Recovering the cosmological constant from affine geometry

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 $n\ge 3$, 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.

17 pages, to appear in Int. Jou. Geom. Meth. Mod. Phys

References in corpus (4)

• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Extended Gravity Cosmography
• Dark energy and dark matter as curvature effects
• Speeding up the universe using dust with pressure

Cited by in corpus (1)

• Emergent metric and geodesic analysis in cosmological solutions of (torsion-free) Polynomial Affine Gravity