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There is an apparent power deficit relative to the Lambda-CDM prediction ofthe CMB spectrum at large scales, which, though not yet statisticallysignificant, persists from WMAP to Planck data. We first present a simple toymodel corresponding to a network of frustrated topological defects of domainwalls or cosmic strings that exist previous to the standard slow-rollinflationary era of the universe. Those features are phenomenologically modeledby a Chaplygin gas that can interpolate between a network of frustratedtopological defects and a de Sitter-like or a power-law inflationary era. Weshow that these scenarios can alleviate the quadrupole anomaly of the CMBspectrum, based on the approximate initial conditions for the long-wavelengthperturbations. We then go further to show that the large-scale spectrum at theend of inflation reflects the super-horizon spectrum of the initial state ofthe inflaton field. By studying the curvature perturbations of a scalar fieldin the FLRW universe parameterized by the equation of state parameter w, wefind that the large-scale spectrum is suppressed if the universe begins withthe adiabatic vacuum in a superinflation (w < -1) or positive-pressure (w > 0)era. In the latter case, there is however no causal mechanism to establish theinitial adiabatic vacuum. To search for a more realistic initial condition ofthe inflationary universe, we consider the Hartle-Hawking no-boundary wavefunction, which is a solution to the Wheeler-DeWitt equation, as the initialcondition of the universe. We find that the power suppression can be theconsequence of a massive inflaton, whose initial vacuum is the Euclideaninstanton in a compact manifold. We calculate the primordial power spectrum ofthe perturbations and show that, as long as the scalar field is moderatelymassive, the power spectrum is suppressed at the long-wavelength scales.

Initial Condition of the Inflationary Universe and Its Imprint on the Cosmic Microwave Background