We show that the singularity in the General Theory of Relativity (GTR) is the
expression of a non-Machian feature. It can be avoided with a scale-invariant
dynamical theory, a property lacking in GTR. It is further argued that the
global non-conservation of energy in GTR also results from the lack of
scale-invariance and the field formulation presented by several authors can
only resolve the problem in part. Assuming the global energy conservation, we
propose a negative energy density component with positive equation of state
that can drive the late-time acceleration in the universe, while the positive
component confines to smaller scales.Comment: 10 pages, no figure