On the non-linear scale of cosmological perturbation theory

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Loop expansion of PS in the limit of small kFor small k Fry AJ421 (1994) 21P L−loop (k, z) →(2L + 1)!2 L−1 L!∫ ∫P lin (k, z) · · · F2L+1(k, s q 1, −q 1, . . . , q L , −q L )q 1 q L× P lin (q 1, z) · · · P lin (q L , z)Using property F s 2L+1 ∝ k 2 for k ≪ q i Goroff, Grinstein, Rey, Wise AJ311 (1986) 6P L−loop (k, z) ∝ k 2 P lin (k, z)for small kMathias Garny (DESY Hamburg / CERN)On the non-linear scale of cosmological perturbation theory
One, two and three loop normalized to k 2 P lin (k, z)10001-loop2-loop3-loop log measureP(k,z=0)/P lin /k 2 [(h/Mpc) -2 ]1001010.001 0.01 0.1 1 10k [h/Mpc]P L−loop (k, z) ∝ k 2 P lin (k, z)up to k = 0.003, 0.06, 0.08 h/Mpc for 1, 2, 3-loop at %-levelMathias 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 12 and 13: Loop expansion of PS in the limit o
Page 14 and 15: 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 22 and 23: ConclusionThree loop larger than on
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

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