Re: Energy conservation in an expanding universe

On Feb 26, 5:22 pm, Igor Khavkine <igor...@xxxxxxxxx> wrote:
However, the idea of "taking the total energy to be zero" is not
fruitful for at least one reason. The reason is that H = 0 is true over
the entire constraint surface.

Thanks, that is certainly a good point!

Thinking about it, the only way I can still see it of being of some
interpretational value is that
H = 0
could be viewed as a 'detailed energy balance' equation, holding at
each point on the constraint surface. In particular, H is a specific
function of the spatial 3-metric h_ij and the conjugate 'momentum'
field p^ij, so that H=0 looks something like an equation for the sum
of a kinetic and a potential term, i.e., of the form
G_{ijkl} p^ij p^kl + V = 0,
where G_{ijkl} and V are functions of h_ij and its derivatives (G is
the deWitt supermetric, and V incorporates matter and curvature
terms).

The two terms do vary individually over the constraint surface, and so
one has in effect a detailed energy balance equation (providing one
can actually give an interesting physical meaning to the kinetic and
potential terms!). The Ashtekar formalism would give something
formally similar.

.