Question: Accelerating Universe = Net Positive Energy?

[HappyMonster3000]

Physicists have observed the cosmic radiation background to conclude that the universe is flat (or within the margin of error of being flat).

This means that the Universe contains the critical density needed to keep it flat, which is a mix of ordinary matter, dark matter and dark energy (I would imagine that other particles such as photons don't contribute to this density as they are massless).

The discovery of this "dark energy", responsible for accelerating the Universe at an increasing rate, brings the critical density from about 0.3 to 1.0. Through the equation E = mc², we can see that empty space really has "mass" that curves spacetime.

However, dark energy has the same density. So, as the Universe expands and its "volume" increases, there is more dark energy. Since E = mc², wouldn't that mean that as the universe expands, its mass expands. And wouldn't that mean that:

• The Universe is gaining energy?

But in order for the universe to be flat, there must be a net energy of 0 (or close enough to it, for any discrepancy to be explained by quantum fluctuations -and possible inflation). This means that the positive energy possessed by matter is canceled out by the negative energy of gravity. However:

• If the Universe is expanding, and objects are getting further and further apart, that would mean that gravitational negative energy is decreasing while there's more dark energy to push it further apart. Wouldn't that imply that the positive accelerating energy of dark energy is increasing, while the negative energy of gravity is decreasing?

And:

• Is there therefore an increasing net positive amount of energy in the Universe (implying that energy is not conserved globally)?

Maybe the universe was just flat at the time of inflation (which we have observed to be flat), and its becoming more and more saddle shaped over time. Maybe the universe just started out as "net zero energy" but this changed once expansion started.

Or maybe, as more dark energy is being produced through expansion, it's creating more "negative energy mass" proportional to the amount of positive acceleration that it is producing?

However, if dark energy's "gravitational pull" is cancelling out its "positive expansion", then why is it still accelerating regardless.

Thanks for your replies!

 

[PeterDonis]

Read this:

http://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

A quick summary: energy in a non-static spacetime, like our universe, doesn't work the way you are thinking it does.

 

[PeterDonis]

in order for the universe to be flat, there must be a net energy of 0

Why do you think this?

 

[HappyMonster3000]

Why do you think this?

That was what my interpretation of it was after reading about it. From what we know the Universe is flat. As well, some love the idea of there being a net zero energy with the negative energy of gravity and the positive energy of acceleration cancelling each other out implies that nothing can rise from nothing, there's no need for a deity, it's beautiful etc...

What are your thoughts regarding this?

 

[HappyMonster3000]

Perhaps it began in equal amounts -eg. during the plasma phase as seen in the CRB, but that changed?

 

[PeterDonis]

That was what my interpretation of it was after reading about it.

Reading about it where? I strongly suspect it was not a textbook or a peer-reviewed paper.

From what we know the Universe is flat.

It is spatially flat (more precisely, it is spatially flat in a particular coordinate chart). But spacetime in the universe is not flat; it's curved.

some love the idea of there being a net zero energy with the negative energy of gravity and the positive energy of acceleration cancelling each other out

To begin with, this idea is not really physics, it's an interpretation of the physics, but not one that all cosmologists use, and it's not required by the physics anyway.

Also, you have mis-stated the idea. The idea is that the negative energy of gravity and the positive energy of all the matter and radiation in the universe cancel each other out. "Energy of acceleration", i.e., dark energy, isn't really included in this, as far as I can tell; the idea was originally invented as a description of a universe with no dark energy (back when cosmologists believed that there wasn't any, before we discovered that the expansion of the universe was accelerating), and I don't know that it is still a good interpretation when dark energy is added to the mix.

In any case, as the Carroll article I linked to explains, the notion of global energy conservation does not really work in GR. Local energy densities have physical meaning; but there's no real physical meaning in trying to muliply those densities by some large-scale volume to get a "total energy".

 

[HappyMonster3000]

Reading about it where? I strongly suspect it was not a textbook or a peer-reviewed paper.
It is spatially flat (more precisely, it is spatially flat in a particular coordinate chart). But spacetime in the universe is not flat; it's curved.
To begin with, this idea is not really physics, it's an interpretation of the physics, but not one that all cosmologists use, and it's not required by the physics anyway.

Also, you have mis-stated the idea. The idea is that the negative energy of gravity and the positive energy of all the matter and radiation in the universe cancel each other out. "Energy of acceleration", i.e., dark energy, isn't really included in this, as far as I can tell; the idea was originally invented as a description of a universe with no dark energy (back when cosmologists believed that there wasn't any, before we discovered that the expansion of the universe was accelerating), and I don't know that it is still a good interpretation when dark energy is added to the mix.

In any case, as the Carroll article I linked to explains, the notion of global energy conservation does not really work in GR. Local energy densities have physical meaning; but there's no real physical meaning in trying to muliply those densities by some large-scale volume to get a "total energy".

Thanks!

I now get that globally, the universe needs not to be conserved and it makes sense that the no net energy would be an outdated or pseudoscientific idea.

One question though: what does it mean that it is spatially flat?

 

[PeterDonis]

what does it mean that it is spatially flat?

It means that the geometry of space is Euclidean as measured by "comoving" observers, which are observers to whom the universe looks homogeneous and isotropic. Whenever you see someone talking about how the universe is flat, that is what they mean.