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Bela Gabriel Schneider 2025-03-20 17:17:19 +00:00 committed by node
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@ -24,6 +24,7 @@
\newcommand*{\so}[1]{\soop\left(#1\right)}
\newcommand*{\rotmat}[1]{\rotmatop\left(#1\right)}
\renewcommand{\S}{\mathbb{S}}
\newcommand{\R}{\mathbb{R}}
% cool color
@ -124,11 +125,12 @@ code-for-last-col = \color{blue}
\end{frame}
\section{CMB radiation in an inhomogeneous spherical space}
\begin{frame}{CMB radiation in an inhomogeneous spherical space}
\begin{frame}{Inhomogeneous spherical space}
\begin{itemize}
\item Manifolds of the form $\mathbb S/\Gamma$ with $\Gamma$ a group acting on $\mathbb S^3$.
\item Manifolds of the form $\S^3/\Gamma$ with $\Gamma$ a group acting on $\S^3$.
\item Multi-connected space: it has non-contractable loops
\item Inhomogeneous space: it does not look identical from every point in space
\item Fixing $|\Gamma|=8$, we have three multi-connected manifolds, up to equivalence:
@ -136,7 +138,7 @@ code-for-last-col = \color{blue}
\item homogeneous: $N3$ and $L(8,1)$
\item inhomogeneous: $N2 \equiv L(8,3)$
\end{enumerate}
\item Results: inhomogeneous spaces have more variety in CMB anisotropies than homogeneous spaces, because different observation points have
\item Results: inhomogeneous spaces have more variety in CMB anisotropies than homogeneous spaces, because the strength of anisotropy suppression is observer dependent.
\end{itemize}