Abstract: The Cosmic Microwave Background radiation has been measured in a series of astronomical observations in extremely high precision. Its confirmation in those experiments has verified the validity of cosmological perturbation theory developed within various paradigms of the very early universe, in particular, inflationary cosmology. It has been noted by the recent CMB experiments such as the Planck data that, there exists observational hints pointing to a potential existence of the power asymmetry in the CMB map. If this were confirmed by forthcoming data, it would strongly indicate new physics beyond the standard paradigm of the inflationary LCDM. We will talk about the extended version of the cosmological perturbation theory within inflationary cosmology which involves multiple scalar fields. We show that the inflationary perturbation theory with multiple sound speed parameters can help to understand such a CMB anomaly from theoretical perspective. This theory also makes explicit prediction on the scale dependence of the power asymmetry and hence is expected to be tested in the future experiments.