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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

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