# Total energy in the universe

## Main Question or Discussion Point

Thermodynamics asserts that energy can neither be created nor destroyed and thus the total energy of the universe is always constant. Thus the accelerating expansion of the universe indicates that some form of energy is being converted into another form at increasing rate? Can this be explained in simple terms? On the other hand, if the total energy of the universe was not constant but was instead tied to, say, the state of evolution of the universe, would this neccessarily violate the first law of thermodynamics?

Nabeshin
How do you figure that the universe accelerating means energy is being converted or at all changed?

Thermodynamics asserts that energy can neither be created nor destroyed and thus the total energy of the universe is always constant. Thus the accelerating expansion of the universe indicates that some form of energy is being converted into another form at increasing rate? Can this be explained in simple terms?
The accelerated expansion is explained not due to the positive energy of the vacuum but due to the negative pressure such a configuration must have. Positive energy without negative pressure would actually slow down the expansion rate.

Thermodynamics asserts that energy can neither be created nor destroyed and thus the total energy of the universe is always constant.
Hi Jackrell,

I don't want to pile on, but in truth the concept of how thermodynamics applies to an expanding universe is surprisingly complex and nonintuitive.

After the first few minutes following the end of inflation in the primordial universe, the density (i.e., the total quantity divided by volume) of radiation energy exceeded the density (or quantity) of matter in the observable universe by many, many orders of magnitude. Over the subsequent millennia, almost all of that radiation energy was lost through redshift resulting from the expansion of the universe. As I understand it, that energy was not merely dissipated across a larger volume, it was actually lost, gone. The density of matter (matter is dissipated but not destroyed by expansion) first exceeded the remaining density of radiation at around 30,000-75,000 years, and the disparity has continued to increase ever since. Today the remaining density of free radiation in the observable universe is a tiny, tiny fraction of the density of matter, and most of it is contained in the CMB.

From a Newtonian perspective, one could perhaps postulate that the lost radiation energy was converted into gravitational potential energy as the universe expanded. But GR apparently does not recognize the concept of potential energy, so there is no specific repository identified in GR into which the lost energy might have been converted.

As MeJennifer mentions, the attribute of the cosmological constant postulated to cause acceleration of expansion is negative pressure, which is also referred to as "tension". Tension in the cosmological constant represents a form of positive energy, just as the tension of a compressed spring is a form of stored energy. According to the Friedmann acceleration equation, the positive energy of the cosmological constant is equal to 1/3 of its negative pressure. This positive energy gravitates, thereby working against the acceleration. Subtracting the 1X gravitation from the 3X negative pressure, the net accelerative force of the cosmological constant is exactly 2X the positive energy content. This 3:1 ratio is called the "equation of state" of the cosmological constant.

As the universe expands, the positive energy content added by the ongoing addition of cosmological constant contributes positive energy density (and "weight") to the observable universe, but at the same time the expansion causes the overall density to decrease. The currently estimated density of the cosmological constant alone is about 6.7E-27 kg / cubic meter, and of course that density remains constant regardless of how much the universe expands. The estimated total density of the universe now is about 9.17E-27 kg / cubic meter. As long as the universe keeps expanding, this total density will continue to decline asymptotically over future eons, towards the density of the cosmological constant. In other words, the radiation and matter content of our observable universe will be dilluted or "washed out" by the expansion. Matter (beyond that which currently is gravitationally bound to our Local Sheet) won't disappear, it will just move beyond our particle horizon so that we can't observe it anymore. Free radiation (e.g. the CMB) will continue to be both destroyed (by redshift) and dilluted.

Jon

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According to the Friedmann acceleration equation, the positive energy of the cosmological constant is equal to 1/3 of its negative pressure. .... This positive energy gravitates, thereby working against the acceleration. This 3:1 ratio is called the "equation of state" of the cosmological constant.
Jon
I want to correct a technical error in my statement. Although the ratio of negative pressure to positive energy is 3:1 as I stated, the equation of state of the cosmological constant is considered to be -1. This is because, for the purposes of the Friedmann equation and the equation of state definition, the pressure factor is divided by 3 before adding it to the density factor. However, this does not change the effective 2x ratio I described as between accelerative force and grativational retardation.

Jon

This is because, for the purposes of the Friedmann equation and the equation of state definition, the pressure factor is divided by 3 before adding it to the density factor.
Jon
Well, I'm moving asymptotically closer to the correct technical description...

I meant to say that the pressure factor is multiplied by 3 before adding it...

Noethers Theorem

Noether's theorem states that every symmetry in nature is connected to a conservation law.

spatial translation symmetry -> conservation of linear momentum
rotational symmetry -> conservation of angular momentum
time translation symmetry -> conservation of energy.

note that the LCDM model is NOT invariant under time translation and therefore should not be expected to conserve energy.

Hi Allday,

Thanks for making that point.

No disrespect intended, but for this kind of issue, Noether's theorem seems like a fancy way of stating the obvious:

"If the energy content of the model changes (is not invariant) with the passage of time, then energy is not conserved"

Jon

I dont think it's that obvious. The Universe is presumably a closed system (although there are brane models where gravity is not confined to our brane) and so one may feel the need to track down the energy lost from photons redshifting. Noether's theorem provides a REASON why its plausible that there is no need to track this energy down. A system with time translation symmetry is the same thing as a system that conserves energy. To tell you the truth, I havent done a huge amount of research on GR and symmetry and so I dont know if this really holds. I know the whole concept of energy in GR is a slippery thing.

-G

Hi Allday, I agree with you.

Jon

Hi Allday,

Thanks for making that point.

No disrespect intended, but for this kind of issue, Noether's theorem seems like a fancy way of stating the obvious:

"If the energy content of the model changes (is not invariant) with the passage of time, then energy is not conserved"

Jon
It is not that trivial. If we want to build a space-time model of event that describes observations in such a way that those descriptions do not depend on the point of view of a specific observer, then that model must contain a quantity called energy that is conserved.

Hi Moridin,

I think you misunderstand my comment. I am NOT suggesting that it is a trivial matter that energy is not conserved in the FLRW model. I was merely suggesting that the way Allday stated how Noether's theorem applies to this situation was a trivial rephrasing of what I already said. My comment was intended to be a throwaway line, not something to create a debate. Sorry if I wasn't clear.

Jon