Account for radiation energy in the statement "total energy of universe is zero" I've read in Hawking's book The Theory of Everything that total energy of the Universe is zero. He explained this by saying that if there are two bodies separated by a distance and having some mass, they possess potential energy and the same amount of negative energy  with the gravitational field. Thus he concluded that total energy of the Universe  is zero. But here I've a question: how do we account for energy which is in the form of radiation?
The total energy of the universe consists of the mass energy of all the matter (both normal and dark), the mass-energy of the radiation and of the dark energy plus the gravitational potential energy of the universe (which is negative).  The hypotheses is that this sums to zero.  As far as I know, there is no experimental evidence for this.

But there is good evidence for the size of the various mass-energy terms.  The best current estimates are that the mass-energy of the universe is:


73% -- Dark energy 
23% -- Dark matter
3.6% -- Interstellar gas 
0.4% -- Stars (includes black holes) 
v. small -- Relativistic neutrinos
v. small -- Radiation (CMB and stellar radiation combined)


This balance changes.  As the universe expands, the density of matter (dark and normal) varies as the inverse 3rd power of the size of the universe. (Matter stays the same and the volume expands as the cube of the radius.)

But the density of dark energy stays constant, since it is a property of empty space.

The density of radiation is proportional to the inverse 4th power of the radius, because not only does the increased volume dilute the radiation like it dilutes the matter, but also the radiation gets red-shifted, contributing an extra power of the radius.

(Incidentally, that means that the fraction of the total mass-energy of the universe in radiation decreases with time, and is estimated presently to be 1000:1 matter:radiation.)

So radiation seems simply to be too small to matter.