Unimodular Constraint on global scale Invariance

TL;DR

This paper explores unimodular gravity combined with global scale invariance, deriving modified gravitational solutions that account for galactic rotation curves and dark energy, without introducing scalar fields.

Contribution

It generalizes conformal theory by incorporating unimodular constraints, providing new solutions for gravitational potential and cosmology that address dark energy and galactic dynamics.

Findings

Modified gravitational potential includes corrections to Schwarzschild solution

Unimodular theory can explain galactic rotation curves

Cosmological solutions preserve de Sitter space, explaining dark energy

Abstract

We study global scale invariance along with the unimodular gravity in the vacuum. The global scale invariant gravitational action which follows the unimodular general coordinate transformations is considered without invoking any scalar field. This is generalization of conformal theory described in the Ref. \cite{Mannheim}. The possible solutions for the gravitational potential under static linear field approximation are discussed. The new modified solution has additional corrections to the Schwarzschild solution which describe the galactic rotational curve. A comparative study of unimodular theory with conformal theory is also presented. Furthermore, the cosmological solution is studied and it is shown that the unimodular constraint preserve the de Sitter solution explaining the dark energy of the universe.