CMB radiation and the program CAMB.

The program CAMB is used to calculate the Power Spectrum of the CMB radiation
mainly based on three parameters: H0, Omega(K) and Omega(m).
Omega(m) being the sum of omega(Baryon) and Omega(CDM).
With the aid of the program CAMB and the Power Spectrum calculated from
the Observed CMB radiation and with H0 calculated based on observations
it is possible to calculate Omega(K), Omega(Baryon) and Omega(CDM)

However this whole procedure raises certain issues.
1. The program CAMB allows for a continuous range of values for
omaga(k). Using Friedmann's equation this means that the parameter
k also should allow a continuous range of values.
This is strange while the only correct values are k=-1, 0 and +1.
2. My impression is that the CMB radiation is a much more powerfull
tool than Supernovae of type 1A.
Using CMBR data you can not only calculate Omega(m) but also omega(B)
and omega(C).
The way this is done generally speaking is by trying different
values for these parameters and using CAMB. The result is that they
do not match with the Observed Power Spectrum, meaning that they must
be wrong. That is most probably true but that does not mean that the
parameters that match the Observed PS are correct because there is no
prove that all the underlying equations of CAMB are correct.
3. The basic problem with the Supernovae data is the relation
between Luminosity and magtitude as a function of luminosity distance.
Literature shows that there are two equations used to calculate the
cosmological parameters. Those results are different meaning that
supernova data is almost not used.
The cause is dispersion/reflection i.e. the fact that photons don't follow
straight lines. I agree that this is a problem for supernovae data.
But I also think that it is a much more severe problem for CMB radiation
data, meaning IMO that it is much more difficult for example based
on CMBR data to claim that k=0 than based on supernovae data.

For more detail about the problems involved go to:
http://users.telenet.be/nicvroom/Ome...and%20CMBR.htm

Nicolaas Vroom

In article , Nicolaas Vroom
writes:

The program CAMB is used to calculate the Power Spectrum of the CMB radiation
mainly based on three parameters: H0, Omega(K) and Omega(m).
Omega(m) being the sum of omega(Baryon) and Omega(CDM).
With the aid of the program CAMB and the Power Spectrum calculated from
the Observed CMB radiation and with H0 calculated based on observations
it is possible to calculate Omega(K), Omega(Baryon) and Omega(CDM)

CAMB is one example of such a program. A very good one, but it is good
to keep in mind that your questions don't necessarily apply to CAMB only
but to the whole basic idea which is expressed in CAMB.

1. The program CAMB allows for a continuous range of values for
omaga(k). Using Friedmann's equation this means that the parameter
k also should allow a continuous range of values.
This is strange while the only correct values are k=-1, 0 and +1.

How is k defined? Some people use it as you do, others use it to be the
sum of lambda and Omega. I prefer the lower-case k for the former and
the upper-case K for the latter. Some people use K to mean what by my
definition would be 1-K.

2. My impression is that the CMB radiation is a much more powerfull
tool than Supernovae of type 1A.

To some extent, yes. However, the CMB is good at measuring the sum of
lambda and Omega but not differentiating them. One can also measure H
from the CMB but, as you point out, putting in H measured elsewhere
improves matters. The values of lambda and Omega from SNIa do not
depend on H at all.

Using CMBR data you can not only calculate Omega(m) but also omega(B)
and omega(C).
The way this is done generally speaking is by trying different
values for these parameters and using CAMB. The result is that they
do not match with the Observed Power Spectrum, meaning that they must
be wrong. That is most probably true but that does not mean that the
parameters that match the Observed PS are correct because there is no
prove that all the underlying equations of CAMB are correct.

What do you mean by proof? (I assume "prove" should be "proof".) There
is a HUGE literature on this subject.

3. The basic problem with the Supernovae data is the relation
between Luminosity and magtitude as a function of luminosity distance.
Literature shows that there are two equations used to calculate the
cosmological parameters.

Which two equations?

Those results are different meaning that
supernova data is almost not used.

What do you mean by "not used"? Not used by CAMB, sure, but then the
supernova people don't use CAMB.

The cause is dispersion/reflection i.e. the fact that photons don't follow
straight lines. I agree that this is a problem for supernovae data.

This is a practically non-existent problem. If you are talking about
gravitational lensing, then it is taken into account in CAMB. If you
are referring to the effects of inhomogeneity on the SNIa results, then
note that these authors also took this into account. If you are talking
about some sort of scattering, then strong upper limits are placed by
the fact that distant objects are not blurred.

But I also think that it is a much more severe problem for CMB radiation
data, meaning IMO that it is much more difficult for example based
on CMBR data to claim that k=0 than based on supernovae data.

Actually, k=0 (or K very close to 0) is one of the most robust results
from the CMB.

Op zaterdag 12 januari 2013 09:33:37 UTC+1 wrote Phillip Helbig:
In article , Nicolaas Vroom
writes:

1. The program CAMB allows for a continuous range of values for
omaga(k). Using Friedmann's equation this means that the parameter
k also should allow a continuous range of values.
This is strange while the only correct values are k=-1, 0 and +1.

How is k defined?
For the definition that k is only -1,0 or +1 See:
a) http://nicadd.niu.edu/~bterzic/PHYS652/Lecture_05.pdf
b) The Big Bang by Joseph Silk
c) Introducing Einstein's Relativity by Ray d'Inverno.

The url http://background.uchicago.edu/~whu/...curvature.html
gives the impression that all O_k values are valid. In reality which each
O_k value belongs a "k value". Only k = -1,0 and 1 are valid.

2. My impression is that the CMB radiation is a much more powerfull
tool than Supernovae of type 1A.

To some extent, yes. However, the CMB is good at measuring the sum of
lambda and Omega but not differentiating them. One can also measure H
from the CMB but, as you point out, putting in H measured elsewhere
improves matters. The values of lambda and Omega from SNIa do not
depend on H at all.

IMO they all depend on each other except Lambda,C,k and the age of the Universe.
See the end of my comments.

Using CMBR data you can not only calculate Omega(m) but also omega(B)
and omega(C).
The way this is done generally speaking is by trying different
values for these parameters and using CAMB. The result is that they
do not match with the Observed Power Spectrum, meaning that they must
be wrong. That is most probably true but that does not mean that the
parameters that match the Observed PS are correct because there is no
prove that all the underlying equations of CAMB are correct.

I understand that CAMB uses a type of friedmann equation with more parameters
included (For example Background temperature)

What do you mean by proof? (I assume "prove" should be "proof".) There
is a HUGE literature on this subject.

Consider: http://background.uchicago.edu/~whu/...curvature.html
This page demonstrates that k=0 and O_k=0 (flat universe)
This is done by modifying O_k. The result are power spectra which do not
match the observed power spectra. The conclusion is that O_k must be zero
and that k=0.
The problem is how do we know that the calculations based on O_k are correct.
Specific how do we know that the calculated power spectra are correct.
The problem is we do not know. This can not be tested.

May be this is not a problem for omega(k), but definitif a problem for
omega(B) versus omega(C)


3. The basic problem with the Supernovae data is the relation
between Luminosity and magtitude as a function of luminosity distance.
Literature shows that there are two equations used to calculate the
cosmological parameters.

Which two equations?
See http://arxiv.org/abs/1001.4538 7 Year WMAP - Cosmological Interpretions.
Page 14
What I mean are the 2 light curve fitters SALT2 and MLCS2K2.

For more detail about SALT2 see also: http://arxiv.org/abs/1010.4743
specific page 16 is interseting.
See also paragraph: 4.4 Residual Scatter.

This document at the beginning mentions:
"but SNe Ia observations are currently the most sensitive technique to study
dark energy or its alternatives, since they can be used to directly measure
the history of the expansion of the Universe."
Is not this what we want ?
Can we also do this with the CMB radiation data? I doubt this.

Those results are different meaning that
supernova data is almost not used.

What do you mean by "not used"? Not used by CAMB, sure, but then the
supernova people don't use CAMB.

The cause is dispersion/reflection i.e. the fact that photons don't follow
straight lines. I agree that this is a problem for supernovae data.

This is a practically non-existent problem.

See also http://en.wikipedia.org/wiki/Sunyaev%E2%80%93Zel'dovich_effect

But I also think that it is a much more severe problem for CMB radiation
data, meaning IMO that it is much more difficult for example based
on CMBR data to claim that k=0 than based on supernovae data.

Actually, k=0 (or K very close to 0) is one of the most robust results
from the CMB.

The friedmann equation is based on four parameters (Lambda, C (mass), k and
the age of the universe) Assuming that k=0 makes everything simpler.
Using SN data and using a light curve fitter we can calculate Lambda, C and
the age of the Universe. When we have those we can calculate
Omega(Lambda), Omega(M) and H0.

IMO using CMBR data only this is much more difficult.
In fact CMBR (CAMB) claims even mo CMBR makes a distiction between
baryon mass and CDM (photon) mass.

This is also the topic he
http://users.telenet.be/nicvroom/Ome...and%20CMBR.htm

Nicolaas Vroom

In article , Nicolaas Vroom
writes:

Op zaterdag 12 januari 2013 09:33:37 UTC+1 wrote Phillip Helbig:
In article , Nicolaas Vroom
writes:

1. The program CAMB allows for a continuous range of values for
omaga(k). Using Friedmann's equation this means that the parameter
k also should allow a continuous range of values.
This is strange while the only correct values are k=-1, 0 and +1.

How is k defined?
For the definition that k is only -1,0 or +1 See:
a) http://nicadd.niu.edu/~bterzic/PHYS652/Lecture_05.pdf
b) The Big Bang by Joseph Silk
c) Introducing Einstein's Relativity by Ray d'Inverno.

The url http://background.uchicago.edu/~whu/...curvature.html
gives the impression that all O_k values are valid. In reality which each
O_k value belongs a "k value". Only k = -1,0 and 1 are valid.

That is how THEY define it. As I pointed out, there are different
conventions. CAMB have certainly not screwed this up. Read the code
and the documentation. They didn't make a simple mistake like this.

IMO they all depend on each other except Lambda,C,k and the age of the
Universe.

Within the context of GR, there are three independent parameters.

I understand that CAMB uses a type of friedmann equation with more parameters
included (For example Background temperature)

So does Ned Wright's cosmology calculator. Apart from the CMB
temperature itself, this has practically no influence on observable
parameters, though it does affect the calculated age of the universe
slightly.

Consider: http://background.uchicago.edu/~whu/...curvature.html
This page demonstrates that k=0 and O_k=0 (flat universe)
This is done by modifying O_k. The result are power spectra which do not
match the observed power spectra. The conclusion is that O_k must be zero
and that k=0.

OK.

The problem is how do we know that the calculations based on O_k are correct.
Specific how do we know that the calculated power spectra are correct.
The problem is we do not know. This can not be tested.

Again, there is a HUGE literature on this topic. The power spectra are
calculated from basic physics via first principles. It's all in the
CAMB code. How can 1+1=2 be tested?

3. The basic problem with the Supernovae data is the relation
between Luminosity and magtitude as a function of luminosity distance.
Literature shows that there are two equations used to calculate the
cosmological parameters.

Which two equations?
See http://arxiv.org/abs/1001.4538 7 Year WMAP - Cosmological Interpretions.
Page 14
What I mean are the 2 light curve fitters SALT2 and MLCS2K2.

For more detail about SALT2 see also: http://arxiv.org/abs/1010.4743
specific page 16 is interseting.
See also paragraph: 4.4 Residual Scatter.

OK, but this is really concerned with technical details, not basic
cosmology.

"but SNe Ia observations are currently the most sensitive technique to study
dark energy or its alternatives, since they can be used to directly measure
the history of the expansion of the Universe."
Is not this what we want ?
Can we also do this with the CMB radiation data? I doubt this.

Since the CMB comes from essentially one redshift, then it indeed can't
directly measure the expansion history of the universe. Again, it
really depends on what one means by "directly" and "measure".

The cause is dispersion/reflection i.e. the fact that photons don't follow
straight lines. I agree that this is a problem for supernovae data.

This is a practically non-existent problem.

See also http://en.wikipedia.org/wiki/Sunyaev%E2%80%93Zel'dovich_effect

Taken into account in CAMB.

The friedmann equation is based on four parameters (Lambda, C (mass), k and
the age of the universe)

But only 3 are independent.

Assuming that k=0 makes everything simpler.

Yes, but that is not the reason for setting k=0 TODAY. (Yes, in the
past decades, some people did make (sometimes invalid) assumptions just
to make calculations simpler, but that is not the case today.

IMO using CMBR data only this is much more difficult.
In fact CMBR (CAMB) claims even mo CMBR makes a distiction between
baryon mass and CDM (photon) mass.

As you can see at Ned's calculator, the difference between 2.73 and 0
degrees for the CMB makes little difference in observable quantities.

"Nicolaas Vroom" wrote in message
...

Op zaterdag 12 januari 2013 09:33:37 UTC+1 wrote Phillip Helbig:
In article , Nicolaas Vroom
writes:

1. The program CAMB allows for a continuous range of values for
omaga(k). Using Friedmann's equation this means that the parameter
k also should allow a continuous range of values.
This is strange while the only correct values are k=-1, 0 and +1.

How is k defined?
For the definition that k is only -1,0 or +1 See:
a) http://nicadd.niu.edu/~bterzic/PHYS652/Lecture_05.pdf
b) The Big Bang by Joseph Silk
c) Introducing Einstein's Relativity by Ray d'Inverno.

The url http://background.uchicago.edu/~whu/...curvature.html
gives the impression that all O_k values are valid. In reality which each
O_k value belongs a "k value". Only k = -1,0 and 1 are valid.

2. My impression is that the CMB radiation is a much more powerfull
tool than Supernovae of type 1A.

To some extent, yes. However, the CMB is good at measuring the sum of
lambda and Omega but not differentiating them. One can also measure H
from the CMB but, as you point out, putting in H measured elsewhere
improves matters. The values of lambda and Omega from SNIa do not
depend on H at all.

IMO they all depend on each other except Lambda,C,k and the age of the
Universe.
See the end of my comments.
==============================================
Opinions are not research, opinions are not science, opinions are not
astronomy, opinions are conjecture.

Using CMBR data you can not only calculate Omega(m) but also omega(B)
and omega(C).
The way this is done generally speaking is by trying different
values for these parameters and using CAMB. The result is that they
do not match with the Observed Power Spectrum, meaning that they must
be wrong. That is most probably true but that does not mean that the
parameters that match the Observed PS are correct because there is no
prove that all the underlying equations of CAMB are correct.

I understand that CAMB uses a type of friedmann equation with more
parameters
included (For example Background temperature)

What do you mean by proof? (I assume "prove" should be "proof".) There
is a HUGE literature on this subject.

Consider: http://background.uchicago.edu/~whu/...curvature.html
This page demonstrates that k=0 and O_k=0 (flat universe)
This is done by modifying O_k. The result are power spectra which do not
match the observed power spectra. The conclusion is that O_k must be zero
and that k=0.
The problem is how do we know that the calculations based on O_k are
correct.
Specific how do we know that the calculated power spectra are correct.
The problem is we do not know. This can not be tested.

May be this is not a problem for omega(k), but definitif a problem for
omega(B) versus omega(C)


3. The basic problem with the Supernovae data is the relation
between Luminosity and magtitude as a function of luminosity distance.
Literature shows that there are two equations used to calculate the
cosmological parameters.

Which two equations?
See http://arxiv.org/abs/1001.4538 7 Year WMAP - Cosmological Interpretions.
Page 14
What I mean are the 2 light curve fitters SALT2 and MLCS2K2.

For more detail about SALT2 see also: http://arxiv.org/abs/1010.4743
specific page 16 is interseting.
See also paragraph: 4.4 Residual Scatter.

This document at the beginning mentions:
"but SNe Ia observations are currently the most sensitive technique to study
dark energy or its alternatives, since they can be used to directly measure
the history of the expansion of the Universe."
Is not this what we want ?
Can we also do this with the CMB radiation data? I doubt this.

Those results are different meaning that
supernova data is almost not used.

What do you mean by "not used"? Not used by CAMB, sure, but then the
supernova people don't use CAMB.

The cause is dispersion/reflection i.e. the fact that photons don't
follow
straight lines. I agree that this is a problem for supernovae data.

This is a practically non-existent problem.

See also http://en.wikipedia.org/wiki/Sunyaev%E2%80%93Zel'dovich_effect

But I also think that it is a much more severe problem for CMB radiation
data, meaning IMO that it is much more difficult for example based
on CMBR data to claim that k=0 than based on supernovae data.

Actually, k=0 (or K very close to 0) is one of the most robust results
from the CMB.

The friedmann equation is based on four parameters (Lambda, C (mass), k and
the age of the universe) Assuming that k=0 makes everything simpler.
Using SN data and using a light curve fitter we can calculate Lambda, C and
the age of the Universe. When we have those we can calculate
Omega(Lambda), Omega(M) and H0.

IMO
==============================================
Opinions are not research, opinions are not science, opinions are not
astronomy, opinions are conjecture.


-- This message is brought to you from the keyboard of
Lord Androcles, Zeroth Earl of Medway.
When I get my O.B.E. I'll be an earlobe.

Op dinsdag 15 januari 2013 10:07:16 UTC+1 schreef Phillip Helbig---undress to reply het volgende:
In article , Nicolaas Vroom

writes:

The url http://background.uchicago.edu/~whu/...curvature.html
gives the impression that all O_k values are valid. In reality which each
O_k value belongs a "k value". Only k = -1,0 and 1 are valid.

That is how THEY define it. As I pointed out, there are different
conventions. CAMB have certainly not screwed this up. Read the code
and the documentation. They didn't make a simple mistake like this.

In order to study the program select:
http://http://users.telenet.be/nicvr...b_all_html.htm
In the program they define omegab, omegac, omegak etc
omegak is calculated in line 4564.
k is not calculated.

I understand that CAMB uses a type of friedmann equation with more parameters
included (For example Background temperature)

So does Ned Wright's cosmology calculator. Apart from the CMB
temperature itself, this has practically no influence on observable
parameters, though it does affect the calculated age of the universe
slightly.
I can not say that the calculations involved are wrong
neither can I claim that they are correct.
Consider: http://background.uchicago.edu/~whu/...curvature.html
This page demonstrates that k=0 and O_k=0 (flat universe)
This is done by modifying O_k. The result are power spectra which do not
match the observed power spectra. The conclusion is that O_k must be zero
and that k=0.

OK.

The problem is how do we know that the calculations based on O_k are correct.
Specific how do we know that the calculated power spectra are correct.
The problem is we do not know. This can not be tested.

Again, there is a HUGE literature on this topic. The power spectra are
calculated from basic physics via first principles.
There are two Power Spectra Involved:
1) What I call Observed PS (OPS). This one is calculated from the CMB radiation.
2) A Calculated PS or CPS. This is calculated based on a set of 6 parameters
Omaga b, Omega C, etc See Table 1 in http://arxiv.org/abs/1001.4635
Using different combinations of parameters you can calculated a CPS that
closest matches the OPS. The unfortunate part is that this solution
could be wrong because there is no way to prove that the equations
involved (i.e the program CAMB) is correct.

It's all in the
CAMB code. How can 1+1=2 be tested?
Two documents to study a
1) http://arxiv.org/abs/astro-ph/9602019
Section 5.2 "acoustic peaks" indicates how difficult everything is.
2) http://arxiv.org/abs/astro-ph/9807130


3. The basic problem with the Supernovae data is the relation
between Luminosity and magtitude as a function of luminosity distance.
Literature shows that there are two equations used to calculate the
cosmological parameters.

Which two equations?
See http://arxiv.org/abs/1001.4538 7 Year WMAP - Cosmological Interpretions.
Page 14
What I mean are the 2 light curve fitters SALT2 and MLCS2K2.

For more detail about SALT2 see also: http://arxiv.org/abs/1010.4743
specific page 16 is interseting.
See also paragraph: 4.4 Residual Scatter.

OK, but this is really concerned with technical details, not basic
cosmology.
IMO the same problems are in the CMB solution (maybe worse)

"but SNe Ia observations are currently the most sensitive technique to study
dark energy or its alternatives, since they can be used to directly measure
the history of the expansion of the Universe."
Is not this what we want ?
Can we also do this with the CMB radiation data? I doubt this.

Since the CMB comes from essentially one redshift, then it indeed can't
directly measure the expansion history of the universe. Again, it
really depends on what one means by "directly" and "measure".
IMO people use the word measure to quickly. Calculated is better.
Only the Background Radiation is measured (?) The Power Spectrum is calculated.

The cause is dispersion/reflection i.e. the fact that photons don't follow
straight lines. I agree that this is a problem for supernovae data.

This is a practically non-existent problem.

See also http://en.wikipedia.org/wiki/Sunyaev%E2%80%93Zel'dovich_effect

Taken into account in CAMB.
The question is: is that done correctly, starting from the moment the photons
were created right after the BigBang.

Hu et all discuss what is called the event of recombination.
(see par 5.2 "The role of baryons" in document 2).
See also http://background.uchicago.edu/~whu/.../redshift.html
The impression is given that before this period the photons stayed close
together caused by Thompson scattering.
After that period they streamed unimpeded. See:
http://background.uchicago.edu/~whu/.../angular4.html
How do we know that this transition happened in such a short period ?

The friedmann equation is based on four parameters (Lambda, C (mass), k and
the age of the universe)

But only 3 are independent.
They are all dependent about observations.

Assuming that k=0 makes everything simpler.

Yes, but that is not the reason for setting k=0 TODAY. (Yes, in the
past decades, some people did make (sometimes invalid) assumptions just
to make calculations simpler, but that is not the case today.

The introduction of document 1 shows:
"If present, the acoustic pattern contains unambiguous information on the curvature
of the universe even in the general case."
When you go to: http://en.wikipedia.org/wiki/Curvature
You can read: "It is natural to define the curvature of a straight line
to be identically zero."
Which means that parallel lines never meat each other. Also at infinity.
How do you know that that is true by studying the micro wave background radiation ?
See also: http://en.wikipedia.org/wiki/Shape_of_the_Universe

Nicolaas Vroom

In article , Nicolaas Vroom
writes:

In order to study the program select:
http://http://users.telenet.be/nicvr...b_all_html.htm
In the program they define omegab, omegac, omegak etc
omegak is calculated in line 4564.
k is not calculated.

As long as the program is self-consistent, it doesn't matter what the
variables are called. Yes, comparing different authors can be
confusing.

There are two Power Spectra Involved:
1) What I call Observed PS (OPS). This one is calculated from the CMB radiation.
2) A Calculated PS or CPS. This is calculated based on a set of 6 parameters
Omaga b, Omega C, etc See Table 1 in http://arxiv.org/abs/1001.4635
Using different combinations of parameters you can calculated a CPS that
closest matches the OPS.

Right. This is how most science is done: quantify the observations,
quantify the theory, and compare.

The unfortunate part is that this solution
could be wrong because there is no way to prove that the equations
involved (i.e the program CAMB) is correct.

What point are you trying to make here? There is the code, comments in
it, papers describing it. Do you have a specific complaint?

Two documents to study a
1) http://arxiv.org/abs/astro-ph/9602019
Section 5.2 "acoustic peaks" indicates how difficult everything is.
2) http://arxiv.org/abs/astro-ph/9807130

I didn't say it is easy. Several person-years went into understanding
the interpretation of CMB data.

IMO people use the word measure to quickly. Calculated is better.

I agree.

Only the Background Radiation is measured (?) The Power Spectrum is
calculated.

Of course the theoretical power spectrum is calculated. Whether the
observed power spectrum is measured or calculated is a matter of
semantics. A map of the sky is not observed directly, but calculated.

The question is: is that done correctly, starting from the moment the photons
were created right after the BigBang.

Again, if you have a specific complaint, say so. I haven't found any
reason to doubt the code.

The friedmann equation is based on four parameters (Lambda, C (mass), k and
the age of the universe)

But only 3 are independent.
They are all dependent about observations.

That is something different. Of course what we observe depends on
observations but, within GR, only 3 are independent. Suppose there are
the three variables height, weight and body-mass index
(weight/(height^2). Only 2 are independent since, given 2, one can
calculate the third.

"If present, the acoustic pattern contains unambiguous information on
the curvature
of the universe even in the general case."

Yes.

When you go to: http://en.wikipedia.org/wiki/Curvature
You can read: "It is natural to define the curvature of a straight line
to be identically zero."

OK.

Which means that parallel lines never meat each other. Also at infinity.

OK.

How do you know that that is true by studying the micro wave
background radiation ?

The position of the first peak is essentially a measure of Omega+lambda.
If the sum is 1, then k=0 and we have a flat universe.

Nicolaas Vroom wrote:
When you go to: http://en.wikipedia.org/wiki/Curvature
You can read: "It is natural to define the curvature of a straight line
to be identically zero."

Beware -- in the context of differential geometry, there are several
different objects which are called "X curvature" for some X.

That Wikipedia article is talking primarily about *extrinsic* curvature,
in this case of a curve as embedded in a Euclidean plane. That's a rather
different mathematical animal from any of the *intrinsic* curvatures which
are of primary interest in cosmology.

[There's also the question of what it means to say that a
line or curve is "straight". This at least has only one
differential-geometry meaning.... but it does depend critically
on context. E.g., is a great circle on a globe "straight"?]

In general, if you're going to use words like "curvature" or "straight",
it's useful to be very explicit about just what you mean.


One other often-confusing point about curvatu the intrinsic curvature
of *space* and the intrinsic curvature of *spacetime* are two quite
different mathematical objects, and one can be zero while the other
is nonzero. To bring this back closer to sci.astro.research relevance,
current evidence suggests that this is approximately true in the universe
today: the intrinsic curvature of *space*
[more precisely, of the usual cosmological
time=constant spacelike slices of spacetime]
is close to zero, while the intrinsic curvature of *spacetime* is
significantly nonzero.


Which means that parallel lines never meat each other.

That's only true if you add "in a Euclidean plane". In a more general
space (or spacetime) the conclusion (parallel lines never meet) may or
may not be true. For example, on the surface of a sphere, great circles
(which are geodesics, i.e., they're "straight" within the surface) *do*
meet.

--
-- "Jonathan Thornburg [remove -animal to reply]"
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
on sabbatical in Canada starting August 2012
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam

Op donderdag 17 januari 2013 08:42:36 UTC+1 schreef Phillip Helbig---undress to reply het volgende:
In article , Nicolaas Vroom

writes:


The friedmann equation is based on four parameters (Lambda, C (mass),
k and the age of the universe)

But only 3 are independent.
They are all dependent about observations.

That is something different. Of course what we observe depends on
observations but, within GR, only 3 are independent.

Using SN data you can calculate the Hubble parameter (and H0), Omaga(L), Omega(m) Omega(k) as a function Lambda, C and the age of the Universe for
the three conditions of k (k=0,-1 or +1).
Ofcourse if you know H0 by some other means than this changes the situation.

The document http://users.telenet.be/nicvroom/H0%20calculation.pdf
shows that it is difficult to calculate H0 only accurate based on local observations.
The observations are in: http://ned.ipac.caltech.edu/level5/NED1D/intro.html

Nicolaas Vroom