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.