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.