Cosmology and Structure Formation 2

Cosmic inflation

• Motivation of cosmic inflation
• Description of inflationary expansion by scalar fields
• Slow-roll approximation
• Inflation and modified gravity
• Quantum fluctuations and primordial perturbations
• Properties of cosmic density perturbations
• Isocurvature modes and non-Gaussianity

Nonlinear structure formation

• Motivation, difficulties, techniques
• Weakly nonlinear regime
• Gravitational collapse, Press-Schechter theory
• Biased tracers

After successful completion of the module the students are able to:

• explain motivations for the paradigm of cosmic inflation using quantitative arguments
• solve the equation of motion for the inflaton field, and explain the relevant approximations
• apply the slow-roll approximation to new models and derive predictions for the statistical properties of density perturbations
• compute the spectral index and tensor-to-scalar ratio
• explain mechanisms leading to isocurvature perturbations and non-Gaussianity, and apply them to new scenarios
• be able to derive a quantitative statement about the size of nonlinear effects for a given observable
• apply methods of perturbation theory for weakly nonlinear observables
• compute at which point a density perturbation collapses into a gravitationally bound object
• explain and apply statistical methods for describing biased tracers

PH2248: Cosmology and structure formation recommended.

This module consists of a lecture and an exercise course. The learning contents are taught in a thematically structured lecture, with special emphasis both on technical skills as well as physical understanding. The relation to contemporary research and the connections between theory and observations are emphasized. In exercise classes the students practice the techniques based on examples and problems. The understanding is deepened by transfer tasks, enabling the students to explain and apply the learning contents independently.

Combination of slides/graphs and blackboard, script containing the contents of each lecture is published on moodle every week, problem sets are being corrected and then discussed interactively in the tutorials

• S. Dodelson: Modern Cosmology, Academic Press, (2014)
• D.H. Lyth, A.R. Liddle: The primordial density perturbation, Cambridge University Press, (2009)

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

• Which problems exits in cosmology without inflation, and how are the solved quantitatively via inflation?
• Waht is the slow-roll approximation? Apply it to an example potential.
• Which properties do primordial density perturbations have in various models of inflation, and how can the be tested by observations?
• How are nonlinearities described, how is the 1-loop power spectrum computed?
• What are biased tracers and how are their properties described quantitatively?

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.