Primordial Perturbations in the Universe: Theory, Detection, and Implication For Inflation

Observation supports the theory that the large-scale structure in the Universe was seeded by primordial curvature perturbations generated during inflation. Measuring the departure from gaussian statistics in the primordial curvature perturbation may reveal the underlying physical mechanism of inflation. Furthermore, a primordial background of gravitational waves can also be produced during inflation, and their imprints may be observed in the recent Universe. Current and upcoming cosmological surveys call for improved theoretical modelling of these primordial perturbations in the hope of detecting new physics. The Total Angular Momentum formalism provides a unified analytic framework to compute for scalar, vector and tensor perturbation fields with manifest symmetry under rotation of the sky, facilitating the calculation of spherical harmonic observables in all-sky surveys. New dynamical degree of freedom during inflation may correlate with the curvature perturbation in a non-trivial scalar-scalar-fossil bispectrum, resulting in a departure from statistical isotropy in the fluctuations of the cosmic microwave background. Large-scale primordial gravitational waves cause polarization rotation of the cosmic microwave background photons. They also modulate a quadrupolar direction dependence in the local clustering power spectrum of small-scale matter perturbation modes. This phenomenon may provide new observational avenue to search for those relic waves. The formalism of Conformal Fermi Coordinates provides a general relativistic framework to study the local impact of long-wavelength perturbations on the dynamics of short-wavelength modes. Applying it to long-wavelength scalar perturbation, we find that general relativity predicts no scale-dependent bias of galaxy clustering in single-field inflation