  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.
