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Add second growth factor to jax-cosmo cache#143

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ASKabalan wants to merge 1 commit intoDifferentiableUniverseInitiative:masterfrom
ASKabalan:add_growth_second_to_cache
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Add second growth factor to jax-cosmo cache#143
ASKabalan wants to merge 1 commit intoDifferentiableUniverseInitiative:masterfrom
ASKabalan:add_growth_second_to_cache

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This pull request adds support for second-order cosmological growth functions to the jax_cosmo.background module, enabling calculations relevant for second-order Lagrangian perturbation theory (2LPT). It introduces new functions and updates the ODE solver to compute and cache both first- and second-order growth factors and rates, along with comprehensive tests for the new functionality.

This is made to simplify code in jaxpm and to partially solve the leak issue with the cosmo cache

As discussed with @hsimonfroy

@ASKabalan ASKabalan mentioned this pull request Feb 17, 2026
@ASKabalan ASKabalan mentioned this pull request Mar 2, 2026
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