# Expansion and conservation of energy

by TrickyDicky
Tags: conservation, energy, expansion
 P: 3,060 According to quantum field theory there is an intrinsic energy of the vacuum or zero point energy (which is being related to cosmological constant by some cosmologists, i.e.:http://philsci-archive.pitt.edu/arch...osconstant.pdf ), so if space stretches with expansion, is the energy of this space vacuum being created all the time? if so, is this in conflict with the energy conservation law?
 Sci Advisor HW Helper P: 1,275 In GR, energy is only (necessarily) conserved locally. This means that the stress tensor satisfies $$\nabla^{\mu}T_{\mu\nu} = 0$$. The stress tensor that can be used to represent vacuum energy $$T_{\mu\nu} = Cg_{\mu\nu}$$ (for some constant C) certainly satisfies this. Alternatively, if you want a Newtonian viewpoint, vacuum energy has a negative pressure, and the field does "negative work" to expand the universe. This "negative works" allows for extra energy in the field taking up more volume. It is the exact opposite situation as with photons, where photons have positive pressure and thus do work in expanding the universe, which exactly compensates for the energy loss (redshift) in the photons).
P: 3,060
 Quote by nicksauce In GR, energy is only (necessarily) conserved locally.
So you are saying GR doesn't have to follow the first law of thermodynamics?
Still expansion is an observed fact not directly derived from GR which is a theory of gravitation.
Maybe someone has a more direct answer to my question?

HW Helper
P: 1,275
Expansion and conservation of energy

 So you are saying GR doesn't have to follow the first law of thermodynamics?
Global energy conservation (or the first law of thermodynamics) comes from the time invariance of the Lagrangian, as a consequence of Noether's theorem. In an expanding universe, the Lagrangian is time dependent. There are other problems with energy in GR: One can't identify the energy of the gravitational field properly because all neighbourhoods look locally flat. However, you can still derive all the basic equations of cosmology just by using Netwon's law of gravity, and basic thermodynamics.

 Still expansion is an observed fact not directly derived from GR which is a theory of gravitation.
If we believe that the universe is isotropic and homogenous on large scales, and that it is governed by GR on large scales, then it is necessarily true that it will be expanding or contracting. The static solution is unstable, meaning that any small perturbations will cause it to start expanding or contracting. Einstein's failure to realize this is why his cosmological constant was called his "greatest mistake."
P: 3,060
 Quote by nicksauce Global energy conservation (or the first law of thermodynamics) comes from the time invariance of the Lagrangian, as a consequence of Noether's theorem. In an expanding universe, the Lagrangian is time dependent. There are other problems with energy in GR: One can't identify the energy of the gravitational field properly because all neighbourhoods look locally flat. However, you can still derive all the basic equations of cosmology just by using Netwon's law of gravity, and basic thermodynamics.
That's correct.

Am I to conclude that the expansion of the universe is somewhat in conflict with global energy conservation ,but that it is a fact assumed by the scientific stablishment and either is not seen as a real problem or simply ignored, or seen as small problem and there is people already figuring it out? Or none of the above?