A novel integrated Sachs-Wolfe effect from Early Dark Energy

We study the nonlinear effects of minimally coupled, massless, cosmological scalar fields on the cosmic microwave background (CMB). These fields can exhibit post-recombination parametric resonance and subsequent nonlinear evolution leading to novel contributions to the gravitational potential. We compute the resulting contributions to the CMB temperature anisotropies through the time-variation of the gravitational potential (i.e., the integrated Sachs-Wolfe (ISW) effect). We find that fields that constitute 5% of the total energy density and become dynamical at $z_c \simeq 10^{4}$ can produce marginally observable ISW signals at multipoles $\ell \simeq 2000$. Fields that become dynamical at earlier times and/or have initial displacements at a flatter part of their potential, produce ISW contributions that are significantly larger and at higher multipoles. We calculate these dynamics and the resulting evolution of gravitational perturbations using analytic estimates alongside detailed nonlinear lattice simulations, which couple scalar fields and cosmological fluids to a perturbed metric. Finally, we discuss the possibility of detecting these features with future high-resolution CMB observations.