Separate the Tensor Perturbation From the CMB Temperature Anisotropy Power Spectrum

For studying the difference effect on the Cosmic Microwave Background Radiation (CMB) anisotropy spectrum by scalar and tensor perturbation, we define another function Alm, which can reflect the effect of different magnetic quantum number m. For a given l, we find that the ratio relations of Alm is different for the scalar perturbation sources and tensor perturbation sources. This give a new way to directly separate the tensor perturbation from CMB anisotropy power spectrum. Applying this method to study the CMB anisotropy quadrupole observed by COBE, we find that this quadrupole is not generated by isotropy scalar perturbation, the contribute of tensor perturbation is obvious. We can also study the anisotropy of the scalar perturbation by measuring the values of Alm in different coordinate system. PACS numbers: 98.80.-k, 98.80.Es, 04.30.-w, 04.62+v, e-mail: [email protected] The inflation models mainly predicted two kind of important perturbations: the scalar perturbation and the tensor perturbation (relic gravitational waves)[1]. The detection of them is the main way to research the inflation physics, especially the tensor perturbation, which directly relate to the energy scale of the inflation, and can give the clearer information about the evolution of the Universe[1, 2]. The detection of these two kind of perturbation are mainly by the researching of the CMB anisotropy and polarization. A lot of people have discussed the anisotropy and polarization power spectrum generated by scalar perturbation and tensor perturbation in numerical method or in analytic method[3]. In these years, the precise observation of the CMB anisotropy and polarization have made an important progress, especially the release of the high resolution full sky Wilkinson Microwave Anisotropy Probe (WMAP) data[4]. These results all fit very well with the prediction of inflation-ΛCDM cosmological model. We all know that the scalar perturbation can generate CMB temperature-temperature power spectrum (C l ), the electric-electric polarization power spectrum (C l ), and the cross-correlation power spectrum (C TE l ); but the tensor perturbation also can generate magnetic-magnetic polarization power spectrum (C l ).