Nikolaos Tetradis
Nikolaos Tetradis
Nikolaos Tetradis
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Time renormalization group (Pietroni (2008))Fourier-transformed density contrast and velocity field:δ i ≡ δρ i (k, τ)/¯ρ i and θ i (k, τ) ≡ ∇ ⃗ · δv ⃗ i (k, τ).They obey∫˙δ i (k, τ)+θ i (k, τ) = − d 3 k 1 d 3 k 2 δ D (k−k 1 −k 2 ) ˜α(k 1 , k 2 )θ i (k 1 , τ)δ i (k 2 , τwhere ˜α(k 1 , k 2 ) = k 1 · (k 1 + k 2 )/k 2 1 , and∑˙θ i (k, τ)+(H − β i˙¯φ)θi (k, τ) + 3H2 j Ω j(2β i β j + 1)δ j (k, τ)∫2= − d 3 k 1 d 3 k 2 δ D (k − k 1 − k 2 ) ˜β(k 1 , k 2 )θ i (k 1 , τ)θ i (k 2 , τ),where ˜β(k 1 , k 2 ) = (k 1 + k 2 ) 2 k 1 · k 2 /(2k 2 1 k 2 2 ).N. <strong>Tetradis</strong> University of AthensThe inhomogeneity of the Universe and the cosmological model