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Re: Cosmology



Regarding John Denker's Comments:

...
At 03:04 PM 2/12/01 -0500, David Bowman quite correctly pointed out that in
our non-imaginary universe we have additional observations; among other
things, we can observe deviations from the Hubble law.

I believe observations of neither positive nor negative values of the
so-called deceleration parameter q count as legitimate deviations from
the Hubble law, even though it means that the *observed* recession rate
of extremely distant galaxies divided by their *observed* distance is not
a strict proportionality. This is beause the Hubble 'constant' is
considered to be only 'constant' *in space*, *not* constant in time. The
Hubble parameter ('constant') is believed to change over billions of
years. If there is no cosmological constant, that change must be to
cause the Hubble parameter to decrease with increasing time. The only
way we can understand an accelerating universe that has the Hubble
parameter *increase* with time is to invoke a sufficiently nonzero value
[Br the CC (assuming the rest of GR is correct).

Nevertheless, when we look back at very distant galaxies, quasars, etc.
the value of the Hubble parameter was different when the light was
emitted from them than it is now when their light is being received by
us. Once this correction is made for the temporal evolution of the
Hubble parameter, it is understood that at each value of cosmic standard
time the recession velocity is strictly proportional to the proper
spatial distance between luminous objects (whose own local motions w.r.t
the cosmic expansion are taken as negligible). I *think* (since I'm not
a cosmologist, I'm not absolutely certain) it is *this* strict
proportionality between *proper distance* and recession velocity *at*
each instant of cosmic time that is supposed to count as the Hubble law,
(rather than the raw observations).

He also pointed out that a nonzero value of the Cosmological Constant is
non-Newtonian.

Questions for David: What value of the CC do you think is right? How well
established is this value? With what confidence can values with the
opposite sign be excluded?

I'm neither an astronomer nor a cosmologist, so I would not hazard any
guesses of my own about these things--esp. the confidence levels. But
*if* the constellation of typical numbers I have recently seen are
correct, (i.e. H_0 ~= 65 km/s/Mpc, [OMEGA]_m = 0.35, and
[OMEGA]_lambda = 0.65, with a spatially flat universe), then the value of
the CC would have to be

[LAMBDA] = 3*([OMEGA]_lambda)*(H_0/c)^2 = 9.6 x 10^(-53) m^(-2)
= 0.0086 (Gly)^-2

The repulsive acceleration constant B in the formula a = B*r (where a
is the strength of the cosmic free acceleration of a test particle away
from any origin in the absence of any gravitating sources, and r is the
displacement of the test particle from that origin) is given by:

B = (1/3)*[LAMBDA]*c^2 = 2.9 x 10^(-36) s^(-2)

This means that to have a repulsive acceleration of g = 9.8 m/s^2 away
from any fixed point (in our coordinate system) we would have to place
our test particle some 3.4 x 10^36 m = 3.6 x 10^20 ly away from that
point. This corresponds to about 10 orders of magnitude farther away
than the current proper observational horizon for the universe (assuming
that the other numbers above are close to being correct so that horizon
is properly calculated). This kind of shows how very small the CC really
is, if it really is nonzero after all.

(The last time I knew, if you asked 3
astronomers you would get 5 different CC values, and you could get several
more if you asked them again a year later.)

I don't know if this situation has changed recently or not. I kind of
doubt it.

David Bowman
David_Bowman@georgetowncollege.edu