# $\tilde{\delta}$ Gravity, $\tilde{\delta}$ matter and the accelerated expansion of the Universe

## TL;DR

This paper introduces a gravity model with two symmetric tensors and additional matter fields, leading to an accelerated universe expansion without dark energy, by modifying particle trajectories and cosmological dynamics.

## Contribution

It proposes a novel gravity framework with $ ilde{ ext{delta}}$ symmetry and $ ilde{ ext{delta}}$ matter, explaining cosmic acceleration without dark energy.

## Key findings

- Massive particles deviate from geodesics.
- Massless particles follow null geodesics of an effective metric.
- Universe exhibits accelerated expansion without dark energy.

## Abstract

A gravitational field model based on two symmetric tensors, $g_{\mu \nu}$ and $\tilde{g}_{\mu \nu}$, is presented. In this model, new matter fields are added to the original matter fields, motivated by an additional symmetry ($\tilde{\delta}$ symmetry). We call them $\tilde{\delta}$ matter fields. We find that massive particles do not follow geodesics, while trajectories of massless particles are null geodesics of an effective metric. Then we study the Cosmological case, where we get an accelerated expansion of the Universe without dark energy.