homogeneity: if the Universe were inhomogeneous one would not expect

to see a uniform expansion”

I do not know if universe is homogeneous or fractal. However, I would add to your comment of above that precisely Baryshev and others showed that the field theory of gravity (FTG), worked by Feynman and others, can explain the Hubble law for fractal structures with D=2. Therefore the verification of the law

cannot be taken as a verification of homogeneity.

PCSz did indeed have the advantage of being nearly all-sky, but it was also extremely sparse. Pan did a really good job on that analysis, I think. He did most of the hard work on it, actually. I just wrote the paper.

Peter

]]>I’ve checked the strategy of the Las Campanas Redshift Survey (Shectman at al., ApJ, 470, 172, 1996), and there were more narrow strips on the sky than I remembered. There were three strips in the South Galactic Cap region, each about 1.5 deg wide and separated by about 1.5 deg. This would give a thicker overall sampled volume than I had thought, and with with a complicated geometry. This illustrates the danger of sounding off without having read the literature that I mentioned above.

Of course, a proper analysis would require a detailed description of the survey boundaries and probably Monte Carlo simulations. And surely that has been done in the published studies.

Your choice of the IRAS PSCz catalogue for your work with Pan was very sensible: the all-sky character lessened the issues of survey geometry (but the problems of dust absorption near the Milky Way would have imposed some residual problems). A student doing his M.Sc. dissertation on redshift surveys with me a few years ago showed interest in your work and I had thought he might want to try some simulations of his own in that subject area. However, he ran out of time and his dissertation was mostly a critical review of the recent scientific literature on redshift surveys.

Bryn.

]]>It’s a bit more complicated that the fractal dimension just reflecting the survey geometry, but it is an issue because it requires you to think about how to deal with boundary effects when trying to estimate *D*. In other words you have to be very careful in what you say about the fractal dimension on scales larger than the smallest dimension of the survey. This is where there’s a strong divergence between the pro-fractal groups and the more orthodox ones. As I’ll explain in a later post if I’ve got time, the effective dimension you get from newer data clearly varies with scale and tends to 3 on large scales, implying that there is a scale at which homogeneity is reached. In fact when I was at Nottingham me and my student Pan (remember him?) showed that this was true of the PSCz survey (which is all-sky so doesn’t suffer from the flatness problem).

Peter

]]>It is usually extremely dangerous to discuss scientific results without reading the original papers, but wouldn’t D =~ 2 be expected from the Las Campanas Redshift Survey as an inevitable consequence of the survey’s strategy? I do recall that the Las Campanas survey used declination strips across the sky: that is to say they measured redshifts of galaxies lying in narrow strips on the sky (a sensible strategy in the face of limited observing time). The volume of the Universe sampled therefore consisted of rather flat wedges.

Surely D = 2 for such a wedge once the radius R is larger than the typical thickness of the wedge? Perhaps Sylos-Labini et al. considered that in their analysis?

(Of course, your discussion is now 12 years old and we have incomparably better results from the 2dFGRS and the SDSS.)

Bryn.

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