# Beyond-one-loop quantum gravity action yielding both inflation and late-time acceleration

## TL;DR

This paper proposes a quadratic gravity model with exponential $F(R)$-gravity that naturally unifies early inflation and late-time cosmic acceleration, aligning well with Planck data and cosmological observations.

## Contribution

It introduces a beyond-one-loop quantum gravity effective action that unifies inflation and dark energy within a single framework, with stabilization mechanisms for dark energy.

## Key findings

- Inflationary parameters match Planck results.
- Model fits recent dark energy observational data.
- Effective action includes higher-derivative quantum corrections.

## Abstract

A unified description of early-time inflation with the current cosmic acceleration is achieved by means of a new theory that uses a quadratic model of gravity, with the inclusion of an exponential $F(R)$-gravity contribution for dark energy. High-curvature corrections of the theory come from higher-derivative quantum gravity and yield an effective action that goes beyond the one-loop approximation. It is shown that, in this theory, viable inflation emerges in a natural way, leading to a spectral index and tensor-to-scalar ratio that are in perfect agreement with the most reliable Planck results. At low energy, late-time accelerated expansion takes place. As exponential gravity, for dark energy, must be stabilized during the matter and radiation eras, we introduce a curing term in order to avoid nonphysical singularities in the effective equation of state parameter. The results of our analysis are confirmed by accurate numerical simulations, which show that our model does fit the most recent cosmological data for dark energy very precisely.