Elliot Nelson
Graduate Student in Physics |
My research focuses on understanding the statistical properties of perturbations in the early universe, especially non-Gaussian features of curvature (or density) perturbations. These primordial statistics may carry crucial information about the physics of inflation, and act as initial conditions for structure formation, influencing quantities measured at all epochs of the universe. Primordial perturbations are therefore a meeting place for observational cosmology and physics of the early universe.
My thesis work has focused on asking how fluctuations on scales larger than the observable universe could influence observed statistics (such as the CMB angular power spectrum) through non-Gaussian mode coupling. The primordial power spectrum, its scale dependence, as well as other quantities such as the dark matter halo power spectrum, can all be “biased” by long-wavelength background modes. Interestingly, a non-Gaussian field can appear nearly Gaussian in small volumes, potentially complicating the interpretation of CMB Gaussianity in terms of inflationary physics. "Squeezed-limit" coupling of modes on different scales can lead to statistical anisotropy and inhomogeneity, including angular power asymmetries and other CMB features.
Other research projects have studied the origin of statistics for primordial perturbations in the nonlinear dynamics of inflation, and its initial conditions. For example, a non-vacuum pre-inflationary state can strengthen the gravitational coupling of scalar and tensor metric perturbations during inflation, leading to a potentially observable signature of primordial gravitational waves in an anisotropic scalar power spectrum. My current research includes the development of a numerical pipeline to generate initial conditions for N-body simulations of structure formation, directly from an action for inflationary fluctuations. This involves using quantum field theory methods to find the non-Gaussian wave functional for inflationary fluctuations, and Monte Carlo sampling of the resulting probability distribution for configurations of metric perturbations.
Coupling of different scales is inevitable with gravity, and can modify the statistics of cosmological perturbations in the late universe. Einstein’s equations nonlinearly couple matter to geometry, allowing UV physics to influence spacetime in the IR. The leading order effect - on the background expansion - is a cosmological constant due to the stress-energy of the vacuum, but two-point and higher correlations of cosmological metric perturbations can also be modified.
Lastly, inflationary mode coupling is relevant for the emergence of classical perturbations from a homogeneous quantum state. Coupling of a system to an environment can lead to measurement of its properties (position, momentum, spin, etc.). Similarly, coupling of inflationary fluctuations may lead to the measurement of a definite configuration for perturbations. I am currently exploring this in the context of the evolution of the wave function for inflationary perturbations, and resulting quantum decoherence.
In summary, the work I have done has focused on understanding the space of nonlinear mode couplings, especially sensitivity of short scale statistics to long wavelength variations, the relation of non-Gaussianity to statistical anisotropy, and distinguishing features that are or are not possible in single-field inflation. Additional projects have focused on inflationary perturbations in a quantum field theory context, and effects from pre-inflationary non-vacuum states.