**Synopsis: **

This is an introductory course in Cosmology, aimed primarily at Masters and PhD students but open to anyone who would like to know more about the Universe. It will focus mainly on describing the Hot Big Bang paradigm, its mathematical properties and the observational basis on which it stands. The course will be mostly self-contained but some parts of the course will require a basic knowledge of general relativity, quantum field theory and thermodynamics, although the main concepts will be revised.

**Lecturer:** João Rosa, Physics Department, Office 3.13.11 (joao.rosa@ua.pt)

**Schedule:** Wednesdays, 16h30. Each lecture will be 45 min + 45 min, with a short break.

**Location:** Room 22.3.21, Mechanical Engineering Department

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**Course plan and material**

**Lecture 1 - The observed Universe (13/Feb)****: **cosmological expansion; large-scale homogeneity and isotropy; age of the Universe; light-element abundances; Cosmic Microwave Background; visible and dark matter; large-scale structure; evidence for acceleration.

Lecture notes; Online lecture: Part 1; Part 2 (available soon)

**Lecture 2 - Newtonian cosmology I (20/Feb): **Friedmann equation; open, closed and flat universes; Einstein's static universe; evolution of the energy density; critical density; simple solutions in a flat universe.

Lecture notes; Online lecture: Part 1; Part 2

**Lecture 3 - Newtonian cosmology II (20/Mar)**: age of the Universe; acceleration equation; CMB and nucleosynthesis; brief thermal history; cosmological perturbations.

Lecture notes; Online lecture: Part 1; Part 2

**Lecture 4 - Standard cosmology I (3/Apr)**: Friedmann-Robertson-Walker geometries; kinematical observables; particle motion in FRW; particle and event horizons.

Lecture notes; Online lecture: Part 1; Part 2

**Lecture 5 - Standard cosmology II (10/Apr)**: Einstein-Hilbert action; Einstein equations in FRW; Energy-momentum tensor for perfect fluids.

Lecture notes; Online lecture: Part 1; Part 2

**Lecture 6 - Thermal history of the Universe I (17/Apr)**: basic concepts in thermodynamics; Boltzmann equations; decoupling and freeze out.

Lecture notes; Online lecture: Part 1; Part 2

**Lecture 7 - Thermal history of the Universe II (2/May)**: baryogenesis; Big Bang nucleosynthesis.

**Lecture 8 - Thermal history of the Universe III (8/May): **recombination and the Cosmic Microwave Background.

Lecture notes; Online lecture: Part 1, Part 2

**Lecture 9 - Inflation I (15/May): **shortcomings of standard cosmology; De Sitter expansion; Klein-Gordon equation in curved space.

Lecture notes; Online lecture: Part 1, Part 2

**Lecture 10 - Inflation II (22/May): **inflaton action and equations of motion; slow-roll inflation; inflationary model building; reheating.

Lecture notes; Online lecture: Part 1, Part 2

**Lecture 11 - Inflation III (5/June): **density perturbations from inflation; Harrison-Zeldovich spectrum and associated observables.

Lecture notes; Online lecture: Part 1, Part 2

**Lecture 12 - Cosmological perturbation theory I (11/June):** perturbations in FRW; linearised Einstein equations; power spectrum for CDM and radiation perturbations.

Lecture notes; Online lecture: Part 1, Part 2

**Lecture 13 - Cosmological perturbation theory II (12/June)**: primordial gravitational waves; non-linear perturbations: spherical collapse model.

Lecture notes; Online lecture: Part 1, Part 2

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**Course bibliography**

** The early universe*, Edward W. Kolb and Michael S. Turner (Westview Press, 1990).

** Cosmological physics*, John A. Peacock (Cambridge University Press, 1999).

** Principles of Physical Cosmology*, P. J. E. Peebles (Princeton University Press, 1993).

** Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity*, Steven Weinberg (Wiley, 1972).