1. Some big picture

Three reasons to study constants:
1. "metrology": measure constants as fundamental parameters in the early universe
2. study tensions H0, w0, wa
3. Pheno: study well motivated models coming from high energies
Three reasons to work with P. Brax:
1. constraint his model with data (which must imply some level of constant variations)
2. avoid local constraints with screening?
3. avoid local constraints with a different dynamics involving multiple coupled fields (axions/dilaton)

2. Key steps for an internship/thesis

First step: treshold variations
- biblio overview
- constants to study: alpha and me in priority. Then G, dimensionless ratios and coupled variations
- plot and interpret cosmological observables with CLASS. Identify how, why and where the code is modified.
- make Fisher forecasts with existing CLASS
- reproduce cte from Planck using PR4
- apply to Planck PR4
- apply to PLK+SPT+ACT
Second: phenomenology?
- implement more complex models (alpha(z), me(z), ...)
- build specific model adapted to tensions

General reviews:
- Uzan (2025) The most important one!
- Martins (2017) Shorter but a bit outdated
- Will (2014) On gravitation theory and equivalence principle
Effective measurements of cte
- change cte Planck: Planck 2015
- m_e: Schöneberg&Vacher 2024
- G: Lamine et al. 2024
- dimensionless numbers in CMB/BAO: Rich (2015)
- Constraints from Planck: Hart&Chluba 2017, Hart&Chluba 2019
- Existing constraints using PK+SPT+ACT Toda&Seto 2025
Model to resolve cosmo tensions
- Vacher&Schoneberg (2023) On difficulty to build simple scalar field models solving H0 with CMB
Spatial variations of constants:
- spatial variations and CMB: Smith+ (2019)
String theories
- dilaton theory Damour+ (2002)
- dilaton pheno: Vacher&Schoneberg (2023)