Dear Dr. Williams:

Title: Cosmological Implications of Classical Kaluza Relativity
Author(s): L. L. Williams

I have read your manuscript and I regret to say that it is not suitable for The
Astrophysical Journal. The exploration of alternative cosmologies is an important
and useful part of astrophysics, but in recent years the number of constraints
on any alternatives has risen sharply. Moreover the lunar ranging experiment
has establish upper bounds on the variation of G with time that rule out any
power law dependence on time with exponent of order unity. There are
additional constraints based on cosmological nucleosynthesis and the evolution
of stars which similarly indicate that G cannot vary as a power law in time.

Sincerely,

Ethan T. Vishniac
Editor-in-Chief

==========================================================

Ethan, thanks very much for your consideration.

Could I trouble you to provide reference for those results you
quoted? I regret to say I was unaware of them but I am of course
interested in them.

thanks

-Lance

======================================================

Hi,

What you want to do is go to http://adsabs.harvard.edu/abstract_service.html

and enter the search term "variation of the gravitational constant". Most of what

comes up will be accessible even without a subscription.

Ethan Vishniac, Editor-in-Chief

The Astrophysical Journal

=========================================================

Hi Ethan, I very much appreciate your feedback and references to the
literature.

I hope I would not be testing the limits of your patience if I were
to ask you to reconsider your decision on ApJ suitability for
publication, for the following reason.

The power law dependence of G on the cosmological time coordinate
that I calculate is for the early radiation-dominated universe, say
when the time is less than 1e5 years and the cosmological scale
factor is less than 1e-3.

While the radiation-dominated assumption is mentioned in the abstract
for the scale factor, it is not clearly stated for G as well. Perhaps
this prejudiced your evaluation. Below equation 14 in the manuscript
where these results are described, the radiation era assumption is
stated in deriving the power law dependence for G.

I took your comments to heart on the evidence regarding the time
dependence of G. Indeed, the LLR data show G constrained to vary less
than a part in 1e13 per year, but these data are for the current
epoch. I was unable to find data based on cosmological
nucleosynthesis which might constrain the evolution of G in the early
radiation-dominated era, but I did see many results of this type
constraining the fine structure constant.

Would you find these grounds for a reconsideration if I were to
clarify the regime of applicability of these calculations, in the
abstract and/or the title? Or have I misunderstood your evaluation?

thanks for your time and consideration

-Lance

========================================================

Hi,

You're right that I misinterpreted your manuscript and thought you were claiming

that G \propto t^{-2} at all epochs instead of only during the radiation dominated epoch.

However, this still fails the constraint imposed by primordial nucleosynthesis. See

Falik (1979) in ApJ Letters. He discusses a model in which G is inversely proportional

to time, but similar reasoning applies to your model as well. (The particular model

he discussed continued to limp along for some years. It had more free parameters

than he allowed for.)

Cheers

Ethan Vishniac, Editor-in-Chief

The Astrophysical Journal

========================================================

Thanks again, Ethan, for your review and reference. I have considered
the elegant arguments of Falik (1979), and it turns out that the
Kaluza-based results I report are not ruled out by the Falik
argument, and here's why.

Falik's argument is really a way to constrain the dependence of the
cosmological scale factor on cosmological time, a quantity called
a(t) in my paper. Falik originally considered a power law dependence
G \propto t^{-1} and from this form in the Friedmann equation,
deduced a \propto t^{1/4}.

Falik then goes on to argue that a certain product of temperature T
and time t (t T^4) must not preclude that T does not fall below 1e9
until t of 100 sec or so. If T drops below 1e9 much earlier, then not
enough helium can be produced to accord with observation. In Falik's
analysis, T drops to 1e9 at 1e-3 sec, and therefore refutes the model
with G \propto t^{-1}.

I found that when I used the canonical radition-dominated form of a
\propto a^{1/2} and formed the constant (t^2 T^4), and used Falik's
numbers, no contradiction ensues. Falik's argument only implies that
T dropped below 1e9 some time less than 1e7 sec.

Likewise, when I plugged in the Kaluza result I report of a \propto
t, the constant is then T^4 t^4. Falik's argument then implies T
dropped below 1e9 some time less than 1e12 sec.

So I find that Falik's result does not constrain all power law forms
G(t). What it does constrain is that any model which has a(t) varying
more weakly than t^{1/4} will be in conflict with observed helium
abundances. For the Kaluza results I report, G \propto t^2 and its
Friedmann implication of a \propto t, there is no contradiction of
helium observations, at least following Falik's arguments. Some other
argument or data is needed to validate models which have a varying
more strongly than the canonical dependence of a \propto t^{1/2}.

I remain appreciative of the time you have invested in explaining
your reasoning and understanding of the observational constraints. It
has better helped me to understand the Kaluza implications. Perhaps
you are aware of research that constrains a(t) in the
radiation-dominated universe for a varying strongly with t.

Had Falik's arguments, applied to the Kaluza results, led to a
contradiction, I would have gladly accepted your verdict. I hope you
will understand why, having not found any contradiction, I would
again ask you to reconsider acceptance of the paper in ApJ.

thanks again for your time and consideration

-Lance

Lance,

=========================================================

This isn't quite right.

If the universe is expanding too rapidly when the temperature drops below 10^9, then

the neutrons don't have time to decay after dropping out of thermal equilibrium, and

virtually all of them end up in He4 rather than decaying. This overproduces He4, by

a large amount.

If the universe is expanding too slowly, then the neutrons all decay before deuterium

becomes stable against photo-disintegration, and no He4 forms at all.

The arguments involved in this are quite sensitive. They don't give a limit on the

expansion rate so much as constrain it to lie within fairly narrow bounds. That is,

Falik's argument is much looser than it needs to be, since he was aiming at a

broad target. Other authors have used this same argument to show that there is

no room for a fourth species of light neutrino (a result supported, much later, by

measuring the width of the Z-boson decay).

The bottom line is that there is no room for a very different value of G at the time

of primordial nucleosynthesis.

Regards,

Ethan Vishniac, Editor-in-Chief

The Astrophysical Journal

==================================================================

Ethan, you will be relieved to hear that I understand what you are
saying, and I concur.

I found a couple recent articles, one using CMB anisotropy data,
another using deuterium abundance from quasar absorption data,
constraining the value of G to be within 10% or so of the current
epoch value. I guess in your previous messages I was getting hung up
on the expansion rate and the rate of change of G, not its absolute
value which I think you were driving at.

Thanks again for your patience and correspondence. I understand why
you don't want to publish any mathematical treatment in conflict with
data, but do you think the treatment would be of interest elsewhere?

best regards,

-Lance

============================================================

Lance,

You're very welcome. I've enjoyed the exchange.

I can't really answer your question. Put that way, the interest is in the

implications of this work for Kaluza-Klein theories rather than for

cosmology (since this particular model doesn't satisfy cosmological

constraints). You'll have to check with the editors of Classical and

Quantum Gravity (I think I have that name right).

Cheers

Ethan Vishniac, Editor-in-Chief

The Astrophysical Journal