The angular homogeneity scale of the Universe - Centre for ...
The angular homogeneity scale of the Universe - Centre for ...
The angular homogeneity scale of the Universe - Centre for ...
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<strong>The</strong> fractal dimension<br />
• Angular <strong>homogeneity</strong> index:<br />
Spheres<br />
Spherical caps <strong>of</strong> radius θ<br />
H 2 (✓) ⌘ d log G 2(✓)<br />
d log V (✓) ! 1<br />
• Modelling H 2 (θ):<br />
G 2 (✓) / V (✓) =2⇡(1 cos ✓)<br />
As <strong>homogeneity</strong><br />
is approached<br />
H 2 (✓) = 1+w(✓)<br />
1+ ¯w(✓)<br />
Non-trivial dependence on θ<br />
1<br />
¯N(✓)<br />
Fiducial cosmology: (⌦ m , ⌦ ⇤ , ⌦ b ,h, 8,n s )=(0.3, 0.7, 0.049, 0.67, 0.8, 0.96)<br />
Alicia Bueno Belloso <strong>The</strong> <strong>angular</strong> <strong>homogeneity</strong> <strong>scale</strong> <strong>of</strong> <strong>the</strong> <strong>Universe</strong> 2 nd September 2013