In a message dated 7/30/2005 1:28:40 A.M. Eastern Daylight Time,
_&&&&&&&&@NETZERO.COM_ (mailto:&&&&&&&&@NETZERO.COM) writes:
But isn't inflation a form of a VSL theory since, iiuc, it posits that the
universe goes through a phase of > c expansion, followed by a < c expansion?
But that's the whole universe and not the *speed of light* per se! So if the
whole universe expands faster than c, but light perhaps does not, there is an
outside-to-slim chance that relativity is still in decent shape. However, for
completeness I should add the caveat that today the 'speed of light' no
longer means the 'speed of light', so I am on very firm ground to claim that I
don't know what I am talking about anymore. Finally, fwiw, inflation seems
awfully ad-hoc to be considered part of a satisfying *theory*. Who said physics
isn't fun?
============
In VSL theory mass energy is not conserved during the expansion and it is
this violation of mass energy conservation that drives omega to unity. This can
be seen from the equation
Here the important thing to notice is the rate of change of the energy
density as a function of the rate of change of c goes to zero when K , the
curvature term , goes to zero. This terminates the energy non conservation.
Now in inflation it is the conservation of energy that drives the inflation.
A constant vacuum energy density requires a corresponding negative pressure
which is what drives the inflation.
This can be seen from
-3(d^2/dt^2)=4*Pi*G*(rho+3*P/c^2)*a
Now I agree with you there is a rather ad hoc component to inflation theory.
However, a rather nutty idea I am playing around with is tying the vacuum
energy to CP violation which might be more natural, at least I think so.
However, we know so little about the origin of matter in the early Universe ,
Leptogenesis verses baryongenesis etc. that it's only the crudest hand waving
argument.
The cosmological constant is related to the vacuum energy by
Lamda=kappa*rho_vac
It can be shown that vacuum energy is given by
rho_vac=(N_b-N_f)*(1/4*pi^2)*INTEGAL { 0 to K_c) w*k^2dk
Where N are the degrees of freedom for bosons and fermions and K_c is the
cutoff wave number, perhaps at the Planck scale.
This of course generates a huge vacuum energy density so something is
very wrong here.
The "standard " answer from SUSY is that
N_b-N_f=0
which eliminates the vacuum energy. The problem with this is that SUSY is a
broken symmetry which still predicts an unacceptably high vacuum energy in the
Universe today. This suggest to me that perhaps there is a new symmetry ,
that is scale invariant , which zeros out the vacuum energy.
In 2003 I posted to the University of Washington physics list the idea
that perhaps we get a zero vacuum energy because the virtual processes include
both positive and negative energy states. I called this the zero sum
Universe. Of course negative energy states in QFT don't work very well and negative
energy particles generate problems like negative probabilities. But if we
restrict these negative energy states to the "unreality " of virtual states
then this is just another way of talking about a symmetry that zeros out the
vacuum energy when a measurement process doesn't occur.
Well this idea has now been proposed by Bob Klauber and even more recently
John Moffat ( the original VSL guy).
So assuming any of this makes sense I propose that perhaps this symmetry
which is related to time symmetry is weakly broken by CP violation which is
generating the small cosmological constant we may be seeing today in our
Universe. It might go like this.
Postulate a cp factor F_cp which is a function of the CP violation phase
angle. Then
For algebraic simplicity let
N_b-N_f=M and C=(1/4*Pi^2)*INTEGRAL {0 to K_c} w*k^2dk
We can propose that
rho_vac= (1+F_cp)*M*C -(1-F_cp)*M*C = 2*F_cp*M*C
Giving us a cosmological constant
Lamda= (1/2)*kappa*F_cp*M*K_c^4
And we have reason to think that CP violation had a larger magnitude in the
early Universe so this might explain inflation and the current acceleration of
the expansion rate in a unified model. HOWEVER, this is nice and good, but a
believable explanation is needed to connect virtual processes and CP
violation and I still don't have a clue how to do this qualitatively or
quantitatively. At this point it's all just a speculation.