This course provides a pedagogical introduction to Effective Field Theory methods (EFTs) for cosmology and gravitational theories, with a particular focus on theories that have been introduced to explain or tackle cosmic acceleration, dark energy, modified gravity, and the cosmological constant problem. Particular emphasis will be given to how low energy global and local symmetries—be they broken or unbroken—determine and organize the EFT expansion of all such theories both at the classical and quantum level. Where possible focus will be given in simple explicit examples.

Lectures 1-2: A brief intro to EFTs and why non-renormalizable theories are renormalizable (at least at low energies). General relativity as the low energy EFT of a massless spin-2 particle, Einstein-Cartan and first-order formulations. Coupling quantized gravity to QFTs, field redefinitions and decoupling limits, 1PI effective actions, loop corrections and the (old) cosmological constant problem.

Lecture 3: EFTs of dark energy, modified gravity I: scalar-tensor theories, large extra dimensions and branes, EFTs of nonlinearly realized global symmetries (axions, DBI, Galileons, conformal Galileons, k-essence, example UV completions).

Lecture 4: EFTs of dark energy, modified gravity II: EFTs of spontaneously broken diffeomorphisms (inflation/quintessence, fluids, solids aka Lorentz-violating massive gravity, Lorentz-invariant massive gravity and its extensions).

Lecture 5: Schwinger-Keldysh formalism, wavefunction of the Universe, cosmological bootstrap and analyticity.

The course only requires basic knowledge of quantum field theory (specifically in the path integral formulation) and general relativity. More details on aspects of the course can be found in the book “The Encyclopaedia of Cosmology”, Set 2: Frontiers in Cosmology: worldscientific.com