2. Large scale structure of the Universe. In visible light (Inflationary perturbations 1)
DmitryThis post is the first one in the series devoted to discussion of the large scale structure of the Universe, inflationary cosmology and inflationary perturbation theory. The series will be essentially based on the lectures I am giving currently at the University of Helsinki for graduate students and advanced undergrads.
Today, I am going to remind you what is our current understanding of the large scale structure of the Universe or, in other words, what do we see on the sky and what is our place in the Universe.
I am going to start with the box of the size of our Solar system, describe in a few words what happens with gravitational potential and matter distribution within it and then will gradually increase the size of the box to understand the distinctive features of the gravitational potential at different scales. The size of the Solar system is about 50 AU (Astronomical Units) 
7.5 billion km if we decide to set its boundary at the Pluto’s orbit. The gravitational field of the Sun dominates over the field of nearest star up to the scale 
km.
1. Universe in visible light
The main source of visible light in the Universe is nuclear fusion within stars (mainly, H into He). Our Sun is a typical yellow dwarf star with approximate mass 
kg - 100 times more massive than all planets of the Solar system combined. We live in the gravitational well of a rather small star, there exist stars within our galaxy 100 times heavier than the Sun. The picture below represents the Sun as seen by the Spitzer space telescope (the most powerful tool we have now in our posession to observe the Universe in the IR).
If we consider only nearest stars, the scale of the box containing them is of the order of 1 light year (1 ly), the path passed by a ray of light during one year. For example, the closest star, Proxima Centauri, is 3.261 ly 1 Parsec (Pc) away from us. The name of the unit “Parsec” comes from the fact that Proxima Centauri has a parallax of approximately 1 second" onclick="javascript:urchinTracker('/outbound/en.wikipedia.org/wiki/arc_strong_sec_/strong_ond');">arcsecond. Taking into account that the velocity of light is about 300000 km/sec, one can check that 1 ly 
km and 1 Pc is trivially 
km.
Thinking in terms of propagating light and recalling that the speed of light is the largest possible speed in Nature, one can understand that distance or length scale in general relativity is quite the same thing as time scale. In other words, larger distances correspond to earlier stages in the evolution of our Universe because more time had to pass for light from distant objects to reach us. Observing the Universe, we are watching a movie, its first shot corresponding to extremely distant objects on the sky and the last - to physics at scales of the order of the Solar system’s size.
If we increase the size of the box 1000-fold, we find that clusters of stars, interstellar gas, dark matter are combined into gravitationally bound conglomerates matter called galaxies. That is how they typically look on the sky:
The typical number of stars within a galaxy is extremely large. For example, our native Galaxy (the Milky Way) contains 100 billion (thous. million) stars. It has a form of disk with the radius 12500 Pcs and the thickness of only about 300 Pcs. This extremely thin disk is rotating differentially with the full period of about 200 million years - dynosaurs were wiped out from the face of the Earth during the previous galactic year :)) Large old galaxies (including the Milky Way) have a form of spiral. The reason is that rotating disk of gravitationally interacting dust particles is unstable, and this gravitational instability breaks the disk into a spiral-like structure.
The Solar system is located way off center in our Galaxy within what is called the Orion spiral arm. The name is due to the fact that stars from Orion constellation such as red giant Betelgeuse - the ninth brightest star on the sky - belong to the same arm. Looking at the next picture you can have some impression how far from us are the stars from some constellations you know:
The chraracteristic length scale on the picture above is 10000 lys. Let us again increase the box size we are looking inside, 10-fold this time, and we will find that the Milky Way resides within a small concentrated group of galaxies (LGG):
All the adjacent galaxies in this box are much smaller than the Milky Way being located within its gravitational well (in other words, they are satellites of our Galaxy in the same sense as the Moon is the satelite of the Earth). The closest galaxy to the Milky Way is Large Magellanic Cloud (50 kPcs away). On the photo below is another satellite of our galaxy - Small Magellanic Cloud (200000 lys away from us):
The cluster of blue stars which looks like being inside SMC actually belongs to our galaxy. The stars of this cluster are about 5 millon years old. Considering that the life time (the period before all the hydrogene within the star is burned out) of a small star like the Sun is some billions of years, you understand that these stars are very young - that is why they are blue; blue is the color of youth on the sky.
The nearest galaxy of the size of our own (actually slightly larger) is 770000 Pcs = 770 kPcs away and is named the Andromeda galaxy. Below you can see the 3D map of the close region with the characteristic scale 1 million lys:
A typical local group of galaxies occupies a volume of few cubic Megaparsecs, i.e., millions of parsecs. Megaparsec is cosmologist’s favorite unit, 1 MPc 
m.
These groups of galaxies in turn are grouped themselves into galaxy clusters (some of these clusters contain more than 10000 galaxies). Looking into the sky through sufficiently powerful telescope such as Hubble Space Telescope, you will see that these groups typically look like this one:
(Abel cluster, 450 million lys away from us. Many points on the photo are actually galaxies and not stars as you might have thought :))
The map of closest clusters of galaxies is presented on the picture below:
Our local group is within the graviational well of the Virgo Cluster (yellow on the right).
Let us again increase the size of the box 10-fold. Not surprisingly, it turns out that galaxy clusters are combined into superclusters, but surprising it is that the latter are the largest gravitationally-collapsed objects in nature, and there is no such thing as supersuperclusters of galaxies in the universe. The structure of superclusters and their interplay through gravitational interaction becomes noticable at scale about some hundreds of millions of lyrs or hundreds of MPcs:
Namely, superclusters are joined by filaments and walls of galaxies creating a foam-like structure of matter and gravitational potential. Voids in this foam are as large as 50 MPcs across:
Understanding that this structure is due to the gravitational instability and the latter needs some time to develop, on can conclude from the fact that superclusters are the largest collapsed objects that the age of the universe was finite and, moreover, its initial state was highly symmetric. Indeed, on the picture above (by 2dF GRS team) it can be rather clearly seen that the Universe becomes more homogeneous at scales larger than 1 billion lys.
Indeed, let us again increase 10 times the scale of the box we are looking at.
What you see above is the map of the Universe (approx. 2 million of nearby galaxies) with characteristic scale about 3000 MPcs. This coincides with the size of the observable patch of the Universe. As one can see , the Universe is extremely smooth, homogeneous and isotropic at the scale of the order 1 GPc . That is why we can reduce an extremely complicated set of Einstein equations describing the dynamics of spacetime to almost trivial-to-solve pair of the Friedmann equations we will use later in the lectures. In a sense, that is why qualitative discussion of the evolution of the Universe is possible.
There are of course fluctuations of the matter density on the picture above, but their relative amplitude is about 
at scales of order 1 GPc. Although we do not have data on the distribution of matter and gravitational potential at larger scales, theory shows that the picture above does not change up to the scale of 13 Glys (the cosmological horizon scale) and above, although the relative amplitude of fluctuations starts to slightly grow while the scale gets larger (see the yesterday’s post on WMAP 5 year data; the positive spectral index 
means exactly this as we will see in the next lectures).
As will also be discussed later, standard inflationary paradigm predicts as well that the relative amplitude of fluctuations of the gravitational potential keeps growing until it becomes of the order of 1 at the so called eternal inflation scale 
Glyrs 
, where the number 
and depends on particular inflationary model. While the Universe is homogeneous and isotropic at scales below, it again ceases to be homogeneous and isotropic at 
. Moreover, it can be considered fractal in a certain sense - the structure of the gravitational potential at these huge scales turns out to be self-reproducing.
To finalize, let me show you a video of a computer simulation (Millenium Simulation) of the Universe by people from the Max Planck Institute. It nicely incorporates all the features (up to the scale of 1 GPc) I have described today: http://www.youtube.com/v/W35SYkfdGtw
Next time I am going to discuss how the Universe looks like in other wavebands.
P.S. Many of the pictures in this post were taken from www.atlasoftheuniverse.com.
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Related posts:
1. WMAP 5 year
DmitryClearly, the most important paper(s) in astro-ph today is the release of the 5 year data of WMAP. The references to papers are:
- “Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation”
- “Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Beam Maps and Window Functions”
- “The Wilkinson Microwave Anisotropy Probe (WMAP) Source Catalog”
- “Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP data”
- “Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Angular Power Spectra”
- “Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Galactic Foreground Emission”
- “Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results”
If you do not know what is WMAP :)
It is NASA satellite mission with the goal to measure the temperature of the cosmic microwave background radiation (CMB). It measures the CMB temperature and its fluctuations over the all sky with angular resolution 0.3 degrees and sensitivity about 20 microKelvin er 0.3 degrees.
The WMAP sattelite was launched on 30 June 2001, first set of data was released in 2003 and the second set - in 2006 (dataset is supposed to be released every two years, and this one was seriously delayed forcing us to think that the WMAP team found something extraordinary :)). Already 2003 data greatly exceeded the old CMB data in accuracy, so 30 June 2001 is considered by many as the beginning of the era of precision cosmology. This data release is the third one.
In this respect, the WMAP project is of extreme significance; thanks to WMAP data, many cosmological parameters are known today with rather high precision.
5 year data and cosmological parameters
Now, I will take for granted that you know what are the cosmological parameters such as 
. If you do not, feel free to ask in comments.
So, what are the results of the 5th year compared to the 3rd year? 5 year data limit the deviation from the minimal Lambda Cold Dark Matter model (LCDM) even more strongly.
As follows from WMAP data combined with the Type IIA supernovae and BAO (Baryon Acoustic Oscillations) measurements, parameters of LCDM are:
1.
,
2. 
, ,
3.
,
4. 
km/s/Mpc,
5. 
, positive spectral index is slightly more favored,
6. 
at the 95% confidence level. WMAP 5 year data alone improve the upper bound for r to 0.43 at the same confidence level,
7. effective equation of state for the dark energy is constrained as 
at the 95% confidence level,
8. 
, 
at the 95% confidence level, so Yadav-Wandelt conclusion regarding primordial non-gaussianity does still look much stronger :)
9. 
. With 5 years of polarization data, the optical depth is measured at 5 sigma significance.
The overall conclusion is a spatially flat universe dominated by the dark energy; primordial fluctuations are adiabatic and nearly scale-invariant Gaussian. No surprises…
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