Dark energy or modified gravity
Distances fix how fast the universe expanded. Growth of structure and gravitational lensing then test whether gravity on that expansion is Einstein’s. Build the test step by step, rerun the model grid, and read the DESI 2024 analysis with its caveats.
L1 · Concept
Can the same expansion come with different gravity?
Yes. Distances fix how fast the universe expanded, but not how hard gravity pulls; growth of structure and lensing tell the two apart.
L1 · Chapter
How distances record the expansion
Derive the expansion rate for evolving dark energy, compute comoving and Hubble distances by hand, and see why gravity's strength never enters.
L2 · Chapter
How growth and lensing feel gravity
Derive the growth equation in the scale factor, solve it exactly for matter alone, and use growth and lensing to measure the pull of gravity.
L3 · Chapter
Modified gravity in four functions, and when it is stable
Braiding and a running Planck mass set the growth and lensing response, and two stability conditions decide which models a fit may use.
L3 · Method
Recompute the expansion and growth grid
Rerun the 364-model stability and growth grid with pinned Python versions, check it against independent limits, and set up the hi_class runs.
L4 · Paper guide
Reading the DESI 2024 modified-gravity paper
A section-by-section guide to the DESI 2024 modified-gravity constraints: what agrees with general relativity, the braiding hint and its caveats.