Lectures on modified gravity: Rodolphe Cledassou/Euclid summer school 2026
Léo Vacher
Disclaimer: These notes are still a work in progress! Let me know if you spot any typos or anything to add at leo.vacher@ijclab.in2p3.fr
Lecture notes
- I. Foundations of general relativity
- What to modify? Foundations of general relativity
- Empirical validation of GR I: solar system and astrophysical constraints
- Empirical validation of GR II: Fundamental constants
- Empirical validation of GR III: Gravity and cosmology
- Theoretical aspects of GR I: field theory or geometry?
- Theoretical aspects of GR II: Alternative but equivalent formulations: the trinity of gravity
- Theoretical aspects of GR III: Other formulations and useful tools: ADM formalism, Palatini action, forms and tetrads
- II. Going beyond GR: phenomenology
- Why going beyond general relativity?
- How to go beyond general relativity? Lovelock theorem
- Additional degrees of freedom: Brans-Dicke and scalar-tensor theories
- Escaping the constraints: Screening
- Additional degrees of freedom: Horndeski theories and more
- Additional degrees of freedom: Massive gravity
- Additional degrees of freedom: Torsion and gauge gravity
- Higher terms: $f(R)$ and more
- Higher dimensions: Kaluza-Klein
- Higher dimensions: DGP gravity, Lovelock gravity
- III.Going beyond GR: high energies
- This part is in prep, it will not be included in this year’s class!
- Is gravity quantum?
- Gravity, black holes and thermodynamics
- High energies and swampland conjectures
- String theory
- Loop quantum gravity
Additional material
Tools you may need:
CLASS and CAMB are usual Boltzmann solvers used in cosmology. They admit special versions to test modified gravity models:
- hi_class: modified class version for Horndeski models.
- mochi_class: a refined version of hi_class
- EFT CAMB: CAMB for effective field theory
- MGCAMB: CAMB for modified gravity
- hi_cola: $N$-body simulations for Horndeski models to test the non-linear regime