Definition of Energy Scale of Inflation

It seems natural to all people, when talking about the energy scale of inflation to take simply $$E_{text{inf}} = Acdot rcdot V^{1/4}$$ Where, $A$ is some factor, $r$ the tensor to scalar ratio and $V$ is the potential.

I know that $V$ is the potential of a Lagrangian density with dimension of 4 in energy, $M^4$ (natural units), and $V$ is an energy density in the space.

For what I understood one takes the DEFINITION of $E_{text{inf}}$ by dimensional analysis.

Buy I thought that for the energy we can also take something like
$int V d^3x$ on some volume. Isn’t this less arbitrary?

Something else that I don’t catch now is in what time is $V$ calculated when we define the energy of the inflation?