Geometry of Look-Back

Not much work seems to be done nowadays on open (aka hyperbolic) or
closed (aka spherical) manifolds, but it's instructive to consider
what they would look like as a nightsky. The answer is they would
look just the same as flat space, but if one were to hop in a rocket
and travel out there, one would find that objects are closer than
their angular size indicates in an open manifold (i.e.,
"foreshortened"), and in a closed manifold they would be further away
than expected.

So nowadays we model that we can't visually distinguish at all between
these alternative curvatures. But spectroscopy illustrates how nature
finds ways to convey information -- astronomers of 100 years ago would
be astonished at how much signal there is in mere light. My
supposition is that there is indeed a visual way to distinguish
between open, flat, and closed manifolds, and that the cosmological
redshift shows us the way.

Regardless of all the complex constructs of standard cosmology, the
simple anchor is that cosmological redshift results from recession.
No recession, no big bang. So alternative viewpoints of the redshift
are not welcome to some -- which is no reason not to try, of course.

Lopez-Corredoira gave a useful review of static models in his paper
"Angular Size Test on the Expansion of the Universe" (2010
IJMP,19,245; arxiv:1002.0525) and observed (as have others) that 1/z
is well-fit to angular size across all redshifts -- without need of
evolution, dark matter, dark energy, whatever. Occam is calling.

So these are threads for me to follow, hopefully to assemble into a
coherent whole, after the holidays. cheers, Eric.

In article , Eric Flesch
writes:

Not much work seems to be done nowadays on open (aka hyperbolic) or
closed (aka spherical) manifolds,

What sort of work should be done?

Observations indicate that the universe is at least very close to
spatial flatness, which is probably why these models aren't mentioned
very much these days.

but it's instructive to consider
what they would look like as a nightsky. The answer is they would
look just the same as flat space, but if one were to hop in a rocket
and travel out there, one would find that objects are closer than
their angular size indicates in an open manifold (i.e.,
"foreshortened"), and in a closed manifold they would be further away
than expected.

Not just geometry but also expansion history determines the relation
between the angular and physical size of an object, for a given
redshift.

So nowadays we model that we can't visually distinguish at all between
these alternative curvatures.

The whole point of classical cosmology is to distinguish between such
models.

But spectroscopy illustrates how nature
finds ways to convey information -- astronomers of 100 years ago would
be astonished at how much signal there is in mere light. My
supposition is that there is indeed a visual way to distinguish
between open, flat, and closed manifolds, and that the cosmological
redshift shows us the way.

OK, classical cosmology also makes use of the redshift.

Regardless of all the complex constructs of standard cosmology, the
simple anchor is that cosmological redshift results from recession.
No recession, no big bang.

OK.

So alternative viewpoints of the redshift
are not welcome to some -- which is no reason not to try, of course.

You make it sound like the big bang is an assumption, but actually it is
a conclusion.

Lopez-Corredoira gave a useful review of static models in his paper
"Angular Size Test on the Expansion of the Universe" (2010
IJMP,19,245; arxiv:1002.0525) and observed (as have others) that 1/z
is well-fit to angular size across all redshifts -- without need of
evolution, dark matter, dark energy, whatever. Occam is calling.

The question is whether, within the observational errors, one can show
that 1/z is a better fit than, say, the current standard cosmological
model. Measuring angular size is easy. The hard part is determining
what physical size it corresponds to. This classical test has, due to
observational (not theoretical) difficulties not produced anything
useful up until now. (In some sense, CMB measurements are an
angular-size test, though.)

So these are threads for me to follow, hopefully to assemble into a
coherent whole, after the holidays. cheers, Eric.

We'll be looking for some testable predictions.

In article ,
Phillip Helbig---undress to reply writes:
The question is whether, within the observational errors, one can show
that 1/z is a better fit than, say, the current standard cosmological
model.

Exactly so. Substantial data sets of supernova distance moduli are
published, so at least a first test shouldn't be hard. The DMs are
luminosity distances, so one has to use some theory to convert to
whatever distance 1/z is supposed to represent.

Measuring angular size is easy.

In principle, at least. Not always so in practice.

The hard part is determining
what physical size it corresponds to. This classical test has, due to
observational (not theoretical) difficulties not produced anything
useful up until now. (In some sense, CMB measurements are an
angular-size test, though.)

Why only "in some sense?" I thought they were exactly an angular
size test. Also baryon acoustic oscillations (BAO). So far, both
are consistent with standard cosmology. Aren't CMB fluctuations one
of the reasons the standard cosmology is standard?

In the standard cosmology, angular size distance _decreases_ as
redshift increases beyond a certain value (around z=1.9 or so). If
1/z is the angular size distance, I wouldn't expect it to come
anywhere close to fitting beyond that even if it fits OK at smaller
redshifts. But there's no substitute for comparison with data.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA

On Tue, 18 Dec 12, Steve Willner wrote:
Exactly so. Substantial data sets of supernova distance moduli are
published, so at least a first test shouldn't be hard. The DMs are
luminosity distances, so one has to use some theory to convert to
whatever distance 1/z is supposed to represent.

A difficulty is that SN DMs are presented with the assumption that
redshift represents time dilation of the SNe. That this yields that
the most distant SNe have sub-par luminosities seems to ring no alarm
bells amongst the researchers. One of the models that I'm juggling
treats time dilation as the square root of the redshift, which would
restore the expected luminosities of the farthest SNe. If raw SNe
data were published instead of the redshift-processed stuff, that
would be a boon to testing alternative models.

Measuring angular size is easy.
In principle, at least. Not always so in practice.

Indeed, just today there's a new preprint
http://arxiv.org/abs/1212.3869 , "Evolution of the Sizes of Galaxies
over 7z12 Revealed by HUDF", in which the highest-z galaxies look
unresolved. They jump through hoops to resolve them, but it reminds
me of the "elliptical hosts" of many hi-z quasars which also look
unresolved. And in that paper they don't publish the raw angular
sizes, it's all presented as kPc after processing using the FRW model.
Oh, for just one graph of raw angular size vs z !!

Eric

In article ,
Eric Flesch writes:
A difficulty is that SN DMs are presented with the assumption that
redshift represents time dilation of the SNe.

Assumption? Light curves are consistent with time scales multiplied
by 1+z. Anything very different is inconsistent with the data.

That this yields that the most distant SNe have sub-par
luminosities seems to ring no alarm bells amongst the researchers.

Introducing an non-zero cosmological constant, when nearly everyone
up to then was convinced it was zero, isn't an "alarm bell?"

One of the models that I'm juggling treats time dilation as the
square root of the redshift,

Easily ruled out by the data.

If raw SNe data were published instead of the redshift-processed
stuff,

Raw data are published. For example, Astier et al. (2006 A&A 447,
31) give references to lots of light curves for nearby SNe. Reiss et
al. (2004 ApJ 607, 665; 2007 ApJ 659, 98) give light curves for z1
SNe. There are lots of others, though nowadays many groups publish
only distance moduli, not full light curves. It would take some
searching around to find more light curves, but quite a few are
available. You could probably get more if you asked for them.

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA

In article , Steve Willner
writes:

That this yields that the most distant SNe have sub-par
luminosities seems to ring no alarm bells amongst the researchers.

Introducing an non-zero cosmological constant, when nearly everyone
up to then was convinced it was zero, isn't an "alarm bell?"

Indeed!

Note also that the currently favoured value for the cosmological
constant predicts not just a dimming with redshift but, at large
redshift, a brightening. This is a very specific prediction, and hard
to get from other models of the dimming.

One of the models that I'm juggling treats time dilation as the
square root of the redshift,

Is there any physical motivation for this? There is a very clear
physical motivation for multiplying by (1+z).

It would take some
searching around to find more light curves, but quite a few are
available. You could probably get more if you asked for them.

These days, it isn't possible to publish all data in a paper journal.
However, probably most of the stuff is available, even back to the raw
data, either by asking or due to some observatory policy which makes all
data public after a certain time. Since only a minority need such data,
and when they do, probably in electronic form, I think it is OK not to
publish it conventionally.

In article , Steve Willner
writes:

The hard part is determining
what physical size it corresponds to. This classical test has, due to
observational (not theoretical) difficulties not produced anything
useful up until now. (In some sense, CMB measurements are an
angular-size test, though.)

Why only "in some sense?" I thought they were exactly an angular
size test. Also baryon acoustic oscillations (BAO). So far, both
are consistent with standard cosmology. Aren't CMB fluctuations one
of the reasons the standard cosmology is standard?

Yes. By "in some sense" I mean that there are other parameters
involved. In other words, the physical length of the "standard rod" is
not known in advance, but depends on some other parameters.