Takemi Okamoto

We investigate the ability to constrain oscillatory features in the primordial power spectrum using current and future cosmic microwave background observations. In particular, we study the observability of an oscillation arising from imprints of physics at the cut-off energy scale. We perform a likelihood analysis on the WMAP data set, and find that the current data set constrains the amplitude of the oscillations to be less than 0.77 at 2-sigma, consistent with a power spectrum without oscillations. In addition, we investigate the fundamental limitations in the measurement of oscillation parameters by studying the constraints from a cosmic variance limited experiment. We find that such an experiment is capable of constraining the amplitude of such oscillations to be below 0.005, implying that reasonable models with cut-off energy scales Lambda>200 H_infl are unobservable through the microwave background.

Gravitational lensing of the microwave background by the intervening dark matter mainly arises from large-angle fluctuations in the projected gravitational potential and hence offers a unique opportunity to study the physics of the dark sector at large scales. Studies with surveys that cover greater than a percent of the sky will require techniques that incorporate the curvature of the sky. We lay the groundwork for these studies by deriving the full sky minimum variance quadratic estimators of the lensing potential from the CMB temperature and polarization fields. We also present a general technique for constructing these estimators, with harmonic space convolutions replaced by real space products, that is appropriate for both the full sky limit and the flat sky approximation. This also extends previous treatments to include estimators involving the temperature-polarization cross-correlation and should be useful for next generation experiments in which most of the additional information from polarization comes from this channel due to sensitivity limitations.

Gravitational lensing of the microwave background by the intervening dark matter mainly arises from large-angle fluctuations in the projected gravitational potential and hence offers a unique opportunity to study the physics of the dark sector at large scales. Studies with surveys that cover greater than a percent of the sky will require techniques that incorporate the curvature of the sky. We lay the groundwork for these studies by deriving the full sky minimum variance quadratic estimators of the lensing potential from the CMB temperature and polarization fields. We also present a general technique for constructing these estimators, with harmonic space convolutions replaced by real space products, that is appropriate for both the full sky limit and the flat sky approximation. This also extends previous treatments to include estimators involving the temperature-polarization cross-correlation and should be useful for next generation experiments in which most of the additional information from polarization comes from this channel due to sensitivity limitations.

We develop the formalism necessary to study four-point functions of the cosmic microwave background (CMB) temperature and polarization fields. We determine the general form of CMB trispectra, with the constraints imposed by the assumption of statistical isotropy of the CMB fields, and derive expressions for their estimators, as well as their Gaussian noise properties. We apply these techniques to initial non-Gaussianity of a form motivated by inflationary models. Due to the large number of four-point configurations, the sensitivity of the trispectra to initial non-Gaussianity approaches that of the temperature bispectrum at high multipole moment. These trispectra techniques will also be useful in the study of secondary anisotropies induced for example by the gravitational lensing of the CMB by the large scale structure of the universe.

We develop the formalism necessary to study four-point functions of the cosmic microwave background (CMB) temperature and polarization fields. We determine the general form of CMB trispectra, with the constraints imposed by the assumption of statistical isotropy of the CMB fields, and derive expressions for their estimators, as well as their Gaussian noise properties. We apply these techniques to initial non-Gaussianity of a form motivated by inflationary models. Because of the large number of four-point configurations, the sensitivity of the trispectra to initial non-Gaussianity approaches that of the temperature bispectrum at high multipole moment. These trispectra techniques will also be useful in the study of secondary anisotropies induced, for example, by the gravitational lensing of the CMB by the large scale structure of the universe.