On the non-linear scale of cosmological perturbation theory

More documents

Recommendations

Info

ConclusionThree loop larger than one loop at z = 0 at all scalesExpected for Eisenstein-Hu-like spectrumLoop expansion exhibits behaviour of asymptotic seriesPadé resummation in small k limitImproved perturbative expansion with better convergence properties atBAO scales, good agreement with N-body dataMathias Garny (DESY Hamburg / CERN)On the non-linear scale of cosmological perturbation theory
Basic formalism for large scale structureDensity contrast ρ(x, τ) = ¯ρ(τ)(1 + δ(x, τ)), pec. velocity u(x, τ)1st and 2nd moment of Vlasov eq. for f (x, p, τ), neglect multi-streaming(pressure, stress/viscosity → talks by Mercolli, Zaldarriaga)∂δ(x, τ)∂τ+ ∇ · {(1 + δ(x, τ)u(x, τ)} = 0 (continuity)∂u(x, τ)∂τ+ Hu + u · ∇u = −∇Φ (Euler)∇ 2 Φ(x, τ) = 3 2 ΩmH2 δ(x, τ) (Poisson)neglect vorticity ∇ × u ≈ 0 ⇒ sufficient to use θ = ∇ · usolution of linearized eqs (D + ∼ a, D − ∼ a −3/2 in EdS)Power spectrum in Fourier spaceδ lin (x, τ) = D +(τ)δ 0(x) + O(D −)〈δ(k, τ)δ(k ′ , τ)〉 = δ (3) (k + k ′ )P(k, τ)assume Gaussian IC described by P 0(k) = P(k, τ 0)Mathias Garny (DESY Hamburg / CERN)On the non-linear scale of cosmological perturbation theory
Page 1: On the non-linear scale of cosmolog
Page 4 and 5: Standard Perturbation TheoryPoisson
Page 6 and 7: Standard Perturbation Theory100Plin
Page 8 and 9: Standard Perturbation TheoryMany ap
Page 10 and 11: Loop expansion of PS in the limit o
Page 16 and 17: Padé ansatzGoal: improve convergen
Page 18 and 19: Result for Padé resummed small-k l
Page 20 and 21: Padé improved PT vs N-body1.4z⩵0
Page 24 and 25: Expansion parameter∫ kσl 2 (k, z
Page 26 and 27: Padé improved PT vs N-body1.4z⩵0

On the non-linear scale of cosmological perturbation theory

Create successful ePaper yourself

Delete template?

Save as template?