TL;DR
This paper introduces Ricci flow gravity, a novel scalar-tensor theory of gravitation that aligns with Einstein gravity in the solar system but predicts significant deviations in cosmological scenarios.
Contribution
It proposes a new gravity model based on Ricci flow with an independent volume, extending Einstein gravity and differing from Jordan-Brans-Dicke theory.
Findings
Passes all classical solar system tests
Predicts deviations from Einstein cosmology
Includes Einstein gravity as a limiting case
Abstract
A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gravity. In particular there is no adjustable coupling constant. For the solar system the effects of Ricci flow gravity cannot be distinguished from Einstein gravity and therefore it passes all classical tests. However for cosmology significant deviations from standard Einstein cosmology will appear.
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