# Homogeneous universe solutions

An important difference between GR and GLET is the difference in their notions of a homogeneous universe. A homogeneous GR universe may be curved. Instead, a homogeneous GLET universe must be flat. This difference remains even in the GR limit of GLET. In this limit, the curved homogeneous universe solutions will be also solutions of the GLET equations — but, as GLET solutions, they will no longer be homogeneous. The point is that a homogeneous GLET solution must be homogeneous in the preferred (harmonic) coordinates.

Therefore in GLET only the flat universe may be homogeneous. Curved Friedman solutions describe inhomogeneous ether configurations. This justifies the use of the flat Robertson-Walker universe as the ansatz for the homogeneous GLET universe:

ds2 = dτ2 - a(τ)2( dx2+ dy2+ dz2)

To have a complete ansatz, we have to define also the preferred coordinates. They should be harmonic. In our case, the coordinates x,y,z are automatically harmonic. Harmonic time T may be easily computed as a function of proper time.

Note that we have, as in any physical theory, the full freedom of choice of coordinates. In the previous ansatz we have used this freedom — instead of the preferred coordinates, we have used the preferred spatial coordinates and proper time instead of preferred time. This makes it easier to compare the equations with the usual GR equations:

 3(a' ⁄ a)2 = -Υa-6 + 3Ξa-2 + Λ + ε 2(a" ⁄ a) + (a' ⁄ a)2 = +Υa-6 + Ξa-2 + Λ - kε

### Big collapse before big bang

For Υ > 0 we have time-symmetric solutions for the homogeneous universe like

a(τ) = a0cosh1/3((3Λ)1/2 τ)

(no matter and Ξ = 0). For a general situation with Υ > 0 we have a minimal value a0 for a(τ):

Υa0-6 = 3Ξa0-2 + Λ + ε

Thus, we have a big collapse before the big bang.

### Dark matter

With the Ξ-term we have a nice candidate for dark matter. AFAIU, this term may be used to explain an essential portion of the dark matter (but certainly not all).