Cosmic microwave background radiation power spectrum in cold dark matter open universes up to second-order perturbations

A second-order perturbation theory approach is developed to calculate temperature anisotropies in the cosmic microwave background. Results are given for open universes and fluctuations corresponding to cold dark matter models with either Harrison-Zeldovich (HZ) or Lyth-Stewart-Ratra-Peebles (LSRP) primordial energy-density fluctuation power spectrum. Our perturbation theory approach provides a distinctive multipole contribution as compared to the primary one, the amplitude of the effect being very dependent on normalization. For low-Omega models, the contribution of the secondary multipoles to the radiation power spectrum is negligible for both standard recombination and reionized scenarios, with the 2 year COBE DMR normalization. For a flat universe this contribution is approximate to 0.1%-10% depending on the reionization history of the universe and on the normalization of the power spectrum.