Nikolaos Tetradis

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Define the spectra, bispectra and trispectra as〈ϕ a (k, η)ϕ b (q, η)〉 ≡δ D (k + q)P ab (k, η)〈ϕ a (k, η)ϕ b (q, η)ϕ c (p, η)〉 ≡δ D (k + q + p)B abc (k, q, p, η)〈ϕ a (k, η)ϕ b (q, η)ϕ c (p, η)ϕ d (r, η)〉 ≡δ D (k + q)δ D (p + r)P ab (k, η)P cd (p, η)+δ D (k + p)δ D (q + r)P ac (k, η)P bd (q, η)+δ D (k + r)δ D (q + p)P ad (k, η)P bc (q, η)+δ D (k + p + q + r)Q abcd (k, p, q, r, η).Essential approximation: Neglect the effect of the trispectrum onthe evolution of the bispectrum.N. <strong>Tetradis</strong> University of AthensThe inhomogeneity of the Universe and the cosmological model
In this way we obtain∂ η P ab (k, η) = −Ω ac P cb (k, η) − Ω bc P ac (k, η)+e η ∫d 3 q [ γ acd (k, −q, q − k)B bcd (k, −q, q − k)+γ bcd (k, −q, q − k)B acd (k, −q, q − k) ] ,∂ η B abc (k, −q, q − k) = −Ω ad B dbc (k, −q, q − k) − Ω bd B adc (k, −q, q − k)−Ω cd B abd (k, −q, q − k)+2e η ∫d 3 q [ γ ade (k, −q, q − k)P db (q, η)P ec (k − q, η)+γ bde (−q, q − k, k)P dc (k − q, η)P ea (k, η)+γ cde (q − k, k, −q)P da (k, η)P eb (q, η) ] .Similarity with the Exact Renormalization Group (Wilson 1971).Path integral representation.Vertex expansion of the effective action.J. Berges, N. T., C. Wetterich, Phys. Rep. 363: 223 (2002)N. <strong>Tetradis</strong> University of AthensThe inhomogeneity of the Universe and the cosmological model
Page 2: Figure: 2MASS Galaxy Catalog (more
Page 5 and 6: Standard frameworkBasic assumptions
Page 7 and 8: Our approachAll the information abo
Page 9 and 10: Luminosity distance and redshiftCon
Page 11 and 12: Observer and source at random posit
Page 13 and 14: A similar problem in brane cosmolog
Page 15 and 16: Basic relationsAction∫S =d 4 x
Page 17 and 18: Static spherically symmetric config
Page 19 and 20: Compact astrophysical objects made
Page 21 and 22: Astrophysical objects made of neutr
Page 23 and 24: Sloan Digital Sky Survey (2005)Figu
Page 25 and 26: Ansatz for the metricds 2 = a 2 (τ
Page 27 and 28: Equations of motion for several non
Page 29 and 30: Time renormalization group (Pietron
Page 31: The non-zero components of the effe
Page 35 and 36: 7Density-Density Power Spectra at z
Page 37 and 38: 1.7BAO Power Spectra at z=0 (β=0.1
Page 39 and 40: wz0.40.60.81.01.41.62 4 6 8 10 zFig
Page 41 and 42: ∆k i k i,lin0.0150.0100.005(2)0.0
Page 43 and 44: Growing neutrino quintessence i , q
Page 45: ConclusionsThe inhomogeneities in t

Nikolaos Tetradis

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