## Date of Award

2019

## Document Type

Thesis

## Degree Name

Bachelor of Science

## Department

Physics

## Abstract

The current methods of simulating the Cosmic Microwave Background (CMB) involve either simulating the entire sky using spherical transforms or simulating a at patch with fast Fourier transforms (FFTs). For patches that are too large to be considered at but much less than the full sky, the former method is inecient and the latter is inaccurate. One alternative method of CMB simulation is to simulate the random processes behind the CMB in a 3-dimensional box that contains the part of the sphere that we want to measure. Then, we can select the points we want from the box. This method should be more ecient than previous methods because it performs simulations over a box instead of a sphere, allowing for the use of FFTs in place of much slower spherical harmonic transforms. For this method to work, there must be a 3-dimensional power spectrum dened on the box that has the same correlation function as the angular power spectrum. Since the angular power spectrum is known, this becomes a linear programming problem, where the constraints for the 3-D power spectrum are that it matches the angular power spectrum over the observed region and that it be non-negative. If a power spectrum satisfying these constraints exists, we can use it to create maps of the CMB with the same statistical properties as the observed CMB. These maps can then be used to test theories about the early universe. We have solved this linear programming problem for a variety of realistic scenarios. We have performed extensive statistical tests comparing the statistics of maps produced via FFT simulation with maps produced via standard spherical harmonic methods, and found the two methods to be statistically indistinguishable.

## Recommended Citation

Goetz, Eric, "Using 3-dimensional FFTs to simulate CMB maps on a spherical cap" (2019). *Honors Theses*. 1376.

https://scholarship.richmond.edu/honors-theses/1376