios, the transition between inflation and radiation domination proceeds through a "graceful reheating" stage. The radiation temperature significantly exceeds the temperature of big bang nucleosynthesis. For this type of model, the observable consequences of the heating process can be summarized in a single parameter, the heating efficiency. Our quantitative analysis of compatibility with cosmological observations reveals the existence of realistic models able to describe the whole history of the Universe using only a single metric and scalar field and involving just a small number of order one parameters.