Area metric gravity and accelerating cosmology

TL;DR

This paper develops the foundations of area metric differential geometry, reinterprets Einstein-Hilbert action within this framework, and predicts late-time cosmic acceleration without dark energy.

Contribution

It introduces a rigorous geometric framework for area metric gravity and demonstrates its potential to explain cosmic acceleration naturally.

Findings

Area metric curvature scalar reduces to Ricci scalar in metric case

Re-interpretation of Einstein-Hilbert action in area metric context

Prediction of late universe acceleration without dark energy

Abstract

Area metric manifolds emerge as effective classical backgrounds in quantum string theory and quantum gauge theory, and present a true generalization of metric geometry. Here, we consider area metric manifolds in their own right, and develop in detail the foundations of area metric differential geometry. Based on the construction of an area metric curvature scalar, which reduces in the metric-induced case to the Ricci scalar, we re-interpret the Einstein-Hilbert action as dynamics for an area metric spacetime. In contrast to modifications of general relativity based on metric geometry, no continuous deformation scale needs to be introduced; the extension to area geometry is purely structural and thus rigid. We present an intriguing prediction of area metric gravity: without dark energy or fine-tuning, the late universe exhibits a small acceleration.