Isocurvature initial conditions for second order Boltzmann solvers

Understand

We study how to set the initial evolution of general cosmological fluctuations at second order, after neutrino decoupling.

• We compute approximate initial solutions for the transfer functions of all the relevant cosmological variables sourced by quadratic combinations of adiabatic and isocurvature modes.
• We perform these calculations in synchronous gauge, assuming a Universe described by the $\Lambda$CDM model and composed of neutrinos, photons, baryons and dark matter.
• We highlight the importance of mixed modes, which are sourced by two different isocurvature or adiabatic modes and do not exist at the linear level.