Conservation of energy in cosmology

[windy miller]

Models like Vilenkin's tunnelling from nothing model described here:
https://www.sciencedirect.com/science/article/abs/pii/0370269382908668
claim the universe came from "nothing". It is claimed this doesn't violate any conservation laws because the negative energy of gravity and the positive energy of matter can cancel each other out. However according to Sean Carroll energy is not conserved in cosmology anyway ,see here:
http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/comment-page-2/
So my question is why do people like Vilenkin even worry about whether or not the positive energy of matter is balanced by the negative energy of gravity if energy is not conserved in cosmology?

Note: please let's not get into a phislophical debate as to the meaning of "nothing: here , my question is not about that.

 

[Demystifier]

Energy of matter alone is not conserved, that's what Carroll is saying. Vilenkin however talks about total energy of matter and gravity together, which is supposed to be conserved. The problem is that the energy of gravity is, in general, not defined uniquely in a covariant way. It can be defined such that the total energy is conserved, but some purists do not take this definition seriously because it's not covariant. For those purists only the matter energy is well defined, which is not conserved.

See also https://www.physicsforums.com/insights/does-gravity-gravitate/ by @PeterDonis .

 

[windy miller]

Energy of matter alone is not conserved, that's what Carroll is saying. Vilenkin however talks about total energy of matter and gravity together, which is supposed to be conserved. The problem is that the energy of gravity is, in general, not defined uniquely in a covariant way. It can be defined such that the total energy is conserved, but some purists do not take this definition seriously because it's not covariant. For those purists only the matter energy is well defined, which is not conserved.

See also https://www.physicsforums.com/insights/does-gravity-gravitate/ by @PeterDonis .

Ah ok thanks very much , appreciate the reply.

 

[martinbn]

http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html