NON-MACHIAN SINGULARITY AND INCONSISTENT EQUIVALENCE PRINCIPLE

We show that the non-Machian feature of singularity in the General Theory of Relativity (GTR) can be avoided with scale-invariance. Further, the global non-conservation of energy in GTR results from inconsistency between scale-invariance and equivalence principle. We propose a negative energy density component with a positive equation of state that can drive the late-time acceleration in the universe, while the positive component confines to smaller scales.