Does the universe have zero total energy?

[DJsTeLF]

Just finished reading Hawking's 'The Grand Design' in which he appears to culminate in saying the Universe was spontaneously created by some sort of quantum mechanical process. He also comments that this is perfectly allowed if the total energy of the Universe is zero, suggesting that mass/energy is balanced with the negative energy associated with gravity.

My questions are therefore:
1/ Can this really be true? Has anyone attempted a more formal/rigorous study of it? (Well, the observable bits anyway.)
2/ What contribution does dark energy have to this Universal energy balancing act?

References / links to papers or articles grately appreciated

I also want to stress that this thread is in no way intended as an opportunity for religious discussion.

 

[Chalnoth]

Just finished reading Hawking's 'The Grand Design' in which he appears to culminate in saying the Universe was spontaneously created by some sort of quantum mechanical process. He also comments that this is perfectly allowed if the total energy of the Universe is zero, suggesting that mass/energy is balanced with the negative energy associated with gravity.

My questions are therefore:
1/ Can this really be true? Has anyone attempted a more formal/rigorous study of it? (Well, the observable bits anyway.)
2/ What contribution does dark energy have to this Universal energy balancing act?

References / links to papers or articles grately appreciated

I also want to stress that this thread is in no way intended as an opportunity for religious discussion.

A well-known result from taking the Hamiltonian formalism of General Relativity is that the total energy (matter energy + gravitational potential energy) for a closed, homogeneous universe is identically equal to zero. If you want more detail, this is an authoritative paper on the subject:
http://www.springerlink.com/content/357757q4g88144p0/

 

[DJsTeLF]

Thanks for your response Chalnoth. That paper was very interesting. I also found this article about the 'weight' (density actually) of the universe:
http://scienceblog.com/community/older/2000/D/200003072.html

One aspect is still troubling me a little though; Einstein's equations posit that mass/energy density exactly cancels the gravitational potential only for a zero cosmological constant. I'm under the impression that the current consensus in the scientific community is that the cosmological constant is small and positive. I.e. the dark energy driving the accelerating expansion of the universe that we observe. A few questions therefore arise:

Have I misunderstood this completely?
Is the effect of dark energy assumed to have changed since the point of last scattering?
If so, how could the universe have begun with zero total energy and now have an imbalance?

Finally I wonder if anyone has any insightful comments about the relationship between dark energy and inflation? Again, any references / links would be much appreciated.

 

[Chalnoth]

One aspect is still troubling me a little though; Einstein's equations posit that mass/energy density exactly cancels the gravitational potential only for a zero cosmological constant.

This isn't the case. The cosmological constant was left out because they didn't specify the matter distribution, and the cosmological constant can easily be included within the matter distribution.

Finally I wonder if anyone has any insightful comments about the relationship between dark energy and inflation? Again, any references / links would be much appreciated.

Well, they're obviously similar in that they both produce an accelerated expansion, but at wildly-different energy scales. There are a number of extremely speculative ideas as to the possibility that they may be the same field (these are usually called "quintessence" models). But so far there is no good reason to believe there is actually a connection.