# Recovering the cosmological constant from affine geometry

## TL;DR

This paper introduces a geometric approach using affine geometry and Minkowski potential to derive the cosmological constant, linking it intrinsically to affine radius and de Sitter spacetime models.

## Contribution

It presents a novel parameterization that reveals the geometric nature of the cosmological constant through affine geometry and Minkowski-Tzitzeica surfaces.

## Key findings

- Derivation of de Sitter models from affine spacelike spheres.
- Connection between the cosmological constant and invariant affine radius.
- New geometric parameterization highlighting intrinsic properties of de Sitter space.

## Abstract

A gravity theory without masses can be constructed in Minkowski spaces using a geometric Minkowski potential. The related affine spacelike spheres can be seen as the regions of the Minkowski spacelike vectors characterized by a constant Minkowski gravitational potential. These spheres point out, for each dimension $n \geq 3$, spacetime models, the de Sitter ones, which satisfy Einstein's field equations in absence of matter. In other words, it is possible to generate geometrically the cosmological constant. Even if a lot of possible parameterizations have been proposed, each one highlighting some geometric and physical properties of the de Sitter space, we present here a new natural parameterization which reveals the intrinsic geometric nature of cosmological constant relating it with the invariant affine radius coming from the so called Minkowski-Tzitzeica surfaces theory.