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Special Topics in Cosmology (Spring 2013)


 This is a Ph.D. course, which will be held in Physics Department of Sharif University of Technology.

Class Time:  Sunday and Tuesday   10:30 - 12:00

Place: Physics department- Room 517

Registered students:  3 (Non registered Audiance: 10 )


I want to say my special thanks to:

About the Course:

The main subject of the course is apllicattion of Structure Formation in the  Universe

and related Cosmological Observations in order to address, the three main open questions in Cosmology:

1)Dark Energy    2)Dark Matter    3) Inflation

+  The Role of Baryons in Cosmology from BBN, BAO up to Missing Baryon Problem

 (This Part will be presented by Dr. Farhang Habibi)

To see the general structure for the Syllabes of the course, click here.

The main goals of Course:

1) An introduction to the main Resseach topics in Cosmology.

2) An inroduction to the skills of Reseach in Cosmology


Assignments:  8 points

Project and Presentation: 8 points

Final Take Home Exam:  6 points  : YOU CAN FIND THE TAKE HOME HERE (due to 1 July 2013)

Total grade: 22

You can find the  grades of the course here.

Suggested Reading:

For the reading material of the  course, (Books, Review Articles , historical books, ...)  click here.

To Find More technical papers related to the course or your projects click here.


Lectrure Notes and Presentations:

You can find some Cosmology notes in Cosmology tab!!!

1) CMB + LSS (1) : PDF file  3 March 2013

2) Questions for 21 century: PDF file 12 March 2013

3) Planck: PDF file 7 April 2013

4) Missing Baryon Problem: PDF file for  21 April 2013

5) In Search of Missing baryon Problem and Scintilation : PDF file for  5 May 2013

6) The history of Modern Cosmology : PDF file for 21 may 2013

Time Line of Lectures:

 Lecture 1: (3/2/2013)

In this Lecture, we present the history of modern cosmology through the 4 categorical divisions:  a) 20 century as a debate century for Cosmology, starting from the Shapley-Curtis debate to Turner-Peebles debate  b) Cosmology as a science of measurement of two numbers: Hubble parameter and deceleration parameter  c) 20 Century as a century of perturbation measurements and unraveling the physics beyond its from Wilson-Penzias (1965) to WMAP 9 year data release.  d) Cosmology as the science of unknowns starting by missing mass problem, lately known as Dark matter. Later the problem of  Horizon and Flatness problem (Inflationary paradigm) pops up and finally accelerated expansion of Universe and Dark Energy Problem shows up.


 Lecture 2: (5/2/2013)

In this lecture we talked about the General Relativity and how we can apply it in Cosmology.  Assuming the Cosmological Principle that the Universe in the large scales is homogeneous and isotropic, we find  the dynamics of Universe  is related to the energy-matter content of  the  Universe. We talked about the relevant Cosmological Observations, concluding that the Universe is filled up by radiation (photons, neutrinos), matter (baryonic and non-baryonic) and cosmological constant. Then we talked about the cosmological constant problem, Its old and new versions. And also we discussed the question: Why the LAMBDA is zero (in the old problem) and Why it is so small (in new Problem)?

For this lecture you can read:  Dark Energy (hereafter DE) by Tsujikawa-Amendola Chapters 2-5-6, Modern Cosmology (hereafter MC) by Dodelson Chapters 1-2,  Galaxy Formation and Evolution (hereafter GFE) by Mo, Bosch, White chapter 3, Cosmolgy(hereafter Co) by weinberg chapter 1.

 Lecture 3: (12/2/2013)

 In this lecture, we  argue that in the case we can solve the old cosmological problem and set the Lambda=0, we face to the question: What is the cause of the accelerating expansion of Universe. The most favorite answer to this question is due to modifying the Einstein Equation by  a)Modifying the geometrical part (Modified Gravity Theories) or b) Modifying the Energy-Momentum tensor introducing a new exotic matter, known as the Dark Energy Model. In the category of Dark Energy Models we introduce the quintessence models and in the category of Modified gravity models we talk about f(R) models.  Then we talk about the observations like measuring the luminosity distance of SNIa as a standard candle. Also we talk about the measurements related to the standard candle. We insist in a couple of important points: a) The evidence of Dark Energy comes from different observations: SNIa -CMB- Large Scale structure power spectrum - Weak gravitational Lensing - Cluster Abundance - Integrated Sachs Wolfe  and etc.  b) Most of the cosmological observations measure the Hubble parameter indirectly. It means that what we really measure is the distances. In order to relate the distance to Hubble parameter, where the cosmological parameters are there, we need to assume a model. The  statement of  accelerating expansion of universe is a result of  Cosmological Principle assumption + the validity of General Relativity in Cosmological Scales.

For this lecture you can read:  DE Chapters 2-5-7,  Co  Chapter 1,  Review artice: P.J.E. Peebles and B. Ratra, "The Cosmological Constant and dark Energy",  arXiv: 0207347, Thomas Sotiroui, PhD thesis, arXiv: 0710:4438, Shant Baghram, Ph.D. thesis (2011)

Lecture 4: (17/2/2013)

In this lecture we start the issue of linear perturbation theory in Cosmology. We discuss the free parameters of GR and the gauge issue. We discuss why we are interested in scalar perturbations. Then we study the perturbations in Energy-Momentum tensor. After that the Einstein equations are solved in first order and then we derive the Poisson Equation which relates the geometric potential to matter density contrast. In the next step we talk about the statistical methods in structure formation, introducing the two point correlation function and Power-Spectrum.

For this lecture you can read:  DE Chapters 4,  Co  Chapter 5,  MC Chapter 7, GFE chapter 7

Lecture 5: (19/2/2013)

 In this lecture, we discuss the Big Bang Nucleosynthesis (BBN), which in one hand is a strong evidence of big bang model, and in the other hand it is the
one observation, which indicate the Baryonic matter budget in the Universe. Starting from the thermodynamic history of Universe, we show how
the distribution function of bosons(photons) and fermions (proton, neutron) and their evolution during the cosmic expansion plus the
weak interactions cross section  pin down the abundance of protons and neutrons . In the other investigating the light elements production (Hydrogen, Deuterium, and Helium)
give us a spectacular opportunity to constraint the baryon matter. At last we discuss the astrophysical observations, which constrain the Helium abundance
in metal poor regions which is the indicator of the primordial He abundance. Finally we open up the question of missing baryon problem, arguing that 
amount of baryon found by  astrophysical observations is less than the total baryonic matter constrained from BBN.

For this lecture you can read:   Cosmic Microwave Background Radiation by Durrer  Chapter 5, Co Chapter 5, Ph.D. Thesis of Farhang Habibi

Lecture 6: (24/2/2013)

In this lecture, the main evidence of Dark Matter in the galactic and cluster scales is presented. Starting from the Virial theorem, we show that high dispersion velocity of galaxies in the clusters indicate the presence of unknown matter/or gravitational law  and the luminous baryonic matter can not explain the high velocity dispersion. On the other hand the evidence of Dark Matter is presented in galactic scale, discussing the rotation curves. There is an indication to the work of Peebels, Oistriker about the stability of Disk and dark matter halos. We also talked about the Modified Newtonian Dynamics(MOND) as an alternative explanation. And finally the Bullet Cluster   as a very important observation (Optical - X ray - Weak Lensing) as an evidence of DM is discussed.

For this lecture you can read:   Roos, M. 2010, Dark Matter: The Evidence from asstronomy, astrophysics and cosmology, arXiv: 1001.0316, , Amico G.D., Kamionkowski M. and Sigurdson K., 2009, Based on Villa Olmo and Hiedlberg Lectures, arXiv: 0907.1912, Ph.D. Thesis of Shant Baghram Chapter 13, Ph.D. Thesis of Farhang Habibi

Lecture 7: (26/2/2013)

In this Lecture we review the concept of perturbation in Einstein equations. Then we define the conservation and Euler equations which with the perturbed Einstein equations make a set to find the dynamic of perturbed quantities(density contrast, velocity dispersion, gravitational potentials). Then we discuss the matter power spectrum which contains the terms (amplitude and spectral index from Inflation, Transfer function from physics of baryons, photons and DM, growth function which shows the growth of density contrast in linear regime). Finally we compare the theoretical matter power spectrum with the observational one and we introduce the concept of Bias.

 For this lecture you can read:   DE chapter 4,  Ph.D. thesis Shant Baghram Chapter 10,  Co Chapter 5, MC chapter 7,  TASI lectures on Cosmological Perturbations Julien Lesgourgues, arXiv: 1302:4640


Lecture 8: (3/3/2013)

In this course we review the concept of perturbation theory and find the evolution of matter density contrast, in different epochs. Then we discuss the concept of matter power spectrum, and it ingredients as initial amplitude and scale dependence, transfer function and growth function. Then we have a slide show, "you can find it in lectures part" which describe the initial concepts of Cosmic Microwave Background Radiation and the scientific journey of WMAP.

For this lecture you can read:   DE chapter 4,  Ph.D. thesis Shant Baghram Chapter 10,  Co Chapter 5, MC chapter 7,  TASI lectures on Cosmological Perturbations Julien Lesgourgues, arXiv: 1302:4640, Power Point in the Lecture Notes part.


Lecture 9: (5/3/2013)

In this lecture we discuss the temperature anisotropy in the last scattering surface. We expand the temperature density in spherical harmonics and find the correlation function of coefficients of spherical harmonics. Then we discuss the different moments in CMB map. In the end we discuss the peculiar velocity dispersion variance and we relate it to matter power spectrum and growth index.

For this lecture you can read:   DE chapter 5.6,    Co Chapter 7, MC chapter 7, Review articles:, ,

Lecture 10: (10/3/2013)

In this lecture we discuss about the transfer function. The physics which related the power spectrum of modes entering to the horizon, to the time of last scattering. We discuss the transfer function for sub and super horizon scales and how the modes are influenced by horizon crossing and matter-radiation equality.

For this lecture you can read:  MC. chapter 7, DE. chapter 4

Lecture 11: (12/3/2013)

In this lecture, we talk about the standard big bang model's problems (The horizon problem and flatness problem). Then we argue that how the inflationary paradigm can solve them. We also discuss how the inflation seeds the primordial perturbations in early Universe, by quantum fluctuations and how it reproduce the scale invariant power spectrum. In the end we discuss the three main problems of modern cosmology, it is open questions. (You can find the slides of this part in lecture notes and presentation part).

For this lecture you can read:   TASI Lecture by Baumann  arXiv:0907.5424,  Physical foundation of Cosmology by V. Mukhanov Ch. 5 and 8,  Co Ch. 10

Lecture 12: (7/4/2013)

As a first course after spring holidays we dedicate a whole session to the latest results of Planck Mission which published its cosmological oriented papers in 21 March 2013.

 For this lecture you can read:  You can find the PDF of Planck presentation in Lecture note part.

Lecture 13: (9/4/2013)

 In this lecture we find the initial power spectrum of structures in the Universe. We discuss the perturbation theory in inflationary models. Show how we can find the initial power spectrum of curvature which is a gauge invarient quantity. Then we argue that the power spectrum calculated in the horizon crossing freezed out until the re-enttrence of mode to horizon. And finally we show how we can relate the primordial power spectrum to the one seen in the last scattering surface.

For this lecture you can read:   TASI Lecture by Baumann  arXiv:0907.5424,  Physical foundation of Cosmology by V. Mukhanov Ch. 5 and 8,  Co Ch. 10


Lecture 14:  (16/4/2013)

In this lecture we start the Non Linear Structure Formation theory, we study the spherical collapse and find the critical density contrast of the structures which undergo a collapse. Then we introduce the work of Press-Schechter and show how we can find the mass function of structures. Then we discuss that the PDF of structures as an observable, how can it be used as a tracer of cosmology.

For this lecture you can read:  Lecture Notes in Cosmology Tab of this webpage


Lecture 15: (21/4/2013)

In this lecture we present the Tully Fisher relation.

For this lecture you can read: PDF Presentation of this work (Missing Baryon Problem)

Lecture 16: (23/4/2013)

In this lecture, we continue the non-linear structure formation, reviewing the concept of spherical collapse and the Press-Schechter formalism we go further by studying the excursion set theory and we derive the mass function of the structures in this formalism. Then we introduce the concept of halo bias and we find the halo bias with Peak Background Splitting method and show this term is related to critical density and variance of large scale power spectrum. In the end we talk about the Non-Gaussianity and its effect on halo bias.

For this lecture you can read: GFE Chapter 7

Lecture 17: (28/4/2013)

In this lecture the missing baryon problem is studied.

For this lecture you can read: PDF Presentation of this work (Missing Baryon Problem)

Lecture 18: (30/4/2013)

In this lecture we study how the anisotropy in the power spectrum of primordial perturbation can be translated to the anisotropy in temperature fluctuation in CMB. We also investigate the relation of primordial Non Gaussianity in squeezed limit and its relation to anisotropy.

For this lecture you can read: 

Lecture 19: (5/5/2013)

In this lecture thescintilation method for finding the molecular hydrogens as a candidate of missing baryon problem is investigated.

For this lecture you can read: PDF Presentation of this work (Missing Baryon Problem)

Lecture 20: (7/5/2013)

In this lecture we will study the weak lensing effect. The power spectrum of shear and convergence also we start the  CMB lensing.

For this lecture you can read:  Dark Energy Chapter 4,  Dodelson Cosmology Chapter 10

Lecture 21: (12/5/2013)

In this lecture Dr. Habibi goes through the BAO in LArge Scale structure Formation and the LSST project. Also a  review is presented  for search in missing baryon problem.

For this lecture you can read:  The presentation for In the search for missing baryon problem in presentation section.

Lecture 22: (14/5/2013)

In this lecture we go through a very intersting concept of CMB lensing.

For this lecture you can read:  The review article by Anthony Lewis and Anthony Challinor  arXiv: 0601594

Lecture 23: (19/5/2013)

In this lecture we discuss the CMB polarization and also we study very briefly the statitical methods in cosmology.

For this lecture you can read:  Dodelson's Modern Cosmology Chapter 10 and the Dark Energy book Chapter 13

Lecture 24: (21/5/2013)

In this lecture we conclude our one semester class going through the history of Modern Cosmology its discoveries and unanswered questions.

 For this lecture you can read:  You can find the PDF of Modern Cosmology history in the Lecture notes presentation part.




Each assignment  set will contain 5 problems which will be updated gradually, please check them time by time to get all the problems of a set. The return date of each problem is mentioned. 

1) Problem Set 1

2) Problem Set 2

3) Problem Set 3

4) Problem Set 4

5)Problem Set 5

Data + Code :

1) In the Link below you can find the SNIa data of Union Sample 2, obtained from SuperNova Cosmology Project (SCP), containing 557 type I SuperNovas, the file has 4 column:  1)Name of SNIa  2)Redshift 3) Distance Modulus 4) Error in distance Modulus




1) Cosmology of Warm dark Matter (WDM)

The standard LCDM model with all it accomplishments in describing the cosmological data, it faces challenges in galactic scale. a)The missing satellite problem,  b)Core cusp Problem c)Too big to be failed problem. One of the possible solutions to these challenges is the modification of  LCDM model, by considering WDM, DM that is not as relativistic as neutrinos and is not completely cold as in the standard scenario. The keV scale of free streaming of this hypothetical DM could be a possible explanation for the lack of structures in the Universe in subgalactic scale. In this project

a)Study and review of the concept of WMD and its cosmological consequences in structure formation is intended.

Ref:  1) Ph.D. thesis of  Katarina Markovic from Munchen University :

2) Primordial Anisotropy and Large Scale Structure

Recenntly the Planck misson, confirmed the anisotropy in Cosmic Microwave Background Radiation  arXiv:1303.5083 previously seen by WMAP. Now the question ari will b ethe effect of the primordial anisotropy in Large Scale Structure Observations (like matter power spectrum, etc...) Th epurpose of this project is to overview the concept of anisotropy in CMB, the inflationary motivated models that produce the anisotropy, the probable Non- Gaussianty and finally the effect of this primordial anisotropy in LSS

Ref: 1) Large angles anomalies in CMB by Copi et al.

2)  Dipole in the Sky Cameron Gibelyou  and Dragan Huterer

3)Large Scale anisotropic Bias from primoordial Non Gaussianity by Shant Baghram et al.

3) Cosmological Tests of Gravity

One of the alternatives for cosmological constant for explaining the cosmic acceleration is the modification of gravity in cosmoloogy. Although General relativity is well established in solar system and local gravity tests, but the validity of GR in galactic scales and furthur must be under investigation. In this project we are going to investigate the Cosmology scale tests of Gravity. First we will review the literature.

Ref: 1) Cosmological Tests of Gravity by Bhuvnesh jain and Justin Khoury :


Useful Links:

arXiv : Find Cosmology papers from arXiv.


The NASA Astrophysics Data System Home Page

 Numerical Recipes in C  and also look here

Ned Wright's Cosmology Tutorial

Microwave Anisotropy Probe Home Page

The Physics of CMB Anisotropies - well-illustrated intro by Wayne Hu

Cosmic Microwave Background - FAQs 

The 2dF Galaxy Redshift Survey

Sloan Digital Sky Survey 

The CfA Redshift Survey and Catalog

The Hubble Deep Field

Ask an Astrophysicist 

CMB/Douglas Scott(UBC) 
Max Tegmark's cosmic microwave background data analysis center: experiments
CMB Resources Page