Cosmology problems and solutions
Universe in Problems · An online problem book
Explore cosmology by solving problems.
From general relativity and black holes to dark matter and the expanding Universe, learn through problems with worked solutions. Start with the warm-up chapter or choose a topic below.
2,016 problems in the collection · 18 subject areas · Worked solutions
Browse topics
Chapter 01
Build intuition with astronomy, geometry, physical scales and gravity.
Chapter 02
Study homogeneous space, general relativity, FLRW geometry and cosmic expansion.
Chapter 03
Explore Friedmann solutions, curvature, horizons and the Big Bang model.
- General questions
- Solutions of Friedman equations in the Big Bang model
- Polytropic equation of state
- The role of curvature in the dynamics of the Universe
- The Milne Universe
- Cosmological horizons
- Energy conditions and the Raychaudhuri equation
- Influence of cosmological expansion on local systems
- Dynamics of the Universe in terms of redshift and conformal time
Chapter 04
Investigate Schwarzschild and Kerr geometry, orbits and gravitational collapse.
Chapter 05
Work with the cosmic microwave background and its anisotropies.
Chapter 06
Connect particle physics, temperature, entropy and the thermal history of the Universe.
Chapter 07
Study the growth and evolution of cosmological perturbations.
Chapter 08
Explore inflationary dynamics and scalar-field models.
Chapter 09
Investigate the cosmological constant and dynamical dark-energy models.
Chapter 10
Study evidence, particle candidates and models of dark matter.
Chapter 11
Explore energy exchange and interacting dark-sector models.
- Physical mechanism of energy exchange
- Phenomenology of interacting models
- Simple linear models
- Cosmological models with a change of the direction of energy transfer
- Non-linear interaction in the dark sector
- Phase space structure of models with interaction
- Peculiarity of dynamics of scalar field coupled to dark matter
- Realization of interaction in the dark sector
- Statefinder parameters for interacting dark energy and cold dark matter
- Interacting holographic dark energy
- Transient acceleration
Chapter 12
Work with the standard cosmological model and its parameters.
Chapter 13
Study weak gravitational fields, wave propagation and binary systems.
- Motivation and symmetries / Introduction
- Linearized Einstein equations
- Gauge transformations and degrees of freedom
- Wave equation
- Transverse traceless gauge
- Gravitational waves and matter
- Energy of gravitational waves
- Binary systems
- Gravitational Waves: scale of the phenomenon
- Generation and detection of gravitational waves
Chapter 14
Connect cosmological models with light, distances and gravitational lensing.
Chapter 15
Explore entropy, information and holographic descriptions of gravity.
Chapter 16
Understand causal structure, conformal diagrams and cosmological horizons.
Chapter 17
Study acceleration, deceleration and the expansion history.
Chapter 18
Explore problems at the interface of quantum theory and cosmology.
About the book
This is the online edition of a cosmology problem book. Familiarity with special and general relativity and elementary particle physics will help you get started.