Expansion and conservation of energy

[J.C.MacSwell]

Is the expansion (Hubble Flow) in agreement with the conservation of energy?

 

I'm not sure how the accounting for the energy balance would work with distant volumes of space approaching/surpassing lightspeed wrt each other.

 

So is the expansion considered to be in agreement or is this question considered not relevant or just unknown?

 

I realize energy is not invariant wrt frames of reference.

 

Also how would entropy increase relate to the above?

[ComradeRob]

Isnt this one of those questions scientists have learnt to answer with *dark energy*?

[J.C.MacSwell]

Isnt this one of those questions scientists have learnt to answer with *dark energy*?

 

Thank you. I Googled "dark energy" and realize (I think) there is no standard answer to what I asked.

[tholan]

The only way to analyze whether energy is conserved or not is to take a look to what happens within a comoving volume with a definite boundary. We want to know what happens to every of the components of this volume as the volume expands with time.

 

First take a look to matter and radiation. Assume that no matter nor radiation cross the boundaries of our volume. The energy content of matter will remain unchanged (we assume that there are basically no interactions with other components within the volume). The energy content of radiation will decrease, as photons will increase their wavelength. As this increase of wavelength is due to expansion of space we might consider that the energy of the photons goes into gravitational energy of spacetime (the energy of the gravitational field or gravitational potential in Newtonian terms). This is a similar situation as for a photon gravitationally redshifted by a mass. It does also loose electromagnetic energy increasing its potential energy (increasing its distance to the mass). However, the exact notion of energy of the gravitational field is not a well-defined concept in general relativity and this explanation must be taken with care.

 

On the other hand we have also dark energy which we will assume to be a cosmological constant. Since the cosmological constant is a scalar field, its energy density is constant in space and time and, therefore, if the volume increases, the total energy of the dark energy contained within it will increase. Where does this energy come from? Honestly I don’t know. You may solace yourself with the fact that energy conservation in general relativity is not always a well-defined concept.