# Errata: Constraining Inflationary B-modes with the BICEP/Keck Array Telescopes

This page contains corrections to known errors in my thesis.

J. Willmert. “Constraining Inflationary B-modes with the Bicep/Keck Array Telescopes” PhD Thesis. University of Minnesota, Nov 2019. URL: http://hdl.handle.net/11299/211821

## Chapter 8¶

• The first sentence of bullet point two at the end of section 8.3 ends with “…but leaves the eigenvalues invariant” — “eigenvalues” should be “eigenvectors”, to instead be “…but leaves the eigenvectors invariant”.

• Footnote 7 is missing a transpose of the $U$ matrix in the the pseudo-inverse expression; it should read $\Phi_B^+ = W \Sigma^+ U^\top$.

## Appendix E¶

• Eqns. E.25 and E.26 have incorrect limits given the definition of the polarization weight functions given in Eqns. E.12–15. They should instead include a factor of $\eta_\ell$ to be \begin{align} F_\ell^{12}(z_{ij}) &= \begin{cases} \frac{1}{2} \eta_\ell & \text{as } z_{ij} \rightarrow +1 \\ \frac{1}{2} (-1)^\ell \eta_\ell & \text{as } z_{ij} \rightarrow -1 \end{cases} \\ F_\ell^{22}(z_{ij}) &= \begin{cases} -\frac{1}{2}\eta_\ell & \text{as } z_{ij} \rightarrow +1 \\ \frac{1}{2} (-1)^\ell \eta_\ell & \text{as } z_{ij} \rightarrow -1 \end{cases} \end{align} The original source (Tegmark et al 2001, Appendix A) includes the factor $\eta_\ell$ as a term in the sums of Eqns. E.6–E.11 whereas here they have been written as a term in the definitions of the $F_\ell^{nm}$ functions.