A question about energy.

There is no time before big bang.

[Short review on Big bang theory:]
Big bang is a cosmological theory determined by general relativity. Assume homogeneous and isotropic universe. Take negative cosmological constant, as fitted by recent astronomical observation. (Take it to zero for the original theory.) Solve the Robertson-Walker metric of space-time. One would find the spacial part is getting smaller and smaller as we go further back in history. Up to a point where the spacial part became zero, i.e. spacial volume of universe = 0, and big bang occurred.

Now whether that is a singularity depends on extra conditions. Stephen Hawking showed in one of his early papers it is possible under some physically allowed condition that there is no singularity at the Big bang. This means one could choose another spacetime coordinate around the big bang on which the metric is non-singular. Vaguely speaking, this is like saying big bang is at the bottom of a parabola or hyperbola, where time is like the vertical axis, and space is like the horizontal cross-section. And you can see there is no singularity at the bottom.

So there is really no time before big bang, and there could be no singularity.



[Energy conservation:]
Energy conservation inherits naturally from the Einstein equation
R = 8 pi G T + lambda
where R is the Einstein curvature (Ricci - scalar / 2), G is the gravitational constant, T is the energy-momentum tensor, and lambda is the cosmological constant. One could show the space-time divergent of R is zero by the definition of curvature. And therefore the space-time divergent of T is zero, i.e. energy-momentum conservation.

Another way to see this is by noting the physical theory (the action or Lagrangian) is space-time translation invariant. So the Noether current, the energy-momentum tensor, got to be divergentless. So energy momentum conservation is due to space-time translation symmetry of the theory.

2009-11-21 01:50:12 補充：
[Answering in simple terms:]
(1) there is no time before big bang. (2) In principal, big bang could be non-singular (not like a black hole) as guaranteed by a set of conditions (Hawking). And (3) energy-momentum conservation is from space-time translation symmetry. So energy is conserved at big bang

2009-11-21 01:54:07 補充：
[Further remarks to my answer:]
The theory could be wrong in the following ways. (1) The Hawking condition are not satisfied and there is indeed a singularity at big bang. Personally, I think this is highly unlikely and the theory has to be very peculiar in order to have this kind of a singularity.

2009-11-21 01:54:45 補充：
(2) Quantum effects need to be taken into account when we go to small length scale. Some strange phenomenon could happen and one might able to draw energy from vacuum (c.f. Casmir effect in curved space-time).

2009-11-21 01:55:16 補充：
Again, I remain very skeptical about going into quantum gravity without worrying renormalizability. One might able to come up with a string theory model that says energy is created at big bang, but I bet there is an equally good (and probably better) model saying there isn't.

Energy can neither be created or destroyed in a law in physics. But all physical laws can only be applied after the Big Bang, i.e. after the birth of the universe.

The laws of physics are based on human knowledge, and at preset, it is still uncertain whether the laws and principles known to us can equally be applied at the singularity where the Big Bang originated.

energy cannot be created or destroyed AFTER our universe was created.

but it is just an assumption. a too good assumption, since, no body found it is not true.

may be someday, we can find a way energy can be created or destroyed.

so, far, it is still an open question about the big bang.