# How is dark energy consistent with conservation of mass and energy?

I initially thought that dark energy must in some way violate conservation of mass and energy since the component of the energy density of space that comes from dark energy is constant, and space is expanding. Therefore, as space expands the energy in the universe that comes from dark energy would increase. I presumed the source of this energy was not coming from the conversion of other types of energy to dark energy, so it must violate conservation.

http://scienceblogs.com/startswithabang/2011/12/02/dark-energy-accelerated-expans/

It says that dark energy does NOT violate conservation and quotes Carroll, Press, and Turner (1992):

"…the patch does negative work on its surroundings, because it has negative pressure. Assuming the patch expands adiabatically [i.e. without loss or gain of heat], one may equate this negative work to the increase of mass/energy of the patch. One thereby recovers the correct equation of state for dark energy: P = – ρ c2. So the mathematics is consistent."

Is there a way to explain this in layman's terms? (The blog attempted to do this, but it was very unclear to me.) More specifically, can you explain where my initial train of thought described above fails when I erroneously concluded that dark energy violates conservation?

Thank you.

• Of course it is conservation of energy you are talking about, since mass is a subset of the manifestations of energy. Aug 4, 2012 at 4:00
• The linked blog seems to have misquoted Carroll, Press & Turner (1992). The paper does have the following quote about the relation P = -rho between pressure and density: "Not by coincidence, this equation of state is precisely the one that, under application of the first law of thermodynamics, causes rho_vac to remain constant if a volume of vacuum is adiabatically compressed or expanded: PdV work provides exactly the amount of mass-energy to fill the new volume dV to the same density rho_vac. Thus rho_vac remains truly a constant." May 20, 2021 at 4:43

The total energy in the space does increase, precisely because of the reason you mention. Energy is not expected to be conserved, because the metric is not invariant under time translations.

What does hold is the first law of thermodynamics, $dU = -P dV + \cdots$. Since the pressure in this system is negative, this is one way of seeing the origin of the extra energy as the space grows.

• Who gave you permission to create "Negative Pressure"? That's like inventing "Negative Temperature" to account for the fact that your formulas don't work. Your formulas don't balance and just giving something a fancy name to the deficit doesn't make it work.
– user32023
Feb 27, 2015 at 11:29
• Negative temperature and negative pressure both have precise technical definitions in Physics. Neither accord with everyday experience, but then no-one is claiming they do. The term negative pressure simply refers to a specific equation of state. Feb 27, 2015 at 16:10
• @DRAirey1: As Philip below mentioned, the negative pressure comes from a positive energy contribution, while the Gravitational potential is overall negative. Positive energy contributions are even in classical physics nothing new. Think of the centrifugal potential. Also if you have a better GR-modell without DE, you should consider to publish it. Mar 3, 2015 at 23:20

"I presumed the source of this energy was not coming from the conversion of other types of energy to dark energy, so it must violate conservation."

This is where you go wrong. The positive dark energy is balanced by the negative energy in the gravitational field. As a volume of space expands more dark energy is created in the volume but this is balanced by a growing negative term in the energy equation that depends on the rate of expansion. That is why dark energy causes the expansion to accelerate.

The reference Carroll, Press, and Turner (1992) explains this in more detail, or see my own paper at http://vixra.org/abs/1305.0034

• I think, the vixra.org is a dubious source. Jan 29, 2018 at 21:13
• @Sergio, I linked to the paper so that people could read it, get a better understanding and make their own judgment. Over 2000 people have done that so far. Either you can read and understand the paper in which case it does not matter what you think of the source, or you do not know enough to understand it in which case you need to learn more about the background physics before trying to understand the answers to this question. Jan 30, 2018 at 22:10