Halo model

The halo model represents the matter density as a sum of normalized halo profiles and decomposes its power spectrum into same-halo and distinct-halo contributions.

The one-halo term comes from pairs of mass elements in the same halo:

P_{1 h} (k) = \int d M \frac{d n}{d M} (\frac{M}{ρ ˉ})^{2} ∣ u (k ∣ M) ∣^{2} .

Two-halo term ( $P_{2 h}$ )

At linear order in halo correlations,

P_{2 h} (k) = [\int d M \frac{d n}{d M} \frac{M}{ρ ˉ} b (M) u (k ∣ M)]^{2} P_{lin} (k) .

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