# A new approach to modified-gravity models

## TL;DR

This paper explores modified gravity models using ADM-slicing, deriving static solutions and cosmological evolution, showing the universe can accelerate at late times without fine-tuning.

## Contribution

It introduces a novel approach to f(R)-gravity models via ADM-slicing, providing new static solutions and insights into late-time cosmic acceleration.

## Key findings

- Derived static spherically-symmetric solutions including Schwarzschild de-Sitter and anti-de-Sitter.
- Found that the universe can naturally accelerate at late epochs without fine-tuning.
- Demonstrated that cosmological evolution follows an algebraic equation, simplifying analysis.

## Abstract

We investigate f(R)-gravity models performing the ADM-slicing of standard General Relativity. We extract the static, spherically-symmetric vacuum solutions in the general case, which correspond to either Schwarzschild de-Sitter or Schwarzschild anti-de-Sitter ones. Additionally, we study the cosmological evolution of a homogeneous and isotropic universe, which is governed by an algebraic and not a differential equation. We show that the universe admits solutions corresponding to acceleration at late cosmological epochs, without the need of fine-tuning the model-parameters or the initial conditions.