Bachelor and Master thesis projects
Bachelor thesis topics
Some topics are suitable for both Bachelor and Masters students (indicated below a topic), with the appropriate adjustment to the workload. Additional topics are possible upon discussion (please contact group members directly).
- Simulations of cosmological structure formation
Kosmologische Strukturen sind nach heutigem Wissen durch den Gravitationskollaps anfänglich kleiner Störungen der Raumzeit entstanden. Dieser Prozess wird in unserer Gruppe durch numerische Simulationen der zugrunde liegenden Gleichungen für die Expansion des Universums und der Dynamik der dunklen Materie und Baryonen untersucht. Wir bieten verschiedene Projekte an, deren Schwerpunkt je nach Interesse von kleineren Skalen (Galaxienentstehung und -entwicklung, Vorhersagen für Beobachtungen mit Großteleskopen) bis zu kosmologischen Skalen (Lyman-alpha-Wald, Galaxiensurveys, Bestimmung kosmologischer Parameter) reichen kann. Eine Mitarbeit im HETDEX-Survey oder dem MUSE-Projekt ist u.U. möglich.
Advisor: J. Niemeyer
- Gravitational collapse in turbulent magnetized gases
Die treibende Kraft in der Astrophysik ist die Gravitation. Von der kosmischen Strukturentstehung bis zur Sternentstehung ist eine wichtige Frage, wann Gas instabil gegen die eigene Gravitation wird und kollabiert. Dafuer gibt es einfache analytische Kriterien wie zum Beispiel das Jeans-Kriterium. Das Gas in Galaxien ist aber stark turbulent und wird ausserdem durch Magnetfelder beeinflusst. Unter diesen Umstaenden ist nicht mehr klar, dass diese einfachen Kriterien ihre Gueltigkeit behalten. Die Aufgabenstellung der Bachelorarbeit besteht darin, Daten aus einer Computersimulation zu verarbeiten, um eine Differentialgleichung fuer die Kontraktion des Gases auszuwerten, die neben der Gravitation auch die Effekte der Turbulenz und der Magnetfelder beruecksichtigt. Die Bedeutung dieser Effekte soll statistisch verglichen werden, und es soll untersucht werden, ob das Jeans-Kriterium naeherungsweise erfuellt ist.
Advisor: W. Schmidt, J. Niemeyer
- Star formation in galaxy simulations
In dreidimensionalen numerischen Simulationen versuchen wir, die Entwicklung scheibenförmiger Galaxien (dazu zählen insbesondere Spiralgalaxien wie z. B. unsere Milchstraße) nachzuvollziehen und wichtige Eigenschaften vorherzusagen. Ein grundlegendes Problem ist dabei die Berechnung der Rate, mit der Sterne gebildet werden. Da die Vorgänge, die zur Entstehung von Sternen führen, auf Längenskalen ablaufen, die viel zu klein im Verhältnis zur Größe einer Galaxie sind, müssen diese durch vereinfachte Modelle beschrieben werden. Die Problemstellung der Bachelorarbeit besteht darin, ein von unserer Arbeitsgruppe entwickeltes Modell in Galaxiensimulationen anzuwenden und die Ergebnisse auszuwerten. Dadurch soll der Einfluss der Modellparameter untersucht werden. Eine weitere Frage ist, ob der beobachtete Zusammenhang zwischen der Sternentstehungsrate und der Gasdichte in der Galaxie (das sogenannte Kennicutt-Schmidt-Gesetz) erfüllt ist.
Advisor: W. Schmidt, J. Niemeyer
- Multi-field Inflation with random potentials
Inflation, a rapid expansion of the early universe, is well accepted in contemporary cosmology. This phase may be driven be several fields, whose potential is not well known, and often includes some random component. Inflation is generically rare, of short duration and ending up at a rare low value of the potential. Thus, anthropic reasoning in an eternally inflation universe is often invoked to reconcile with observations (at least 60 e-folds of inflation solve problems of the big bang, the observation of a small but positive cosmological constant, etc.). The thesis would build upon a prior Bachelor prior, with the main aim to compute observables and test the often peculiar potentials that appear to be favoured.
Advisor: D.Battefeld, T.Battefeld, J.Niemeyer
- Open inflation: observational tests
After tunnelling out of a metastable deSitter vacuum (eternal inflation) by a CDL instanton, the universe is fist dominated by curvature before entering a slow roll inflationary phase. This scenario appears to be generic for inflationary models on the string theory landscape, and several observational consequences for single field models are known. The aim of this project is to extract observational signatures in a concrete multi-field setup, following a prior Masters thesis.
Advisor: D.Battefeld, T.Battefeld, J.Niemeyer
- Observational tests of eternal inflation and/or measures
Eternal inflation is hampered by the measure problem, that is the inability to compute probabilities of observables if the set of bubble universes in the multi-verse is infinite. A pragmatic approach is to introduce cutoffs/measures by hand to regulate infinities. The aim of this project is to investigate possibilities to distinguish between different cutoffs/measures observationally.
(Also suitable for Masters students.)
Advisor: D.Battefeld, T.Battefeld, J.Niemeyer
- The topography of eternal inflation
Eternal inflation caused by field sitting in metastable vacua is likely in string theory, and the topography of such a multi-verses has been investigated in the literature for simple toy models, identifying several distinct phases depending on the tunneling rate out of the minimum. However, little is known about the topography in eternal inflation of the Linde type (a field so high in its smooth potential that quantum fluctuations dominate over the classical force, preventing a smooth evolution down the potential). The aim of this project is to investigate if a similar classification can be performed in this type of inflation. Results would help visualizing the multi-verse, even though direct observational consequences will most likely be absent.
(Also suitable for Masters students.)
Advisor: D.Battefeld, T.Battefeld, J.Niemeyer
- Modal decompositions of Non-Gaussianities in selected classes of early universe models
Non-Gaussianities (potentially observable in the three-point correlation function of fluctuations in the CMBR) offer a discriminator between different models of the early universe, particularly if the full shape function were to be used. To make the computational challenges tractable (for data analysis and N-body simulations), decompositions of this shape into a complete set of functions have been proposed. The aim of this project is to apply the theoretical techniques worked out in a recent masters thesis to concrete models (i.e. to NG from backscattering in trapped inflation, or inflation including an extra-species point encounter; following unpublished preliminary work by D.B. and T.B. ). The student could potentially collaborate with a Doktorand.
(Also suitable for Masters students.)
Advisor: D.Battefeld, T.Battefeld, J.Niemeyer
- The status of bouncing models of the early universe
Alternative models in lieu of inflation are rare to come by and usually hampered by sever problems. They are nevertheless interesting, even if it is only to strengthen our belief in the inflationary paradigm. In recent years, several non-singular models of the universe were proposed, claiming to avoid some of the problems (such as fatal instabilities as the null-energy condition is violated, or more pedestrian instabilities in the contracting phase). The aim of this project is to focus on one particular model of the students choice and investigate critically its viability as an alternative to inflation.
Advisor: D.Battefeld, T.Battefeld, J.Niemeyer
- Circular structures in the CMBR from particle production during inflation
Particle production during inflation can occur in the presence of Extra-Species-Locations (ESL) in field space, which are common in moduli-spaces of string theory. Once produced, they can influence the background evolution (trapped inflation) and/or fluctuations (backscattering of the inflaton condensate). As inflation continues, these particles become massive and, if they are stable enough, dilute to the point where a single massive particles is present in a given Hubble patch. The expectation is that this particle will hold back the inflaton(s) in its vicinity, leading to a hot spot in the CMBR. The thesis would build upon several related studies in the literature with the aim to first improve upon some problems in these studies and, if possible, determine the observational signature of an individual massive particle.
Advisor: D.Battefeld, T.Battefeld, J.Niemeyer
- The superposition of circular structures in the CMBR in trapped inflation
This project is related to the one above, with the aim to computed the observational consequences of a superposition of circular structures in the CMBR at varying scales. This phenomenon can occur in trapped inflation. The expectation is an additional contribution to the nearly scale invariant spectrum of scalar fluctuations. The aim of this project is to compute the amplitude of this contribution, and its scale dependence.
Advisor: D.Battefeld, T.Battefeld, J.Niemeyer
- Entering slow roll inflation after tunnelling out of a metastable vacuum
Eternal inflation in a metastable vacuum is likely in string theory, yet it is observationally ruled out during the last sixty e-foldings of inflation. The latter appears to be in a so called slow roll regime, where field(s) slowly roll down a smooth potential. The transition from the first to the second regime takes place through a tunnelling event. Several simple studies exist in the literature to investigate such a model, but little is known about ``realistic'' scenarios. The aim of this thesis is to investigate the feasibility of slow roll inflation after a tunnelling event in more realistic scenarios.
Advisor: D.Battefeld, T.Battefeld, J.Niemeyer
Master thesis topics
- Simulations of cosmological structure formation
Kosmologische Strukturen sind nach heutigem Wissen durch den Gravitationskollaps anfänglich kleiner Störungen der Raumzeit entstanden. Dieser Prozess wird in unserer Gruppe durch numerische Simulationen der zugrunde liegenden Gleichungen für die Expansion des Universums und der Dynamik der dunklen Materie und Baryonen untersucht. Wir bieten verschiedene Projekte an, deren Schwerpunkt je nach Interesse von kleineren Skalen (Galaxienentstehung und -entwicklung, Vorhersagen für Beobachtungen mit Großteleskopen) bis zu kosmologischen Skalen (Lyman-alpha-Wald, Galaxiensurveys, Bestimmung kosmologischer Parameter) reichen kann. Eine Mitarbeit im HETDEX-Survey oder dem MUSE-Projekt ist u.U. möglich.
Advisor: J. Niemeyer
- Simulation of a dwarf galaxy with magnetic field
Magnetfelder im Inneren und außerhalb von Galaxien sind ein hochaktuelles Thema in der astrophysikalischen Forschung. Zwerggalaxien kam möglicherweise eine bedeutende Rolle bei der Magnetisierung des Universums zu. Ziel der Massenarbeit ist es, in numerischen Simulationen die Verstärkung von Magnetfeldern und deren Ausbreitung in den intergalaktischen Raum durch Supernovae zu untersuchen. Als Teil der Aufgabenstellung soll ein von unserer Arbeitsgruppe entwickeltes Modell zur Berechnung der Sternentstehungs- und Supernovarate für Zwergalaxien angepasst und in den Simulationscode implementiert werden. Ein solches Modell ist notwendig, da der Prozess der Sternentstehung in Simulationen ganzer Galaxien nicht direkt berechnet werden kann. Durch einen Vergleich mit früheren Ergebnissen, die auf einem Standardmodell für die Sternentstehung beruhen, soll geklärt werden, welchen Einfluss Details der Sternentstehung und der in weiterer Folge durch massive Sterne ausgelösten Supernovaexplosionen auf die Magnetfelder haben.
Advisor: W. Schmidt, J. Niemeyer
- Cooling instability in the interstellar medium
Ein wichtiger Schritt zur Entstehung von Sternen aus dem interstellaren Gas ist das Kondensieren kalter Gaswolken aus dem warmen diffusen Medium. Die Bildung dieser Wolken wird durch sogenannte Kühlinstabilitäten ausgelöst. Darunter versteht man einen Rückkopplungsprozess aus zunehmender Verdichtung und Abkühlung des Gases. Dieser Vorgang soll in numerischen Simulationen untersucht werden. Unsere Arbeitsgruppe entwickelt zusammen mit dem Berkeley National Laboratory einen Computercode, der für diese Art von Simulationen bestens geeignet ist. Um die Ausbildung der kalten Gaswolken durch die Kühlinstabilität möglichst genau zu verfolgen, können adaptive Methoden eingesetzt werden, die eine besonders hohe räumliche und zeitliche Auflösung in bestimmten Regionen ermöglichen. Die Ergebnisse dieser Masterarbeit werden helfen, aktuelle Fragen über die Dynamik des interstellaren Mediums zu klären.
Advisor: W. Schmidt, J. Niemeyer
- Stoachastic inflation and its theoretical underpinning
Stochastic inflation is a simple approach to incorporate the effect of long-wavelength perturbations onto dynamics during inflation. The long wavelength modes act as a stoachastic noise term in the equations. The aim of this project is to provide a more rigorous theoretical underpinning of stochastic inflation by the application of stochastic calculus. Further, the computation of observational signatures is desirable (it follows preliminary work of T.B. and a collaborator; a strong background in mathematics is useful).
(Also suitable for Bachelor students if stochastic calculus is known already.)
Advisor: T.Battefeld, J.Niemeyer
- Effective field theory approach to Large Scale Structure
To make analytic predictions on large cosmological scales, an eff ective field theory formulated in terms of an IR e ffective
fluid characterized by several parameters, such as speed of sound and viscosity, was recently proposed by Senatore et.al. This promising line of research potentially offers a systematic, analytic approach to structure formation on large scales superior to standard perturbative treatments, potentially alleviating the need to carry out N-body simulations for the largest scales. The goal of this research project is to develop the effective field theory further. A strong background in theoretical physics is desirable.
Advisor: T.Battefeld, J.Niemeyer
- The effective field theory of inflation: selected applications
In the last years, the effective field theory to inflation has been worked out considerably with the aim to classify possible observational consequences of inflation given that a single light field dominates the dynamics; the effects of moderately heavier fields is retained in this approach. The aim of a thesis would be to apply these techniques to concrete events (i.e. a turn in field space, oscillations around a slow roll attractor etc.) and compute observables (power-spectrum, non-Gaussianities, ...). Extensions to a more general multi-field effective-field theory are conceivable (see below), and there is an overlap with the application of modal techniques to the shape function of non-Gaussianities (see below).
(Also suitable for Bachelor Students.)
Advisor: T.Battefeld, J.Niemeyer
- Effective field theory approach to multi-field inflation
An effective field theory approach to single field inflation has been developed and put to good use in recent years. A similar approach to multi-field inflation has been proposed, however with sever limitations. The goal of this project is to investigate this proposal, to identify the shortcomings, and, if feasible, improve upon them. A strong background in theoretical physics is desirable.
Advisor: T.Battefeld, J.Niemeyer
- The use of modal decompositions of Non-Gaussianities in N-body simulations
In a recent Diplom thesis, modal techniques where used to set up non-Gaussian initial conditions for N-body simulations. Based on this preliminary work, as well as a prior Masters thesis on modal techniques, the goal of this project is the improvement of the current code and the development of tools to extract primordial non-Gaussianities after a simulation is run. One science goal could be to test predictions based on a recently developed effective field theory that should be valid on large scales (the latter could in principle be used to model large scales analytically, only requiring N-body simulations on small scales). The student could potentially collaborate with a PhD student. A strong background in programming is required.
Advisor: T.Battefeld, J.Niemeyer
- Turbulence during Preheating
Preheating is the rapid transfer of energy after inflation by means of non-perturbative effects (if they are present, they dominate over slower, perturbative ones). The state immediately after the decay of the inflaton(s) is non-thermal: a thermal, radiation dominated universe is only present after an extended turbulent regime, which has only been studied in a few publications over the years. The aim of this project is to use up to date numerical techniques to investigate this turbulent regime. Further, the feasibility to test for the presence of such a regime observationally should be investigated. Some background in programming is required.
Advisor: D.Battefeld, T.Battefeld, J.Niemeyer
- Observational consequences of oscillons
Oscillons are quasi-stable, localized field configurations that can occur after inflation (i.e. during preheating), but before the time of nucleosynthesis. The goal of this project is to investigate whether these field configurations have any observational consequences. For example, if they dominate the energy density of the universe for a time, they would lead to a matter dominated epoch before the radiation dominated one, which might have observational consequences. Some experience of coding would be desirable to run/improve complementary lattice simulations.
Advisor: T.Battefeld, J.Niemeyer