Speaking of Statistical Significance!

In article ,
"Phillip Helbig (undress to reply)" writes:
From a completely different point of view, my latest paper
(arXiv:1505.02917) also argues that uncertainties in the cosmological
parameters are larger than is generally assumed.

Very nice paper. If I understand it, something I hadn't appreciated
before is that what the SN results _by themselves_ really do is
constrain [lambda - Omega] to a value near 0.4 while not strongly
constraining the individual values of lambda and Omega. Combining
the SN results with flatness (from the CMB, requiring [lambda +
Omega] = 0) is what gives the concordance values. If you ignore the
flatness constraint, the SN results still require a positive lambda
but maybe not as large as 0.7.

By the way, I goofed in my earlier message trying to translate "w =
-1" to English. I should have written _metric_, not co-moving,
coordinates. Existing evidence is consistent with dark energy being
a cosmological constant, and there is no significant evidence for any
other form of dark energy.

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

In article ,
"Phillip Helbig (undress to reply)" writes:
I'm not sure what you mean by your last sentence.

I meant that w = -1 (consistent with dark energy being a cosmological
constant) to within the uncertainties.

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

On Tuesday, June 16, 2015 at 11:21:05 AM UTC-4, Phillip Helbig (undress to =
reply) wrote:
=20
However, as George Efstathiou pointed out, any alternative theory has to=
=20
explain at least as much as the "standard model" does. He then made an=20
interesting offer: "If your model explains everything the standard model=
=20
does, then I will give you a job."

Being able to reproduce the successes of the old paradigm is always
nice, but what a new paradigm must do initially is to explain things
the old paradigm cannot, such as the explicit nature of the dark
matter, dark energy (if it exists at all), how to reconcile GR and
QM, galactic physics, stellar physics, etc.

RLO
Fractal Cosmology

In article , Steve Willner
writes:

In article ,
"Phillip Helbig (undress to reply)" writes:
From a completely different point of view, my latest paper
(arXiv:1505.02917) also argues that uncertainties in the cosmological
parameters are larger than is generally assumed.

Very nice paper.

Glad you enjoyed it.

If I understand it, something I hadn't appreciated
before is that what the SN results _by themselves_ really do is
constrain [lambda - Omega] to a value near 0.4 while not strongly
constraining the individual values of lambda and Omega.

Right. The CMB has a similar degeneracy, constraining lambda+Omega
quite strongly. Since these two degeneracies are orthogonal, the result
is a small region of overlap. BAO constraints are at about 45 degrees
to these, and it is a great demonstration of consistency that these
cross the other two constraints where those other two constraints cross
each other.

Combining
the SN results with flatness (from the CMB, requiring [lambda +
Omega] = 0) is what gives the concordance values.

Right. And Omega works out to be about 0.3, which is what observers
have been telling us for decades. And these values of lambda and Omega
together with the value of the Hubble constant (however measured) give
an age of the universe a bit older than the oldest objects we have
discovered.

If you ignore the
flatness constraint, the SN results still require a positive lambda
but maybe not as large as 0.7.

Right. I think they are also the only test which, by themselves,
require a positive lambda at high significance. Interestingly, this is
still the case even with the relaxed assumptions involving homogeneity,
as I showed in my paper. However, one gets good compatibility with the
concordance value only if local homogeneity holds (in some appropriate
sense). Interestingly, the best-fit value, again assuming local
homogeneity, is very close to the concordance value.

By the way, I goofed in my earlier message trying to translate "w =
-1" to English. I should have written _metric_, not co-moving,
coordinates.

So you meant:

Observational tests show that
the acceleration is positive and its time variation (in metric
units) smaller than can be measured.

I THINK I know what you mean now, but some might still be confused. I
don't think you mean metric units as opposed to Imperial units. :-)

Existing evidence is consistent with dark energy being
a cosmological constant, and there is no significant evidence for any
other form of dark energy.

Right. The pure cosmological constant has w = -1. Is this what you
meant by time variation? If so, I still don't get the "metric" bit.

However, even if w = -1, this doesn't mean that the time variation of
the acceleration is negligible.

By the way, my article was officially published online a few days ago;
you should be able to access a FREE version of the FULL PAPER he

abstract with links to HTML and PDF:

http://mnras.oxfordjournals.org/cgi/...NL&keytype=ref

HTML:

http://mnras.oxfordjournals.org/cgi/...NL&keytype=ref

PDF:

http://mnras.oxfordjournals.org/cgi/...NL&keytype=ref

However, you might have to clear your browser cache and/or delete some
obviously named cookies in order to make it work, especially if
following the other links from the abstract.

In article ,
"Robert L. Oldershaw" writes:

On Tuesday, June 16, 2015 at 11:21:05 AM UTC-4, Phillip Helbig (undress to
reply) wrote:

However, as George Efstathiou pointed out, any alternative theory has to
explain at least as much as the "standard model" does. He then made an
interesting offer: "If your model explains everything the standard model
does, then I will give you a job."

Being able to reproduce the successes of the old paradigm is always
nice, but what a new paradigm must do initially is to explain things
the old paradigm cannot, such as the explicit nature of the dark
matter, dark energy (if it exists at all), how to reconcile GR and
QM, galactic physics, stellar physics, etc.

The more the merrier. Still, explaining the old paradigm with a
"better" theory is also quite an accomplishment.

To test theories, of course, we need predictions which are unique to the
theory. To even be worth testing, though, it has to explain the old
paradigm.

George's point was that most new theories can't even do this.
Tailor-made theories might explain, say, the m-z relation for type Ia
supernovae without a cosmological constant, but they should also be able
to calculate the CMB power spectrum and so on.

On Thursday, June 18, 2015 at 12:32:12 AM UTC-4, Phillip Helbig (undress to=
reply) wrote:
=20
George's point was that most new theories can't even do this.=20
Tailor-made theories might explain, say, the m-z relation for type Ia=20
supernovae without a cosmological constant, but they should also be able=
=20
to calculate the CMB power spectrum and so on.

And here is my point. If you look at most new paradigms that deserve
this appellation, i.e., an overarching new conceptual framework
that unifies existing knowledge for a whole field in an elegant
manner, then you will find that the new paradigm begins with one
or a very small number of people working on it.

The new paradigm must eventually retrodict all well-tested empirical
results, but it is not expected that the one person working alone
or with a small group of co-workers can prove this immediately.

The new paradigm must first solve major unsolved problems using its
new conceptual framework.

The new paradigm must also make definitive predictions that are
feasibly tested, prior to testing, quantitative, non-adjustable,
and unique to the new paradigm.

Typically the older paradigm has had a large number of people working
very hard over many decades to adjust the paradigm (via model-building)
so as to fit all well-tested empirical data. It often looks like
an unassailable model. However there are cracks in its formidable
foundation as revealed by observational discoveries that it cannot
easily accommodate (although its proponents with go to great lengths
to attempt that).

The above explains why new paradigms are usually at a great
disadvantage with respect to the older paradigm. However, if the
new paradigm truly represents a major advance, it will win out in
the end, although this result may be delayed for years, decades or
even centuries.

RLO
Fractal Cosmology

In article ,
"Phillip Helbig (undress to reply)" writes:
The pure cosmological constant has w = -1. Is this what you
meant by time variation? If so, I still don't get the "metric" bit.

It's sometimes hard to translate the math into words, and I may have
it wrong, but I think we went through this some months ago.

As I understand the situation for a pure cosmological constant, if
you consider two points in empty space one meter apart, those points
will be accelerating away from each other at a constant rate,
regardless of the cosmic epoch. Of course you have to pick
successively different points over time as the two you started with
move continuously farther apart. I used "metric" to mean keeping
this constant separation. (Perhaps think of space "flowing past" a
meter stick of constant length.) The opposite case "comoving" refers
to keeping 1tracking the original points; I would say the "metric
distance" or "proper distance" between them grows _at an increasing
rate_ over time.

If the dark energy is something other than a cosmological constant,
the acceleration will in general have a different time dependence.
Ultimately the observational data will tell us what the universe is
doing.

--
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:

The pure cosmological constant has w = -1. Is this what you
meant by time variation? If so, I still don't get the "metric" bit.

It's sometimes hard to translate the math into words, and I may have
it wrong, but I think we went through this some months ago.

Maybe.

As I understand the situation for a pure cosmological constant, if
you consider two points in empty space one meter apart, those points
will be accelerating away from each other at a constant rate,
regardless of the cosmic epoch.

No. Consider the standard version of the standard model, or any other
universe with non-zero matter content and a cosmological constant. For
some time after the big bang, it will DEcelerate. As z approaches
infinity, i.e. the big bang, the physical matter density overwhelms
everything else. (This is one aspect of what some see as the "flatness
problem", i.e. all non-empty big-bang models (with or without a
cosmological constant) start out arbitrarily close to the Einstein-de
Sitter model). After a time, the effects of the cosmological constant
will become more important. This is because matter is thinned out by
the expansion of the universe, but the cosmological constant is, well,
constant. (That is why it is called the cosmological constant; it is
constant in time. The Hubble constant, on the other hnad, is in general
not constant in time, but is called a constant because at any given time
it is a constant when plotting observable quantities as a function of
redshift, like m is constant in y = mx+b.) At some point, the
acceleration due to the cosmological constant will be larger than the
deceleration due to matter. The limiting case, when matter is too thin
to matter (pun, as always, intended), is the de Sitter universe, which
has exponential expansion. Since "constant acceleration" implies that
the third derivative is zero (and the second constant), this is
obviously not true of exponential expansion. In other words, even
without the complication of matter, there isn't constant acceleration.

So, obviously, if the universe first decelerates then accelerates, there
is no constant acceleration. This wouldn't even be the case if there
were no matter.

In the case of the de Sitter universe, the Hubble constant is actually
constant in time. It is defined as \frac{\dot R}{R}, and of course this
is more or less the definition of the exponential function (i.e. all
derivatives are proportional to the value of the function).

Of course you have to pick
successively different points over time as the two you started with
move continuously farther apart. I used "metric" to mean keeping
this constant separation. (Perhaps think of space "flowing past" a
meter stick of constant length.) The opposite case "comoving" refers
to keeping 1tracking the original points; I would say the "metric
distance" or "proper distance" between them grows _at an increasing
rate_ over time.

Yes, but a) only after the deceleration phase and b) not at a constant
acceleration.

If the dark energy is something other than a cosmological constant,
the acceleration will in general have a different time dependence.
Ultimately the observational data will tell us what the universe is
doing.

Right.

In article , Steve Willner
writes:

From a completely different point of view, my latest paper
(arXiv:1505.02917) also argues that uncertainties in the cosmological
parameters are larger than is generally assumed.

Very nice paper. If I understand it, something I hadn't appreciated
before is that what the SN results _by themselves_ really do is
constrain [lambda - Omega] to a value near 0.4 while not strongly
constraining the individual values of lambda and Omega. Combining
the SN results with flatness (from the CMB, requiring [lambda +
Omega] = 0) is what gives the concordance values. If you ignore the
flatness constraint, the SN results still require a positive lambda
but maybe not as large as 0.7.

Right, as mentioned previously in this thread. However, the best-fit
values for lambda and Omega using just the supernova data (specifically,
the publicly available Union 2.1 data set), if one assumes a completely
homogeneous universe, are lambda=0.721 and Omega=0.277. The sum is
0.998, where 1.000 corresponds to a flat universe. I think that this
agreement is remarkable. Of course, this is just the best-fit value,
and even the one-sigma error ellipse allows models which are ruled out
at several sigma from other tests.

I'm not sure what this means. It might be just chance. It could mean
that the observational uncertainties in the supernova data have been
overestimated. Compared to the original papers of the two teams which
claimed evidence for positive lambda, not only have the error ellipses
grown smaller with more and higher-redshift data, but also the best-fit
value has moved. Of course, with more and better data one expects the
best-fit value to move, but to be compatible, within the errors, with
the older data. The interesting thing is, because we know the values of
the concordance parameters very well completely independent of the
supernova data, in the future we do NOT expect the best-fit values to
change appreciably, but DO expect the error ellipses to grow smaller.

In article ,
"Phillip Helbig (undress to reply)" writes:
Consider the standard version of the standard model, or any other
universe with non-zero matter content...

Thus proving how hard it is to discuss this stuff in words. In the
earlier discussion, I thought it was clear from the context that we
were discussing _only_ the effect of the cosmological constant, not
anything about matter.

Now considering an empty universe with the dark energy being a
cosmological constant and nothing else:
The limiting case, when matter is too thin to matter (pun, as
always, intended), is the de Sitter universe, which has exponential
expansion.

Exponential in what I've called "comoving coordinates." Divide by
the scale factor to get what I called "metric coordinates," and the
result is...?

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