CMB radiation power spectrum in CDM open universes up to 2nd 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 CDM 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–$\mathrm{\Omega }$ models, the contribution of the secondary multipoles to the radiation power spectrum is negligible both for standard recombination and reionized scenarios, with the 2–year COBE–DMR normalization. For a flat universe this contribution is $\approx 0.1-10\mathrm{\%}$ depending on the reionization history of the universe and on the normalization of the power spectrum.