# A de Sitter like Universe with matter

1. Aug 12, 2011

### johne1618

As I understand it the de Sitter model is a model of the Universe with:

rho = matter density = rho = 0

p = pressure = 0

k = spatial curvature = 0

cosmological constant = Lambda = non zero

Putting these values in the Friedmann equations one finds the solution for the scale factor a(t) is:

a(t) = exp( sqrt(Lambda c^2/3) * t)

This describes an accelerating empty universe with a non-zero cosmological constant.

Although this model has the right deceleration parameter q = -1 it is contrary to observations as we know there is matter in the Universe.

Now consider the following model:

p = - rho c^2

k = 0

Plugging these values into the Friedmann equations we find we are left with the following equation for the scale factor a:

a'^2 = a a''

This also has the solution:

a(t) = exp(H * t)

where

H^2 = 8 Pi G rho' / 3

where rho' = rho + Lambda c^2

Now this model describes a matter-filled accelerating Universe with no explicit cosmological constant provided that the equation of state of the matter is:

p = -rho c^2

Is this right?

Does this latter model describe the present Universe provided that p = -rho c^2 holds for present day matter?

In this model the negative pressure is associated with the particles of matter themselves rather than having a cosmological constant that is associated with the background space.

Perhaps the negative pressure is a zero-point energy phenomenon holding the individual particles of matter together (in the same manner as the Casimir effect pushes conducting plates together).

Last edited: Aug 12, 2011
2. Aug 12, 2011

### IsometricPion

The http://en.wikipedia.org/wiki/Einstein_field_equations" [Broken].

Last edited by a moderator: May 5, 2017
3. Aug 13, 2011

### Chalnoth

There's no difference between an empty universe with a cosmological constant and a universe that is filled only with matter that has negative pressure equal to its energy density. They are just two different ways of describing the same thing.

Just bear in mind that our own universe has quite a bit of normal matter that has no pressure on cosmological scales.

4. Aug 13, 2011

### johne1618

Maybe each baryon of normal and dark matter is held together by the excess pressure of zero-point gluon fields outside the particle. Thus there would be a region of negative pressure hiding inside every baryon in the Universe.

Last edited: Aug 13, 2011
5. Aug 13, 2011

### Chalnoth

But then matter wouldn't collapse and form structures.

6. Aug 13, 2011

### johne1618

Good point - I'll have to think about that one!