Testing Gaussianity, Homogeneity, and Isotropy with the Cosmic Microwave Background

<table>Diagrammatic representation of the 2, 3, 4, and 5-point correlation functions in harmonic space. Here <svg height="15.875" id="M215" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 9.1750002 15.875" width="9.1750002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.875)">
<g transform="translate(72,-59.3)">
<text transform="matrix(1,0,0,-1,-65.04,62.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">⃗</tspan>
<tspan style="font-size: 12.50px; " x="-6.9099998" y="2.97">ℓ</tspan>
</text>
</g>
</g>
</svg> actually represents the pair <svg height="13.625" id="M216" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 37.1875 13.625" width="37.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.625)">
<g transform="translate(72,-61.1)">
<text transform="matrix(1,0,0,-1,-71.95,63.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">ℓ</tspan>
<tspan style="font-size: 12.50px; " x="11.402736" y="0">,</tspan>
<tspan style="font-size: 12.50px; " x="16.603985" y="0">𝑚</tspan>
<tspan style="font-size: 12.50px; " x="25.481113" y="0">)</tspan>
</text>
</g>
</g>
</svg>.</table>

Advances in Astronomy

fig2

Figure 2

Figure 2: Testing Gaussianity, Homogeneity, and Isotropy with the Cosmic Microwave Background 