The hypothesis that the universe is expanding, taken by itself –-that is taking this hypothesis alone--makes very few testable predictions.
"that hypothesis alone" is sort of odd. You can imagine hypothesizing a sort of clockwork universe. "The creator has glued all of the galaxies to mysterious mounting-pegs, and then arranged some unseen clockworks to move the pegs apart according to some formula." Sure, in that case there are very few predictions. But nobody (I hope not you) seems to hypothesize that.
The more sensible hypothesis is "things are moving apart
governed by some regular laws of motion". And here your statement is wrong. If you hypothesize that the law of motion is "the usual one", i.e. GR, which seems parsimonious, you get a very tightly constrained world in which to make predictions---indeed, under this assumption,
any initial-condition hypothesis you which to make can be easily turned into a suite of predictions.
One very well-known one is that the surface brightness of objects drops as (1+z)^3. Equivalently, it makes quantitative predictions about the apparent size of objects of a given luminosity.
That is not a generic expansion hypothesis. That is a very specific expansion hypothesis---it corresponds to the hypothesis that things are flying apart (to use Newtonian language) without being decelerated by (e.g.) their mutual gravitational attractions. That sounds like the sort of thing we should be testing rather than assuming.
My colleagues and I assumed z, redshift, is linearly proportional to distance at all distances (as we know it is at small z).
What an odd assumption. What actual physics does this correspond to? Do you suppose that gravity is just "turned off" and unable to affect large-scale structure?
This relationship fits the data set of apparent magnitudes vs redshift of the supernova 1a data just as well as the LCDM model does, and it is almost mathematically indistinguishable from those predictions for that data set.
"almost" is doing a lot of work in that sentence. Your expansion history is the "empty universe" one, and yes it's been tested. It's known to be
close to the data but it is NOT a match. It corresponds precisely to the "omegaM = omegaL = 0" hypothesis in mainstream cosmology, which is ruled out at high confidence on the supernova data alone. (Note: these contours include systematic errors. If you think it's "almost" a match based on statistical errors alone, you're even more wrong.)
http://supernova.lbl.gov/Union/figures/Union2.1_Om-Ol_systematics_slide.pdf
It however has the Occam’s razor advantage that it fits the data set using only one adjustable parameter—the Hubble constant—while LCDM requires 3 adjustable parameters—H, the density of matter(including dark matter) and the energy density of “dark energy”. If you accept the LCDM model, the fact that the non-expanding model with linear Hubble relation fits just as well has to be considered a big coincidence.
Part of this is the well-known "cosmic coincidence"---why are omega_M and omega_L anywhere in the same ballpark? 0.3 and 0.7? Why aren't they, say, 0.01 and 0.99? Or 10^-9 and 0.9999999? Nobody knows and this is an active debate. But for your purposes, "hey the supernovae don't rule me out too badly" is precisely this
one-parameter coincidence. Any cosmology for which "the blue supernova blob is nearer the middle than the corners" will prompt your claim of a coincidence. (The actual "it's a coincidence" parameter moves the blue blob back and forth the black "flat-space" line. You mention that LCDM has an extra fit parameter---and indeed it does, constraining the blob to lie
near the line rather than far from it---apparently confirming the predictions of inflation.)
Also, I repeat,
given that we know that the Universe isn't devoid of matter, what makes you think a zero-deceleration, Omega_M=0 model is parsimonious? Do you have a hypothesis telling us to turn gravitational attraction off? We know galaxies are massive, right?
The data set of disk galaxies, discussed in our published paper, and the data set of elliptical galaxies, taken from others work and used in this presentation, both show no change in surface brightness with distance. So the simple, no-parameter prediction of the non-expanding hypothesis is confirmed with these two data sets.
Discussed in your published paper which
arbitrarily assumes it can treat galaxies as standard candles. Serious file-drawer effect here, Eric: if your analysis had concluded that there
was surface brightness evolution, you'd have say "oops, I guess those weren't good candles". For all we know you did that with a bunch of different datasets.
So, to fit these two data sets, the non-expanding hypothesis takes no free parameters,
a) Your decision to turn off gravity (or set Omega-M=0) is a
parameter choice, Eric.
b) These are not "two data sets", they are two different candles measuring a single expansion history. They are degenerate in the Bayesian sense.
c) There are dozens of astrophysical systems which in principle can test cosmological theories. You chose
one, i.e. the late-time redshift-distance relation. In stats this raises the issue of "p-hacking". If you have dozens of tests to choose from, it's easy to find one that happens to sort-of-match. Saying "I found a test where my theory is only ruled out at 99%, could be worse, so nyah nyah" is not particularly surprising, and does not make me excited about your theory.
! It is never time to switch to a bunch of "plasma cosmology" (note the small p) that cannot match fundamental observations about the universe, e.g. the temperature, black body spectrum and power spectrum of the CMB.
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