Avoidance of Singularity and Global Non-Conservation of Energy in General Relativity

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

Cosmological wheel or the arrow of time: A classical versus quantum perspective of gravity

It is shown that the structures in the universe can be interpreted to show a closed wheel of time, rather than a straight arrow. An analysis in $f(R)$ gravity model has been carried out to show that due to local observations a small arc at any given spacetime point would invariably indicate an arrow of time from past to future, though on a quantum scale it is not a linear flow but a closed loop, a fact that can be examined through future observations.Comment: 4 pages, 3 figure