# Bachelor thesis with Prof. Lesgourgues in 2016

**For the summer semester 2016, Prof. Lesgourgues and his research group propose six topics related to cosmology and astroparticle physics. Since we do not speak fluent german yet, most of the interactions between students and myself will be in English.**

Simplified numerical calculation of the Cosmic Microwave Background spectrum

**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:**

- Under the guidance of Pr. Lesgourgues and of members of the cosmology group, 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.
- Study the work of previous bachelor students on this topics: last year, 3 students specialised on 3 parts of the problem, and wrote simple C++ modules solving the equations of each part.
- Gather the three C++ modules of previous students into a single code, and write the final module, leading to the calculation of the ``fingerprint of the universe'', that is, the spectrum of CMB anisotropies.
- Compare the output of this simplified code with accurate results obtained with existing sophisticated codes.
- 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, the student should enjoy coding, and have basic notions of C++.

Calculation of the Dark Matter relic density: the WIMP and axion cases

**Context:**

We know that the universe contains 25% of Dark matter today, but we don't know what it is made of. Among the most popular candidates, one finds: Weakly Interacting Massive Particles (WIMPs), like those predicted by supersymmetry; and axions, like those predicted by the Peccei-Quinn symmetry.

**Goal:**

To reproduce the steps of the calculation allowing cosmologists to estimate the relic abundance of these particles in the universe. These steps are extremely different for these two models, so they are interesting to compare.

**Steps:**

- Understand why we are sure that the universe contains dark matter, and what are the main motivations behind the WIMP and axion scenarios.
- Understand the Boltzmann equation allowing to compute the relic density of WIMPs.
- Solve this equation numerically. This is an interesting numerical problem since this is a stiff equation (calling for an implicit differential equation solver).
- Understand the Klein-Gordon equation allowing to compute the relic density of axions throught the misalignement angle.
- If time permits, solve also this equation numerically.

**Remarks:**

No strong prerequisite in coding are needed for this project, but the student should be willing to improve or practise his/her numerical skills.

Dark Matter constraints from AMS02 cosmic-ray antiprotons

**Context:**

The AMS detector, located on the International Space Station, measures theflux of several particles propagating in the cosmos, including anti-protons. Researchers are trying to interpret the anti-proton spectrum in terms of astrophysical phenomena, plus eventually signatures from Dark matter annihilation (this activity could lead to ``indirect dark matter detection'').

**Goals:**

To solve numerically a smiplified set of equation allowing to predict approximately the anti-proton spectrum in different modelo, and to compare the results to the observed AMS spectrum.

**Steps:**

- Under the guidance of of members of the cosmology and astroparticle group (and mainly of Dr. A. Cuoco, astroparticle expert), understand the basic physical notions behind antiproton production and propagation.
- Understand the main lines of a simplified method proposed in a recent research article for an easy calculation of the anti-proton spectrum.
- Implement this semi-analytical calculation.
- Compare it with existing more sophisticated numerical codes.
- Compare the results with AMS data.

**Remarks:**

No strong prerequisite in coding are needed for this project, but the student should be willing to improve or practise his numerical skills.

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. It is interesting to try to compute the sensitivity of this future experiment to cosmological parameters. This 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).

**Steps:**

Under the guidance of Pr. Lesgourgues and members of the cosmology group, learn a minimum of cosmology in order to understand the physical framework of the project. To understand Bayes theorem, and the principle of a few Monte Carlo algorithms (Metropolis-Hastings, Multinest, EMCEE, etc.

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 in the future, the student will 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. The language used for this project will be Python. In order to save time, for this project, we would prefer to take a student who already knows some Python.

Sensitivity of future CMB experiments to cosmological parameters

**Context:**

In several years, a satellite might be launched by ESA in order to map the fluctuations of CMB anisotropies and measure more accurately the free parameters of the cosmological model. It is interesting to estimate the sensitivity of this epxeriment to comsological parameters. This 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 calculate the expected sensitivity of futre CMB satellite projects a a few parameters beyond the minimal cosmological model. Understanding the methodology will be as important than the actual final results. There is a mixed purpose in this project: understanding cosmology basics (like in project A) and Bayesian statistics (like in project D).

**Steps:**

- Under the guidance of Pr. Lesgourgues and members of the cosmology group, learn a minimum of cosmology in order to understand the physical framework of the project.
- To understand Bayes theorem, and the principle of one Monte Carlo algorithms (Metropolis-Hastings).
- To write a small code using the Metropolis-Hastings algorithm to fit a toy model to a mock observation.
- To switch to a professional code doing the same in the context of comsology, and use it to make forecasts of the sensitivity of the future CMB satellite.

**Remarks:**

No strong prerequisite in coding are needed for this project, but the student should be willing to improve or practise his/her numerical skills.

Simulation of the merging of primordial black holes

**Context:**

It has been proposed recently that Dark Matter, accounting for about 25% of the energy content of the Universe today, could be made of massive primordial black holes (larger than a stellar mass), formed in the early Universe. In order to pass the most recent astronomical and cosmological constraints, those black holes should have experienced high rates of merging, in order to acquire large masses today.

**Goals:**

The first goal of the project is to develop a simple N-body code to study the evolution of a network of such black holes in the early Universe, accounting for the Newtonian force between them at short distances. The second objective is to determine if the merging process is efficient enough for the model to pass the observational constraints.

**Steps:**

- Under the guidance of members of the cosmology group (in aprticular Dr. Sebastien Clesse, expert in primordial black holes), to understand why we are sure that the universe contains dark matter, and what are the most popular dark matter candidates.
- To understand the main lines of the dark matter model consisting in primordial black holes: what are they, how are they produces, ho do they behave.
- To write a numerical code simulating the evolution and merging of black holes inside a box. This code will use simplifying assumptions and wll be much easier than usual N-body code simulating the clustering of ordinary dark matter particles.

**Remarks:**

This project is probably the most challenging from the coding point of view. The student should really enjoy coding, and have solid notions in at least one programming language (C, C++, fortran, python...).