Consistent Initial Conditions for Early Modified Gravity in Effective Field Theory

Precise initial conditions (ICs) are crucial for accurate computation in cosmological perturbation theory. We derive the consistent ICs for Horndeski theory in the Effective Field Theory (EFT) approach, assuming constant EFT functions at early times. We implement the ICs into the public Boltzmann code \texttt{EFTCAMB}, and demonstrate that the expected early-time behavior of perturbations and Weyl potential can be obtained with theory-consistent MG ICs. We identify significant deviations when comparing Cosmic Microwave Background angular power spectra in MG models obtained with consistent MG ICs versus inconsistent GR ICs. Our findings underline the importance of using accurate, theory-consistent MG ICs to ensure robust cosmological constraints on early MG models.