Nikolaos Tetradis

Hierarchy of scalesFor subhorizon perturbations with momenta k ≫ H = ȧ/a, thelinear analysis predicts |δ⃗v| ∼ (k/H)Φ ∼ (H/k)(δρ/¯ρ).We assume the hierarchy of scales: Φ, δφ/¯φ ≪ |δ⃗v| ≪ δρ/¯ρ 1.As we are dealing with subhorizon perturbations, we assumethat the spatial derivatives of Φ, δφ, δ⃗v dominate over their timederivatives. We also assume that a spatial derivative acting on Φ,δφ or δ⃗v increases the position of that quantity in the hierarchy byone level: ⃗ ∇Φ is comparable to Hδ⃗v, while ∇ 2 Φ is comparable toH 2 δρ/¯ρ.F. Saracco, M. Pietroni, N. T., V. Pettorino, G. RobbersarXiv:0911.5396[astro-ph], Phys. Rev. D 82: 023528 (2010)N. Tetradis University of AthensThe inhomogeneity of the Universe and the cosmological model