Looking once around the universe

[birulami]

What are the farest reaching astronomical observations of visible light or radio waves? Is it something like 10 billion (10^9) light years? I just wonder: are we sure that the universe is bigger than these 10 billion light years? What if it were only 8 billion light years in diameter? Would we then be able to see the Milky Way like it was 8 billion years ago? Does anyone know what kind of observation tells us that the universe is not actually quite "small" and we are looking once, twice, three times around it already?

Thanks,
Harald.

 

[marcus]

What are the farest reaching astronomical observations of visible light or radio waves? Is it something like 10 billion (10^9) light years? I just wonder: are we sure that the universe is bigger than these 10 billion light years? What if it were only 8 billion light years in diameter? Would we then be able to see the Milky Way like it was 8 billion years ago? Does anyone know what kind of observation tells us that the universe is not actually quite "small" and we are looking once, twice, three times around it already?

Thanks,
Harald.

that possibility has been studied, for example in several papers by David Spergel and Neil Cornish et al.

they looked for repetitions of patterns seen in different directions as you might see in a mirror box

they found none, so they concluded that none of the patterns large and clear enough to detect in the sky are made by light that has "been around" once already.

this only places a LOWER BOUND on the unrepeating size of the universe.
It could STILL BE TOROIDAL or some other closed shape so that we would (if we had sharp enough eyes and could see far enough) see the same pattern coming to us from two different directions
but they were able to prove that if it is toroidal or has some such topology then IT MUST BE AT LEAST SO AND SOMUCH BIG----like 70 or 80 billion light years.

Cornish and Spergel et al are big name cosmologists and they were trying to disprove the toroidal and repeating dodecahedron pictures as much as they possibly could, but you can't completely rule it out-----you can only say it isn't happening within a particular range of you.

 

[marcus]

If you don't already know how to use the arxiv search engine, then as a SW engineer interested in cosmology and physics you might like it.

this is how to find Neil Cornish papers, for example

Go to
http://arxiv.org/
(then you get to look at all the new papers in your area of interest) and then go
http://arxiv.org/search

and put "Cornish" or else "N Cornish" in the author box and press "search"
but this gives too many papers
so change the "title" box to be another author box and put in "Spergel" and press search
be sure that you are allowing it to search in all years, not just in one year or the latest year. then you get
1. arXiv:astro-ph/0604616 [ps, pdf, other]
Title: Extending the WMAP Bound on the Size of the Universe
Authors: Joey Shapiro Key, Neil J. Cornish, David N. Spergel, Glenn D. Starkman
Comments: 9 pages, 16 figures
Subjects: Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc)

2. arXiv:astro-ph/0310233 [ps, pdf, other]
Title: Constraining the Topology of the Universe
Authors: Neil J. Cornish, David N. Spergel, Glenn D. Starkman, Eiichiro Komatsu
Comments: Submitted to PRL
Journal-ref: Phys.Rev.Lett. 92 (2004) 201302
Subjects: Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc)

3. arXiv:astro-ph/0202001 [ps, pdf, other]
Title: Journey to the edge of time: The GREAT mission
Authors: Neil J. Cornish, David N. Spergel, Charles L. Bennett
Comments: 6 pages, 4 figures. White paper submitted to NASA's 2003 SEU Roadmap Team
Subjects: Astrophysics (astro-ph)

4. arXiv:astro-ph/9906401 [ps, pdf, other]
Title: A small universe after all?
Authors: Neil J. Cornish, David N. Spergel (Princeton University)
Comments: 4 pages, RevTeX, 7 Figures
Journal-ref: Phys.Rev. D62 (2000) 087304
Subjects: Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc)

5. arXiv:math/9906017 [ps, pdf, other]
Title: On the eigenmodes of compact hyperbolic 3-manifolds
Authors: Neil J. Cornish, David N. Spergel
Comments: 8 pages, 10 figures. Submitted to Experimental Mathematics
Subjects: Differential Geometry (math.DG); General Relativity and Quantum Cosmology (gr-qc)

6. arXiv:astro-ph/9801212 [ps, pdf, other]
Title: Circles in the Sky: Finding Topology with the Microwave Background Radiation
Authors: Neil Cornish (Cambridge), David Spergel (Princeton), Glenn Starkman (Case Western)
Comments: 14 pages, 10 figures, IOP format. This paper is a direct descendant of gr-qc/9602039. To appear in a special proceedings issue of Class. Quant. Grav. covering the Cleveland Topology & Cosmology Workshop
Journal-ref: Class.Quant.Grav. 15 (1998) 2657-2670
Subjects: Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)

7. arXiv:astro-ph/9708225 [ps, pdf, other]
Title: Can COBE see the shape of the universe?
Authors: Neil Cornish (Cambridge), David Spergel (Princeton), Glenn Starkman (Case Western)
Comments: 16 Pages, 5 Figures. Version published in Phys. Rev. D
Journal-ref: Phys.Rev. D57 (1998) 5982-5996
Subjects: Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc)

8. arXiv:astro-ph/9708083 [ps, pdf, other]
Title: Measuring the Topology of the Universe
Authors: Neil J. Cornish (DAMTP), David N. Spergel (Princeton), Glenn D. Starkman (CWRU)
Comments: 11 pages, LaTex, Talk at NAS Cosmology Conference, Irvine, CA, March 1997
Journal-ref: Proc.Nat.Acad.Sci. 95 (1998) 82
Subjects: Astrophysics (astro-ph)

9. arXiv:gr-qc/9602039 [ps, pdf, other]
Title: Circles in the Sky: Finding Topology with the Microwave Background Radiation
Authors: Neil J. Cornish (Case Western Reserve Univ.), David N. Spergel (Princeton U. and U of Maryland), Glenn D. Starkman (C.W.R.U.)
Comments: 6 pages, 1 latex file, no figures
Journal-ref: Class.Quant.Grav. 15 (1998) 2657-2670
Subjects: General Relativity and Quantum Cosmology (gr-qc)

The arxiv search engine is very good for KEYWORD searches. Like you could look for "cosmology AND topology" occurring in the abstract summary of the article.

 

[marcus]

To answer a technical question you asked, what is the farthest away stuff we can see. That is the stuff that radiated the CMB.
The redshift of the CMB is typically given as 1100.
If you want to convert a redshift into a light travel time
or to a distance (either at present or sometime in the past) then go to Ned Wright's page
http://www.astro.ucla.edu/~wright/cosmolog.htm
and find his calculator
http://www.astro.ucla.edu/~wright/CosmoCalc.html

and put in the redshift
if you put in z = 1100 and press flat, or general you will get
light travel time = 13.6 billion years
and the PRESENT DISTANCE TO THE STUFF that emitted the light is 45.6 billion lightyears (because of expansion)
and it also tells how far it was from milkyway matter in the PAST WHEN IT EMITTED the light, that is shown
by the ANGULAR SIZE DISTANCE which is 0.0414 billion LY, which is the same as 41 million LY.

so the stuff that emitted the CMB that we are now receiving was 41 million lightyear from our matter when it emitted the light
and now at present day it is 45.6 billion lightyear from us
and the light has taken about 13.6 billion years to get here
and in the course of travel it has stretched out wavelength by a factor of about 1100

we can't see any farther with light because the CMB was emitted by an opaque partial ionized fog that older light could not come thru and it was just then becoming transparent, so it is the oldest light

it was from when universe was about 380,000 years old

we may someday be able to see neutrinos from older time, but not light.

BTW welcome Harald. Thanks for voting on the MIP poll! Good to have SW engineers around here.

 

[birulami]

Expansion Factor of the universe?

Hi Marcus,

thanks for the extensive answers. Interesting to see that some cosmologists took this question already seriously. Yes I knew arxiv and I'll have a look at some of the papers you recommend.

As for the current distance of the "stuff that send the CMB" I was not really aware that it must have such a far distance now due to expansion. Although I heard about the expansion, I did not really add it to the mental picture.

The really startling fact is, that expansion seems to drive things apart faster than the speed of light c. Thinking of it, this is easily accomplished if expansion is goverened by an expansion factor per unit time rather than by adding a fixed amount of space per unit time.

If the expansion is by a factor of b per unit time, then two objects being d apart at the start will after time t have a distance of $d(t)=t b d$. Consequently, if d is large enough at the start, we get for the average receding speed $v(t)=d(t)/t=b d>c$.

Is it correct that expansion is goverened by factor per unit time rather than by just adding a fixed amount of space? How big is b then?

Thanks,
Harald.

 

[birulami]

Uuuh, something must be wrong with my reasoning about $v(t)=d(t)/t=b d>c$. If d is just a bit to small for $d b>c$ at the start, it soon will be big enough, suggesting that the speed changes with time, but the formula does not show this.

Have to check later, need to leave now.

Cheers,
Harald.

 

[marcus]

Have to check later, need to leave now.

Cheers,
Harald.

the definitions of basic quantities are most easily given in terms of the scale factor a(t), which is arbitrarily set to be unity in the present
a_0 = a(t_present) = 1

and the Hubble parameter H(t) is defined to be a'/a
so it can change with time. In fact it has been declining almost all the time, but more and more slowly.
(because it is a ratio a'/a it is even possible to have it decrease even while a'' is positive---the Hubble can decrease even during a period of accelerating expansion as long as the acceleration is not too abrupt, because the denominator of the fraction is increasing too)

we mostly hear about the present value of H(t) which is H_0 = H(t_present) = 71 km/s per Megaparsec.

but back in time of redshift z = 6 the Hubble parameter was around 700
=================

your calculation assumes the Hubble is constant in time, this is a GOOD approximation in certain regimes because it does in fact change only very very slowly.
If one makes this approximation of a contant Hubble parameter then one can see how the recession speed of any given object must increase EXPONENTIALLY with time because the farther away it gets the faster it recedes.

it is quite usual for recession speeds to be faster than light, as you have noticed---they are not governed by the local rules of special relativity.
================
Check out Morgan's calculator. Be sure to put in the accepted parameters of (0.27, 0.73, 71) for (matter, dark energy or lambda, Hubble parameter)

then you can type in any redshift z and find out the distance, and how long ago it emitted the light, and what the recession speed was. and also what the Hubble parameter was
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

================
I expect that as a SW engineer your time is very limited. My son is a SW engineer and they work long hours. So take your time with this cosmology, there is no hurry (with the universe).

 

[birulami]

If you don't already know how to use the arxiv search engine, then as a SW engineer interested in cosmology and physics you might like it.

this is how to find Neil Cornish papers, for example

Go to
http://arxiv.org/
(then you get to look at all the new papers in your area of interest) and then go
http://arxiv.org/search

Have to move my https://www.physicsforums.com/showthread.php?p=1365853#post1365853" to the general discussion.

Cheers,
Harald.