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Caution!! Although I am happy to share my research notes below with all visitors to my webpages, these pages are mainly designed for my own use and subject to change without warning. I do not guarantee the correctness of all contents as well.



Dr. Ned Wright's colosmology tutorial: link

Basic concepts: 

dark matter (Wiki)
dark energy (Wiki)
An web version of the ARA&A review on baryonic dark matter (here).
Lambda cold dark matter model (Lambda_CDM, see Wiki), the standard model of cosmology.
The time line of the cosmology evolution according to Big Bang theory (from Wiki): 
Zero time: The Augustinian era ==> String theory epoch ==> 10-43s: The Planck epoch ==> 10-35s: The grand unification epoch ==> 10-32s: The inflationary epoch ==> 10-12s: The electroweak epoch ==> 10-6s: The quark epoch ==>  1s: The hadron epoch ==> 3s: The lepton epoch ==> 380,000 years: The photon epoch (matter domination: 70,000 yrs; Recombination 380,000yrs) ==> The dark ages ==> structure formation ==> Reionization ==> Formation of Stars ==> 500,000,000 yrs: Formation of galaxies ==> Formation of groups, clusters and superclusters ==> 8 billion years: Formation of our solar system ==> 13.7 billion year: today.
13.7+-2 billion years ago: Big Bang ==> z=1100, Recombination (); z=10~6, Reionization; 
List of particles
        elementary fermions (quarks and leptons and their anti-particles) and 
        elementary bosons (photon, W, Z, Gluon, Graviton, Higgs) and 
        hypothetical particals 
==> composite particles: hadrons (baryons and mesons) 
==> neuclei 
==> atoms 
==> molecules 
==> condensed matter 
==> other particles. 
(See the original Wiki page here)


Weak lensing and dark matter(DM). (from Kiichi Umetsu's lunch talk on 9 March, 2007 at ASIAA) 
Weak and strong lensing: Radiation from a distant galaxy can be lensed by the gravitational field of a nearer galaxy cluster when the two overlap  along the line of sight. The lensing forms several images of the distant galaxy around the lensing galaxy cluster. Theoretically, a normal galaxy cluster lense will produce 5 images of the lensed distant galaxy. If the distant galaxy is shifted a little away from the lense center, the position, intensity, and shape of the 5 images will change and several images tend merge with each other. When the distant galaxy is shifted far enough away from the lense center, only one image can be seen (at the same side of the distant galaxy).  It's called Weak Gravatational Lensing (WGL) when only one image of the distant galaxy can be seen, otherwise, it's called Strong Gravatational Lensing (SGL).  (Following figures from left to right: strong, intermediate and weak lensing.)
gravitylense01.PNG (5901 字节) gravitylense02.PNG (5837 字节) gravitylense03.PNG (5380 字节) 
Examples of gravitational lensing: 
Abell 1689: red shift Z = 0.183, distance = 550 kpc, the strongest lensing cluster known to date.
Abell 2218: an example of weak lensing.
weak shear: If we assume the lensed image is an ellipse, the major and minor axis a and b define an ellipticity r = (a-b)/(a+b). One can define the ellipticity in two different coordinate systems so as to describe both the shape and orientation of the elliptical lensed image, say, r1 and r2. Then, we have a shear matrix ((r1,r2),(r2,r1)) that fully describes the geometry of the lensed image. 
Dark matter: It's said that the universe is composed of 74% of dark energy (DE), 22% of dark matter (DM), and only 4% of baryons. It's still not clear what DM is. DM might be the so called weak interaction massive particals (WIMPs), such as Neutralino. DM can be divided into two classes: hot dark matter (HDM) and cold dark matter (CDM). People argue that, based on some simulations, HDM is not the major component of our Universe, because the observed power spectral (power versus spatial wavelength) of galaxies and CMB don't agree with HDM model. Therefore, only CDM model is favorable.
Multi-resolution analysis (MRA) of computational cosmology. (from the colloquium talk by Prof. Long-Long Feng on May 30, 2007 at ASIAA)
decomposite the n point correlation function onto a serial of complete and orthogonal base functions with different resolutions.
Relationship between dark matter and galaxies. (From the colloquium talk by Dr. Houjun Mo on May 30, 2007 at ASIAA)
Both observed galaxy luminosity function and simulated dark matter halo mass function are broken exponential functions. But the two function have different slope and broken points. The difference reflects the different efficiency of star formation in dark matter halos with different masses. The formation of galaxies is believed to be induced by the hierachical density structure of dark matter through gravity gathering.
A conditional galaxy luminosity funciton (CLF) is defined to connect the two different broken exponential functions. The meaning of CLF is the probability of a galaxy with luminosity between L and L+dL to live in a dark matter halo with mass M. 
With the Cold Dark Matter (CDM) initial condition, and the assumed Schechter form of the CLF:

The paramter of the CLF can be determined. It is found that the star formation is the most efficient in the dark matter halo with mass of logM = 11.

Properties of dark matter: there is no electric-magnetic and strong interaction with any kind of particle, but only have gravity and weak interaction with each other. Therefore, there is no collision for Dark Matter particles. Dark matter should be a kind of basic particle, and is very tiny. Dark matter can not form Black Hole, because there is no way to cool down DM, due to the lack of electro-magnetical interaction (no collision, no radiation).
Whether dark matter affect the energy level structure or populatioin of normal matter? If yes, how can we observe the effects through radiation?
Torsion cosmology and the oscillating universe (from colloquium talk by Dr. James Nester at ASIAA on Sep. 21, 2007) 
Geometry of the space includes two aspects: metric and connection. Metric of the universe is related to mass that produces curvature to the space; connection of the universe is related to spin that causes torsion to the space. Torsion of a space can be imagined as such: When a reference frame in a space with torsion translate for a distance, the direction of the reference frame will rotate. Although an oscillating universe usually means the recurrence of Big Bang and Big Crunch, in this talk another kind of oscillating universe in which the torsion oscillates periodically while the whole universe keeps homogeneous and isotropic was shown to be possible in their simple model. In another word, the universe could be periodically twisting itself. This possibility gives a new view of the currently accelerating universe, without the help of the Einstein constant Lambda in the equation of cosmology.
Detection of integrated Sachs-Wolfe effect by cross-correlation of the CMB and radio galaxies. (from the lunch talk given by Dr. Guo-Chin, Liu at ASIAA on Sep. 17, 2007)
Sachs [sa:hs] - Wolfe effect is caused by scattering in galaxies after the recombination stage of the early universe. Polarization component of the CMB images are found to be correlated with radio galaxy distributions. Such correlation allows the separation of the Sachs-Wolfe contribution out of the CMB.
The Quadrupole Power Spectrum for the SDSS Liminous Red Galaxies. (from the lunch talk by Dr. Hiroaki Nishioka at ASIAA on Jan. 7, 2008)
When converting redshift into radial distance, the effect of peculiar velocity of galaxies will cause distorsion to the 3D distribution of the galaxies. There are two related particular effects related to galaxy clusters: Alcock-Paczynski effect and finger-of-god effect. A galaxy cluster is usually collapsing due to gravity force. At larger scale, e.g., the outer skirt of the cluster, the infalling velocity of the galaxies will result in a overestimate of distance at the near side of the cluster and a underestimate of distance at the far side of the cluster, which will result in over estimate of galaxy number density in the cluster (Alcock-Paczynski effect). At smaller scale, e.g., near the center of a galaxy cluster, the infalling velocity is so large and so the overestimate and underestimate of the galaxy distance is so large that the far side galaxies will be mis-placed to near side of the cluster and the near side galaxies will be mis-placed to the far side (finger-of-god effect).
Both the Alcock-Paczynski and finger-of-god effects only affect the radial distribution of galaxies when radial distance is calculated from redshift. Therefore, with the 3D Cartesian coordinate (X, Y, Z, with Z along the line of sight), the power spectrum along Z axis is distorted by the above effects while it remains the intact in both X and Y directions. In this case, the 3D power spectrum P(k_x, k_y, k_z) collapses into a 2D power spectrum P(k_z,mu) where mu is the cosine of the angle of the considered direction w.r.t. Z axis, the line-of-sight. This dependence of power spectrum on direction cosine mu can be decomposed into different multipole components: monopole, dipole, quadrupole, ... Among the multipole components, the quadrupole component is the best one to reflect the Alcock-Paczynski and finger-of-god effects. This quadrupole component of the power spectrum is named quadrupole power spectrum. Now, quadrupole power spectrum has been constructed from the 3D distribution of liuminous red galaxies in SDSS database using galaxy number density. It was found that the quadrupole power spectrum changes with redshift, which may indicate the time variation of galaxy distributions during the evolution of the cosmos.


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