# Nonlocal Cosmology II --- Cosmic acceleration without fine tuning or dark energy

## TL;DR

This paper develops an improved nonlocal quantum gravity model explaining cosmic acceleration without dark energy, using a scalar function that varies between cosmological and local systems to match observations.

## Contribution

It introduces a refined nonlocal gravitational action depending on a scalar function that reproduces the universe's acceleration without fine-tuning or dark energy.

## Key findings

- Reproduces the ΛCDM expansion history without a cosmological constant.
- Ensures compatibility with solar system tests by vanishing in local systems.
- Determines the nonlocal distortion function as a simple exponential form.

## Abstract

We present an improved version of our original cosmological model to explain the current phase of cosmological acceleration without resorting to a cosmological constant or any other mass scale. Like the original, this phenomenological approach is based on an effective quantum gravitational action, but now depends on the original nonlocal dimensionless scalar $X = \square^{-1} R$ only through $Y = \square^{-1} g^{\mu\nu} X_{,\mu} X_{,\nu}$. Both $X$ and $Y$ are quiescent during the radiation-dominated ($R=0$) era, both only grow logarithmically during matter dominance, and neither affects the propagation of gravitational radiation. However, while $X$ has the same sign for gravitationally bound systems as for cosmology, we show that the sign of $Y$ differs for the two cases: it is positive for cosmology and negative for strongly gravitationally bound systems. We can therefore enforce the $\Lambda$CDM expansion history by making a suitable choice of the nonlocal distortion function $f(Y)$ for $Y > 0$, while ensuring that there is no change in the heavily constrained solar system phenomenology simply by making $f$ vanish for $Y < 0$ without discontinuity. The required $f(Y>0)$ is determined numerically to have a strikingly simple exponential form.