       model for early cosmological symmetry breaking as a 3d surface

• To: mathgroup at smc.vnet.net
• Subject: [mg101979] model for early cosmological symmetry breaking as a 3d surface
• From: Roger Bagula <roger.bagula at gmail.com>
• Date: Sat, 25 Jul 2009 04:16:23 -0400 (EDT)

```http://www.flickr.com/photos/fractalmusic/3743178759/

This model is a Lorentzian model for the SO(8)
that existed after SU(6)
broken symmetry gave:
SU(6)->U(1)*SU(2)*SU(5)~ SO(8)
where the constant e broke into G gravity constant ~10^-8 ( a force
that attracts)
and Gstar tachyon constant ~10^-12 ( a force that repels).
Some where after Pi solidified at the present valure at t=10^(-11)
second.
The first inflationary era of cosmology.
The second era is the standard model  breaking:
SU(5)->U(1)*SU(2)*SU(3)

What I did was put in likely values and
plot as a 4d Clifford torus projection.
The x and y are each representations of three spacial dimensions.
The resulting surface looks like a bent pseudosphere.
Mathematica:
Clear[x, y, c, tau, t, vg, vp, gamma, n]
(* basic velocity and cordinates as cyclic on radius one*)
x = Cos[t];
y = Cosh[tau];
vg = 1/Sqrt;
gamma = vg2/c2;
c = 1;

(* Lorentz: negative curvature: vg=group velociry <c*)
x1 = (x - vg*t)/Sqrt[1 - vg2/c2];
t1 = (t - vg*x/c2)/Sqrt[1 - vg2/c2];
FullSimplify[x12 - c2*t12]

(* anti - Lorentz: positive curvature : vp=phase velocity>c*)
y1 = (y + vp*tau)/Sqrt[1 + vp2/c2];
tau1 = (tau - vp*y/c2)/Sqrt[1 + vp2/c2];
FullSimplify[y12 + c2*tau12]

(* tachyonic phase velocity*)
vp = c2/vg - ((1 - gamma)/(1 + gamma))*vg
(* Lorentz 4d Clifford torus projection*)
g0 = ParametricPlot3D[{x1/(Sqrt - c*tau1),
y1/(Sqrt - c*tau1), c*t1/(Sqrt - c*
tau1), {EdgeForm[]}}, {t, -Pi, Pi}, {tau, -Pi, Pi}, Boxed -> False,
Axes -> False]
g1 = ParametricPlot3D[{-x1/(Sqrt[
3] - c*tau1), y1/(
Sqrt - c*tau1), -1 - c*t1/(Sqrt - c*tau1), {EdgeForm
[]}}, {
t, -Pi, Pi}, {tau, -Pi, Pi}, Boxed -> False, Axes -> False]
Show[{g0, g1}, ViewPoint -> {-0.047, 3.170, 1.184}]
Show[{g0, g1}, ViewPoint -> {-1.314, 2.830, 1.310}]

I'd like to put in a plug for the Mathematica programming yahoo group:
http://tech.groups.yahoo.com/group/Active_Mathematica/

```