# Bachelor thesis with Prof. Lesgourgues in 2015

For the summer semester 2015, I propose five topics related to cosmology. Since I do not speak fluent german yet, most of the interactions between students and myself will be in English.

Why is the map of Cosmic Microwave Anisotropies the fingerprint of our Universe?

Context:
our best knowledge of the evolution of our Universe on cosmological scales comes from the observation of fluctuations in the Cosmic Microwave Background (CMB) radiation, observed by experiments like the WMAP or Planck satellite. This topic is among the most fascinating of modern physics.

Goal:
to acquire an approximate and intuitive understanding of the CMB and of its fluctuations, based only on easy concepts (fluid mechanics, geometry, Fourier transforms, etc.). To reach the conclusion that CMB fluctuations encode a lot of information on the composition and history of our Universe.

Steps:

1. Under the guidance of Pr. Lesgourgues, get familiar with important concepts in cosmology (expansion of the universe, photon decoupling, propagation of sound waves in the early universe), using only simple known physics and intuition (this can be done together with students choosing other projects).
2. Understand a set of simplified equations expected to describe CMB anisotropies in an approximate way.
3. Implement these simplified equations in a short numerical code written from scratch by the student (could be in Mathematica, python, C, fortran, as the student prefers).
4. Compare the output of this simplified code with accurate results obtained from existing sophisticated codes.
5. Explain in the thesis these simplified equations, and the way in which CMB anisotropies would depend on the composition and evolution of the universe according to the simplified code.

Remarks:
for this project, a student interested in precision calculations and reasoning could be frustrated by the use of many crude approximations, not always thoroughly justified. Instead, people privileging physical intuition will have the satisfaction to get an intuitive understanding of lots of concepts in modern cosmology. The coding part is really simple, and does not requires advanced skills - but the student should have very basic notions of how to solve differential equations numerically, at least in one language.

Producing pedagogical animations showing the evolution of sound waves in the early universe

Context:
our best knowledge of the cosmological evolution of the universe comes from the observation of fluctuations in the Cosmic Microwave Background (CMB) radiation, observed by experiments like the WMAP or Planck satellite. The main physical mechanism involved in CMB physics is the propagation of sound waves in the early universe (with a huge wavelength).

Goal:
to produce some sequences of plots (i.e. some graphical animations) showing the evolution of a simulated sound wave in the early universe. This is an occasion for the student to understand some aspects of cosmology; moreover, the produced animation could be posted on a website, and be used in the future for pedagogical purposes (to illustrate cosmology course at the master/doctoral level).

Steps:

1. Under the guidance of Pr. Lesgourgues, get familiar with important concepts in cosmology (expansion of the universe, photon decoupling, propagation of sound waves in the early universe), using only simple known physics and intuition (this can be done together with students choosing other projects).
2. Generate some data representing an arbitrary over-density in the early universe, and plot it graphically.
3. Fourier transform this configuration.
4. Compute the evolution of the system in Fourier space using an existing code, that simulates the physics of the early universe (no need to modify that big code).
5. At different time steps, store the new configuration in Fourier space, transform it back to real space, and plot it graphically.
6. Assemble the plots together to create a small movie.
7. [Optionally, create a nice web page presenting the results, with some interface allowing on-line users to produce similar movies for different choices of physical parameters.]

Remarks:
Among all the topics of this year, this is the one with less analytic calculations and more numerics. It offers an opportunity for the student to understand some fascinating concepts in the physics of the early universe, using simulations and self-generated plots, rather than equations (before choosing the project, be sure that this is something you like!). Something will remain from this project, since it could be used by many people in the community of students and professors in cosmology (in courses and presentations). The student will also learn how to manipulate, Fourier transform and visualise graphically some simple data. The most convenient would be to use the python language. Previous knowledge of python would be a plus, but a very motivated student can learn it on-the-fly during the project.

What can we infer from recent observational data on the reionisation of atoms in the recent universe?

Context:
our universe went through many different stages related to particle physics (phase transitions, reactions between particles, etc.) The simplest one to understand at the bachelor level is probably the reionisation of the universe a few billion years ago, caused by star formation.

Goals:
To play with models of reionisation, and to use observational data (i.e. experimental astrophysical data) to constrain these models.

Steps:

1. To understand the basic principles of reionisation and the simple equations describing it.
2. To study a bit the literature in order to understand how reionisation can be constrained with different types of observations.
3. To learn how to use a code simulating the evolution of the universe (including reionisation), and another code allowing to compare each model with observations.
4. To run these codes on a cluster of computers, and infer from existing observational data some constraints on a set of parameters describing reionisation. This will be done with a different parametrisation than used in recent research articles, in order to try to get some original results.

Remarks:
This project allows the student to go through a full research project, like a professional phenomenology-oriented researcher. He/she must go through the steps of understanding, modelling, using a simulation code, comparing with data, plotting and presenting the results. This project sounds ambitious, but it is doable within a barchelorarbeit, because reionisation is one of the simplest aspects of cosmology. The students will use computers to run (big) programs/softwares, but without modifying them: there is no programming involved.

Recombination of electrons and hydrogen nuclei in the early universe: the Peebles model and beyond.

Context:
our universe went through many different stages related to particle physics (phase transitions, reactions between particles, etc.) Recombination is an important stage, during which electrons and hydrogen nuclei combine in neutral hydrogen. This explains why the universe is transparent, and why we can observe the CMB.

Goals:
To understand recombination at the physical and analytical level, as well as various approximation schemes used to model it.

Steps:

1. To understand which equations should be used to describe recombination exactly. They rely on the model of the hydrogen atom provided by quantum mechanics, and on kinetic equations accounting for the transition between different levels, when the atoms are in a time-dependent background (a gas of photons in the expanding universe).
2. To understand the simplest approximation to recombination, proposed by James Peebles in the seventies.
3. To understand more recent approximations that have been derived more recently, in order to make fast and accurate computations.

Remarks:
this is a traditional project, consisting in studying a few research papers, in reproducing the most important analytic calculations, and in summarising this topic in the thesis. This project involves no numerics at all, but it is the most involved from the point of view of physics.

Model comparison with observations: Monte Carlo methods for Bayesian parameter extraction.

Context:
in general, comparing theoretical models to experimental/observational data is not so trivial, especially when the number of model parameters is large. A very well-defined framework is called Bayesian parameter extraction. Used in many fields of science, this elegant approach is very efficient when used in combination with algorithms performing a random exploration of parameter space (Monte Carlo algorithms).

Goals:
to use and compare several Monte Carlo algorithms used for Bayesian parameter extraction, in the context of fitting a simple cosmological model to recent cosmological data.

Steps:

1. To learn a minimum of cosmology in order to understand the physical framework of the project.
2. To understand Bayes theorem, and the principle of a few Monte Carlo algorithms (Metropolis-Hastings, Multinest, emcee, etc.
3. Using an existing code for parameter extraction, and picking up an example of cosmological model and dataset, perform a few experiments (numerical runs) on a computer cluster in order to prove that the different algorithms converge to the same results, that they are more or less efficient in different contexts (different likelihoods, different numbers of CPU and running time limits, etc.)

Remarks:
this project is more on statistics and methodology than on physics. An advantage is that the student may have opportunities to apply what he has learned during this bachelorarbeit in many different areas of science (even, maybe, outside of academic research). Cosmology is here a pretext to perform parameter extraction. Nevertheless, this project is also an occasion to learn a bit about this field, without entering into details.