Understanding Energy Density and Cosmic Expansion

[benk99nenm312]

I know the concept of the accelerating universe and expansion and all, but what exactly is energy density and how does it cause or explain the cosmic expansion of our universe?

Thanks in advance.

 

[JinChang]

I guess you're referring to Dark Energy?

http://en.wikipedia.org/wiki/Dark_energy

 

[benk99nenm312]

I guess you're referring to Dark Energy?

http://en.wikipedia.org/wiki/Dark_energy

In a sense. What I really want to focus on though is the concept of a negative energy density. This quote explains it.

"Observations that the expanding universe appears to be accelerating seem to support the cosmic inflation theory in which the universe is passing through a phase of exponential expansion driven by a negative vacuum energy density (positive vacuum pressure)."

 

[chronon]

In a sense. What I really want to focus on though is the concept of a negative energy density. This quote explains it.

"Observations that the expanding universe appears to be accelerating seem to support the cosmic inflation theory in which the universe is passing through a phase of exponential expansion driven by a negative vacuum energy density (positive vacuum pressure)."

My understanding is that it's positive vacuum energy density and negative pressure which drives the acceleration.

 

[benk99nenm312]

My understanding is that it's positive vacuum energy density and negative pressure which drives the acceleration.

I'm in an awkward position because I don't know what I could be defending. I want to know exactly what energy density is, and why this causes an outward expansion of the universe.

I do know that a negative energy density would essentially cause an antigravity effect. I have read this in numerous places, so I'm pretty sure that that's not wrong. I have always found articles that say it is a negative energy density.

Besides, a positive pressure in a gas expands the volume of a gas when the volume is not fixed. I'm pretty sure that is a generalization of pressure. Positive pressure causes an outward movement of the medium, so a negative pressure would cause an inward tug on the medium. We are obviously looking at positive pressure, so that would infer a negative energy density.

I just want to know, what exactly is energy density, and how does it infer a pressure of any kind at all?

 

[Chalnoth]

I'm in an awkward position because I don't know what I could be defending. I want to know exactly what energy density is, and why this causes an outward expansion of the universe.

It's not about it being just energy density, but rather, as chronon mentioned, about the pressure. Specifically, this relationship determines how quickly the energy density dilutes. If an energy density dilutes slowly, it causes an accelerated expansion. This can be trivially seen from the Friedmann equation for a flat universe:

$$H^2 = H_0^2\frac{\rho}{\rho_0}$$

...where $$\rho$$ is the energy density of whatever stuff there is in the universe. The Hubble parameter, $$H$$ is shorthand for $$\dot{a}/a$$, with the dot denoting a derivative with respect to time, and a being the scale factor. If the energy density is a constant (thus $$\rho = \rho_0$$), as with the cosmological constant, then we have a simple differential equation:

$$\frac{1}{a}\frac{da}{dt} = H_0$$
$$\frac{da}{dt} = H_0 a$$

Since on the left hand side we have a derivative with respect to a, and the right hand side is proportional to a, we simply have an exponential:

$$a(t) = a(0)e^{H_0 t}$$

...which is an equation for accelerated expansion.

I do know that a negative energy density would essentially cause an antigravity effect. I have read this in numerous places, so I'm pretty sure that that's not wrong. I have always found articles that say it is a negative energy density.

Well, it's certainly wrong in the context of a cosmological constant. I mean, sure, if your total energy density of the universe was negative, then you would have a very large negative curvature, which would cause everything to fly apart. But since inflation forces the universe to be nearly flat, this basically can't happen, so what would happen with a negative cosmological constant (or other, similar energy density) is that you'd have a large matter density, and it would just collapse right back in upon itself.

Besides, a positive pressure in a gas expands the volume of a gas when the volume is not fixed. I'm pretty sure that is a generalization of pressure. Positive pressure causes an outward movement of the medium, so a negative pressure would cause an inward tug on the medium. We are obviously looking at positive pressure, so that would infer a negative energy density.

This are different when that gas is not surrounded by vacuum, but permeates all of space.

 

[benk99nenm312]

It's not about it being just energy density, but rather, as chronon mentioned, about the pressure. Specifically, this relationship determines how quickly the energy density dilutes. If an energy density dilutes slowly, it causes an accelerated expansion. This can be trivially seen from the Friedmann equation for a flat universe:

$$H^2 = H_0^2\frac{\rho}{\rho_0}$$

...where $$\rho$$ is the energy density of whatever stuff there is in the universe. The Hubble parameter, $$H$$ is shorthand for $$\dot{a}/a$$, with the dot denoting a derivative with respect to time, and a being the scale factor. If the energy density is a constant (thus $$\rho = \rho_0$$), as with the cosmological constant, then we have a simple differential equation:

$$\frac{1}{a}\frac{da}{dt} = H_0$$
$$\frac{da}{dt} = H_0 a$$

Since on the left hand side we have a derivative with respect to a, and the right hand side is proportional to a, we simply have an exponential:

$$a(t) = a(0)e^{H_0 t}$$

...which is an equation for accelerated expansion.


Well, it's certainly wrong in the context of a cosmological constant. I mean, sure, if your total energy density of the universe was negative, then you would have a very large negative curvature, which would cause everything to fly apart. But since inflation forces the universe to be nearly flat, this basically can't happen, so what would happen with a negative cosmological constant (or other, similar energy density) is that you'd have a large matter density, and it would just collapse right back in upon itself.


This are different when that gas is not surrounded by vacuum, but permeates all of space.

Thanks a lot. Can you explain the energy density bit at the beginning in a more conceptual way?

 

[Chalnoth]

Thanks a lot. Can you explain the energy density bit at the beginning in a more conceptual way?

Well, how quickly the energy density of a certain type of matter dilutes as the universe expands depends upon the properties of that matter. Specifically, it depends upon the pressure.

One way to think of this is to think of work. Imagine I have a single box with a piston that I can use to compress or stretch the gas inside the box. Outside this box is pure vacuum (with zero energy density). Inside the box is some sort of matter.

If inside the box we have a normal gas, for example, then it will have some positive pressure. This means that it will tend to push up on the piston, so that I have to press on the piston to keep it from coming out, or if I want to compress the gas. Now, if I let the piston out so that the gas expands, I'm doing negative work on the gas (or, alternatively, the gas is doing positive work on the piston). This means that energy is being transferred from the gas to me: the gas loses energy as it expands if it has positive pressure.

If, on the other hand, the stuff inside has negative pressure, then the opposite is true. It wants to pull the piston in on itself: I have to physically pull on the piston to keep it from collapsing. So if I do pull back on the piston, then I am performing positive work on the stuff inside This adds energy to the material, making it so that it has more total energy after expansion than before.

 

[benk99nenm312]

Well, how quickly the energy density of a certain type of matter dilutes as the universe expands depends upon the properties of that matter. Specifically, it depends upon the pressure.

One way to think of this is to think of work. Imagine I have a single box with a piston that I can use to compress or stretch the gas inside the box. Outside this box is pure vacuum (with zero energy density). Inside the box is some sort of matter.

If inside the box we have a normal gas, for example, then it will have some positive pressure. This means that it will tend to push up on the piston, so that I have to press on the piston to keep it from coming out, or if I want to compress the gas. Now, if I let the piston out so that the gas expands, I'm doing negative work on the gas (or, alternatively, the gas is doing positive work on the piston). This means that energy is being transferred from the gas to me: the gas loses energy as it expands if it has positive pressure.

If, on the other hand, the stuff inside has negative pressure, then the opposite is true. It wants to pull the piston in on itself: I have to physically pull on the piston to keep it from collapsing. So if I do pull back on the piston, then I am performing positive work on the stuff inside This adds energy to the material, making it so that it has more total energy after expansion than before.

Wouldn't this technically violate the conservation of energy?

 

[Chalnoth]

Wouldn't this technically violate the conservation of energy?

No. In the example I'm showing, the energy is just being transferred between whatever is inside the box and the person holding onto the piston.

 

[benk99nenm312]

No. In the example I'm showing, the energy is just being transferred between whatever is inside the box and the person holding onto the piston.

So what exactly does the piston represent in the real model?

 

[Chalnoth]

So what exactly does the piston represent in the real model?

The action of gravity, though in this case the behavior of gravity in turn depends upon the current rate of expansion as well as the properties of the material in question. So the "piston" is moved in a very specific way dependent upon how matter interacts with gravity, and what the initial motion is.

 

[v2kkim]

I like to ask a related question on expansion and gravity.
Assuming that we (earth) are receiving light from a remote galaxy, and we believe light traveled 1 million light year. Now we want to calculate the gravitational force by that galaxy.

My questions are :
(1) Can we use Newton gravitation equation with distance=1 million light yr ?
(2) Should be consider space expansion happened past 1 million years ? My thinking is space expansion might caused decrease of graviton density near earth, compared to non-expanding space case.

 

[Chalnoth]

My questions are :
(1) Can we use Newton gravitation equation with distance=1 million light yr ?

Since a million light years is quite small compared to the expansion rate, I'd say most likely yes, that would give an accurate result.

(2) Should be consider space expansion happened past 1 million years ? My thinking is space expansion might caused decrease of graviton density near earth, compared to non-expanding space case.

How the gravitational potentials evolve with expansion depends upon the contents of the universe. The cosmological constant does cause gravitational potentials to get slightly more shallow.

The density of gravitons isn't really meaningful here as the gravitons are being emitted and reabsorbed by matter all the time, such that their abundance is fully dependent upon the local value of the stress-energy tensor.