Dark energy

[Martin]

what is dark energy

why does it have negative pressure

how does negative pressure accelerate the universe's expansion

 

does anyone want to offer some explanations?

 

I will try to give some partial answers for a start, which can be elaborated or disagreed with

 

The key to the whole discussion of dark energy is the Friedmann equation

(a simplified version of the basic Einstein equation of GR gotten from

the Einstein equation by assuming a kind of uniformity to the universe

that makes things easier to calculate)

 

[math]\frac{a''}{a}= -\frac{4\pi G}{3}(\rho + 3p)[/math]

 

a is the scale factor, so expansion corresponds to a' positive

and acceleration corresponds to a'' positive

 

and so we cant have acceleration unless

[math](\rho + 3p)[/math] is negative.

 

rho is the average energy density in space and p is the average pressure

both change with time

for most of the history of the universe the large-scale pressure from matter and light has been negligible (we are talking global averages, not local concentrations around stars etc.) so we can forget about pressure except what comes from dark energy

 

rho the density of energy of all kinds, total, is always positive

so how can that term up there be negative?

 

only if there is some energy in space with negative pressure

 

what is negative pressure, well there is negative pressure inside a cylinder with a sliding piston if pulling the piston out a ways takes work

if there were positive pressure then you could extract work by letting the piston be pushed out some distance.

 

any constant energy---so and so much per cubic meter---has negative pressure because if you enlarge a volume you increase the amount of energy in it and so it must (by conservation) take work to enlarge the volume

 

I got this argument from a cosmologist and I still think there is something tricky about it, but I dont know any better argument so I pass it along.

 

Vacuum energy therefore has to have negative pressure! If there is a constant so and so much per cubic meter, then by that pump piston argument it must represent a constant negative pressure throughout all space and time.

 

Indeed the equation of state for a constant vacuum energy is

p = - rho

the pressure is equal minus the energy density

(energy density has the same units as pressure so theres no constant of proportionality, joules per cubic meter is the same as newtons per square meter)

 

So even though dark energy is estimated currently 73% of the total rho, the energy density, and contributing in that way (with all the other forms of energy) to the slowing down of expansion, it is also by its negative pressure contributing to the speeding up of expansion

 

And its accelerating effect dominates because of that number 3

in the equation (three comes from the number of spatial dimensions in the original GR equation)

and they calculate the figure of 0.73 because it is just the right amount

to produce the observed spatial flatness and the observed rate of acceleration.

 

I'm still celebrating the arrival of LaTex. Dark energy comes out of the Friedmann equation which with LaTex we can write recognizably, so my feeling is let us say what comes out of the equations, but maybe this dark energy homily has been delivered in another thread?

[Aeschylus]

Inflationary (that is acclerating expansion as opposed to inflation theory) Freidmann-Lemaitre cosmological models are nothing new, they've been around since the start of big bang theory, it's just that they never really tallied with observation.

[Martin]

Inflationary (that is acclerating expansion as opposed to inflation theory) Freidmann-Lemaitre cosmological models are nothing new, they've been around since the start of big bang theory, it's just that they never really tallied with observation.

 

I think you are right!

 

the simplest version of dark energy is an energy density that just corresponds to Einstein's cosmological constant

Einstein himself is supposed to have toyed with the idea of a positive cosmological constant with just this inflationary (or accelerative) effect.

I believe he thought of it as a way of keeping a static universe from collapsing

 

so Lambda has been waiting in the wings all this time and finally

in 1998 there were the supernovae observations so that at last it, as you say, "tallied with observation." wonderful story---human discoveries walk a crooked path to unimagined destinations