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Special Topics in Cosmology (Fall 2015)

General:   (The webpage of the course is updated gradually)  - Last Update 4 Feb. 2016

TAKE HOME due to 31 January 2016

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

Class Time:  Saturday and Monday   13:30 -  15:00

Place: Chemistry department - Room No. 2

Office Hours:  Mondays 13:30 - 14:30  /  Tuesdays 9:00 - 10:00  (Or by appointment) 

Number of Registered Students: 8

About the Course:

The main subject of the course is  the

Cosmology with Large Scale Structures.

 The topics that will be covered or touched are as below:

(The 30 % of time that will be focus on the subjects depends on the background and research interest of the audiance)

A) Observational Cosmology and AstroPhysics

A1) An introduction to observational Cosmology from Milky way to CMB (Historical Percpective).

A2) Structures in the Universe from Galaxies to Voids.

A3) Astrophysical problems related to Cosmology (Sunyeav -Zeldovich effect and ...)

A4) Cluster Counts and physics of galaxy clusters and Missing Baryon Problem

A4) Voids from Theory to Observation

B) Accelerated Expansion of Universe

B1) Accelerated Expansion of the Universe (Observational Evidence)

B2) Accelerated Expansion of Universe (Cosmological Constant Problem, Dark Energy / Modified Gravity and Observational tests)

B3) BAO,Velocity field and Redshift Space distortion

B4) Weak lensing and Cosmic shear

C) Structure Formation

C1) Perturbation Theory and Linear structure formation (Eulerian, Lagrangian and etc )

C2) Statistics of galaxies from two point function to matter power spectrum and observations

C3) Non-linear structure Formation, Spherical collapse,  Excursion set theory and Halo model

C4) Dark Matter - Baryon connection, Bias, HOD and etc...

 C5) Effective field theory approach to LSS

D) Dark Matter

 D1) Observational Evidence of Dark Matter

D2) Dark Matter and  small Scale challenges

D3) Indirect detection of  Dark Matter

E) Early Universe

E1) From Inflation to CMB and LSS

E2) Early Universe Physics

E3) Alternatives to Inflation


F1)  Introduction to CMB

F2) CMB Polarization

F3) CMB Lensing

G) Relativistic Cosmology

G1) Propagation of light in clumpy Universe

H) Statistical Methods in Cosmology and Data

H1) Model selection and foreast

H2) Data Mining adn data analyses


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  Depends on Performance ( 7 points)

Code + Paper Reading: 5 points  Depends on Performance ( 2 points)

Project and Presentation: 6 points  Depends on Performance ( 8 points)

Final Take Home Exam:  3 points   Depends on Performance ( 5 points)

Total grade: 22

You can find your  Total  grades Here

Suggested Reading:

It is strongly recommendet to check the web-page of Special topics in Cosmology lectured in Spring 2013.

Suggested readings on topic below:


1) 1980 - The Large Scale Structure of Universe by James Peebles - Princeton University Press.

2 ) 1993 - Principles of Physical Cosmology by James Peebles -  Princeton University Press.

3) 1993 -  Structure Formation in the Universe  by T. Padmanabhan - Cambridge University Press.

4) 1994 - The Early Universe by by Edward Kolb and Michael Turner, Westview Press.

5) 1999- Cosmological Physics by John A. Peacock - Cambridge University Press.

6) 2003 - Modern Cosmology  by Scott Dodelson - Academic Press.

7) 2005- Physical Foundation of Cosmology by V. Mukhanov - Cambridge University Press.

8) 2008- Cosmology by Steven Weinberg -  Oxford University Press.

9) 2010 - Dark Energy: Theory and Observation  by  Luca Amendola and Shinji Tsiujikawa - Cambridge University Press.

10) 2010 - Galaxy Formation and Evolution  by Houjon Mo, Frank van den Bosch and Simon White - Cambridge University Press.

Some Specific books:

1) Cosmology and Astrophysics through problems - T. Padmanabhan - Cambridge University Press - 1996. (GRADUAE)

A very nice self study book with many mind provoking questions and answers in astrophysics and cosmology. Padmanabhan sketch a very interesting path from questions using the first principles of physics in statistical mechanics, classical mechanics and electrodynamics in to the very hard and research oriented questions in modern cosmology. It is a very good book for a starting graduate student and suitable one for self study in a summer time.

2) Extragalactic Astronomy and Cosmology - Peter Schneider - 2006

For observational cosmology

3) Galactic Dynamics by  James Binney and Scott Tremaine , Princeton University Press - 2008

For galactic dynamics and DM in small scales

4) The Cosmic Microwave Background by Ruth Durrer - Cambridge University Press;  2008


5) Lectures on Cosmology Editors: Wolschin, Georg (Ed.), Springer Edition (2010)

For data analysis, inflation and accelerated expansion of Universe


RA- Halo models of large scale structure
Asantha Cooray (Caltech), Ravi K. Sheth (Pittsburgh U. & Fermilab). Jun 2002. 166 pp.
Published in Phys.Rept. 372 (2002) 1-129
DOI: 10.1016/S0370-1573(02)00276-4
e-Print: astro-ph/0206508

RA- Weak gravitational lensing of the cmb
Antony Lewis (Cambridge U., Inst. of Astron.), Anthony Challinor (Cambridge U.). Jan 2006. 87 pp.
Published in Phys.Rept. 429 (2006) 1-65
DOI: 10.1016/j.physrep.2006.03.002
e-Print: astro-ph/0601594

 RA-Observational Probes of Cosmic Acceleration
David H. Weinberg, Michael J. Mortonson, Daniel J. Eisenstein, Christopher Hirata, Adam G. Riess, Eduardo Rozo - arXiv:1201.2434



A) Expanding Homogenious Universe

1-  Dark Energy by Luca Amendola and Shiniji Tsujikawa 2010 - CHAPTER 2

 2- Lecture Notes by Daniel Baumann - Chapter 1 (

B) Cosmological Perturbation Theory

1- Dark Energy by Luca Amendola and Shiniji Tsujikawa 2010 - CHAPTER 4

2- Lecture Notes by Daniel Baumann - Chapter 4 (

3- Galaxy Formation and Evolution by Houjun Mo, Franck van den Bosch and Simon White - 2010 - Chapter 4

C) Non-Linear Structure Formation

1- Structure Formation in The Universe by T. Padmanabhan, Cambridge University Press - 1993 - Chapter 8.

2- Cosmology and Astrophysics through problems by T. Padmanabhan, Cambridge University Press- 1993 - Chapter 8

Lectrure Notes and Presentations:

Time Line of Lectures:

Lecture 1: (19/ 9 / 2015)

* Topic that will be covered in this course is discussed

* References and grading

* Brief History of Cosmology in perspective of 1998 debate between M. Turner and J. Peebles

* The observables ( Position, Distance) and Spectral Energy Density

* The Pillars of Modern Cosmology ( Cosmological Principle, Expanding Universe, General Relativity)

* Distance measurement

* Friedmann Equation and  cosmological constant problem

* Supernova distance modulus

Lecture 2: (21/ 9 / 2015)

* A review on Background Cosmology

* Old and New Cosmological Problem

* An introduction to Dark Energy (Quintessence Models), Modified Gravity

* Phenomenological approach to dark energy problem.

* On Eratosthenes: See the link placed in its section

Lecture 3: (26/ 9 / 2015)

* A review on Previous session.

* Vanilla 6 parameter cosmology model and the calculated parameters

* LCDM extensions via parameters

Lecture 4: (28/ 9 / 2015)

*Introduction to Statistical Methods in cosmology

* Chi-square fitting - SNe data and LCDM standard model

Lecture 5: ( 3/ 10 / 2015)

* The Monte Carlo Markov Chain as a statistical tool for Cosmology

* An introduction to Perturbed Universe.

Lecture 6: ( 5/ 10 / 2015)

* Perturbed Universe, density contrast, Jeans Length and the evolution of Horizon

* Newtonian Perturbation Theory and evolution of matter density contrast.

* Introduction to Relativistic Perturbation theory

* The concept of correlation function

Lecture 7: (  10 / 10 / 2015)

* The dynamic of density contrast

* The matter distribuution observables (Power Spectrum, Growth rate and redshift sapce distortion, ... )

*  The concept of Bias.

Lecture 8: (  12 / 10 / 2015)

* Linear Perturbation theory in relativistic regime.

* The concept of gauge invariant quantities.

 Lecture 9: ( 17 / 10 / 2015)

* The perturbation theory of dark matter

* Concept of Transfer function and Growth function

 Lecture 10: ( 19 / 10 / 2015)

* The matter power spectrum and observational constraints on its shape

* Introduction to galaxy clustering, Weak Lensing, Lyman alpha forest

Lecture 11: (  26 / 10 / 2015)

* The boltzman equation for relativistic components of universe

* Introduction to the CMB and the consept of angular power spectrum

* Monopole and dipole study of the temperature perturbation in evolutionary scheme.

Lecture 12: (  31 / 10 / 2015)

* The horizon Problem

* The shrink of the Hubble sphere and Inflationary models with slow roll condition

* Introduction to perturbation theory in inflation

Lecture 13: (  2 / 11 / 2015)

* A lecture by Mr.  Baygi  on Critics on inflation

* Perturbation theory in inflation and primordial power spectrum


After this session each Lecture will devoted to a very specific topic:

Lecture 14: (  7 / 11 / 2015)

Excursion Set Theory

Lecture 15: (  9 / 11 / 2015)


Lecture 16: (  14 / 11 / 2015)

Velocity Field and Redshift Space distortion

Lecture 17: (  16 / 11 / 2015)

Galactic Scale challenges of Dark matter (Missing satellite problem, Too big to fail and ...)

Lecture 18: (  21 / 11 / 2015)

Baryon Acoustic OScillation

Lecture 19: (  28 / 11 / 2015)

Weak Lensing and Cosmic Shear

Lecture 20: (  30 / 11 / 2015)

CMB Polarization


1) Show how different representation of FRW metric is equal and define the luminosity distance and angular diameter distance in FRW metric.

2) Plot the distance modulus curve \mu=\mu(z) for standard cold dark matter model and LCDM model and compare it with the Union2 data points. The data is available in Data+Code part.

3) Why the equation of the state of a vacuum energy is equal to -1?

4) Derive the Friedmann Equations from Einstein field equations for FRW Universe.

5) By using the variational method, derive the field equation from the action of Einstein-Hilbert + Cosmological constant term.

6) Plot the distance modulus curve \mu=\mu(z) for  LCDM  and dark energy models with equation of state w=w_0 + w_a (z / (1+z)) and compare it with the Union2 data points. The data is available in Data+Code part.

7) Use the Joint Light curve Analysis SNe data 

to find the best parameter of matter density contrast and Hubble parameter in flat Universe.

8) Use the MCMC method to find best parameters matter density contrast and Hubble parameter in flat Universe.

9) Derive the equation for the evolution of dark matter density contrast from the continuity, Euler and Poisson equation.

10) Write a numercial code to solve the growth dunction \times (1+z) versus redshift for standard LCDM model.

11) Find out the evolutionary equation of CMB temperature monopole which is coupled to the other moment.

12) Derive the slow roll parameters of inflation in terms of inflaton's potetial.

13) Show that curvature perturbation which is a gauge invariant quantity is constant in super horizon? Which conditions is needed to fulfil this.

Paper Reading:

Assignment on Paper reading:

1) Paper 1 and 2

2) Choose one of the papers (3, 4, 5, 6, 7)


List of The Papers:

1)  Is Cosmology Solved? by P. J. E. Peebles - arXiv:astro-ph/9810497

2)  Cosmology Solved? Quite Possibly! by Michael S. Turner - arXiv:astro-ph/9811364

3)  The Cosmological Constant and Dark Energy by P. J. E. Peebles, Bharat Ratra - arXiv:astro-ph/0207347

4) Dynamics of dark energy by Edmund J. Copeland, M. Sami, Shinji Tsujikawa arXiv:hep-th/0603057

5) Is Cosmic Speed-Up Due to New Gravitational Physics? by Sean M. Carroll, Vikram Duvvuri, Mark Trodden, Michael S. Turner - arXiv:astro-ph/0306438

6) f(R) theories by Antonio De Felice, Shinji Tsujikawa arXiv:1002.4928

7) The Physics of Cosmic Acceleration by Robert R. Caldwell, Marc Kamionkowski arXiv:0903.0866

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

* SNIa-Union2

* The Pilot code on SNe distance modulus can be found here


Classic Papers:

1) A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae, Hubble, Edwin, Proceedings of the National Academy of Sciences of the United States of America, Volume 15, Issue 3, pp. 168-173 Publication 1929

2) Cosmic Black-Body Radiation. Authors: Dicke, R. H.; Peebles, P. J. E.; Roll, P. G.; Wilkinson, D. T. - Astrophysical Journal, vol. 142, p.414-419 - 1965

3) A Measurement of Excess Antenna Temperature at 4080 Mc/s. Penzias, A. A.; Wilson, R. W. Affiliation: AA(Bell Telephone Laboratories Inc.), AB(Bell Telephone Laboratories Inc.) - Astrophysical Journal, vol. 142, p.419-421 - 1965

4)Clustering in real space and in redshift space by Kaiser, Nick
Monthly Notices of the Royal Astronomical Society (ISSN 0035-8711), vol. 227, July 1, 1987, p. 1-21. (MNRAS Homepage)



You can choose one of the projects below for the paper reading, presentation and paper work of this class. The projects are going under an intensive update by adding references and review articles and key papers about them.

1) ISW effect, bias of dark matter and galaxies and Weak Lensing to address the bias Problem. (Mollazadeh)

Key papers: , , 

2) Degeneracy of Neutrino Physics, Primordial Non Gaussianity and Modified Gravity on LSS observations. (Khaloei)

Key papers:,

Review articles: arXiv:astro-ph/0603494

3) The 2sigma tension of LCDM on amplitude of fluctuations (\sigma_8) and CMB lensing amplitude

4) Corrections on BAO: Non-linear effects - RSD - WL  (Khoraminezhad)

Key papers:,,

5) Too big to fail Problem and the kinematic of stars in dwarf galaxies. (Bagheri)

Key papers: , ,

6) Inflation, Alternatives (Conformal Point of view) and  observational effects (Khanbeig)

Key papers: ,

7) A  particle physics motivated inflationary model and observational prediction (Zahraie)

8) Long mode, Primordial Non Gaussianity and LSS observations (Farsian- Jalilvand)

Key papers: ,

9) Effect of the peculiar velocity of the host galaxy of SNe on distance measurment (Gholami)

10) Halo Occupation Distribution

11) Assembly bias, halo merger tree and merger rates (Ayromlou)

Galaxy Formation and Evolution - Chapter  7

12) Evolution of the bias

13) Void Phenomenology and its cosmologial implications

14) Effective Field Theory of LSS and Halo model (Chartab)

Review article:

15) CMB Polarization (Ansari)

Cosmology by Scott Dodelson - Chapter 10

16) Kinetic Sunyaev Zeldovich, thermal Sunyaev Zeldovich and its cosmological implications

17) Supermassive black holes, accretion disks and cosmology

18) Missing Baryon Probllem





Interesting Links:

1)  Eratosthenes - Circumference of Earth by Carl Sagan  Click here

2) Annual Review Conversesion with P. James E. Peebles Click Here

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