As I understand it the de Sitter model is a model of the Universe with:(adsbygoogle = window.adsbygoogle || []).push({});

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).

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# A de Sitter like Universe with matter

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