- Page 1 and 2: Abstract Primordial non-Gaussianity
- Page 3 and 4: Contents I Introduction 6 1 The Fri
- Page 5 and 6: 12 Symmetries of the de Sitter geom
- Page 7 and 8: Figure 2: The CMB radiation project
- Page 9 and 10: ds 2 = −dt 2 + a 2 dr2 (t) 1 −
- Page 11 and 12: Now, let us introduce the polar coo
- Page 13 and 14: It should be noted that the assumpt
- Page 15 and 16: 1.3 Particle kinematics of a partic
- Page 17 and 18: δt0 δt = . (37) a(t0) a(t) Theref
- Page 19 and 20: For relativistic particles, radiati
- Page 21 and 22: Because of isotropy, there are only
- Page 23 and 24: the present epoch or at a generic i
- Page 25 and 26: 4. For sufficiently large a, a nonz
- Page 27 and 28: Figure 3: Qualitative behaviour of
- Page 29 and 30: where µ is the chemical potential
- Page 31 and 32: The total energy density and pressu
- Page 33 and 34: s = S V = ρ + P T . (126) It is do
- Page 35 and 36: H = ˙a a a′ H = = a2 a , ˙a = a
- Page 37 and 38: curvature Ω − 1 = k H2 , (143)
- Page 39: On the other hand, during the MD pe
- Page 43 and 44: Figure 7: An illustration of the ho
- Page 45 and 46: Notice that is equivalent to requir
- Page 47 and 48: Figure 9: The solution of the horiz
- Page 49 and 50: always remain flat or closed, indep
- Page 51 and 52: If we require that ˙ φ 2 0 ≪ V
- Page 53 and 54: where ∆Nλ indicates the number o
- Page 55 and 56: as Bose condensates, and they behav
- Page 57 and 58: Figure 11: Large field models of in
- Page 59 and 60: V (φ) ∝ φ −p used in intermed
- Page 61 and 62: averaged over some macroscopically
- Page 63 and 64: we can write the equation for the f
- Page 65 and 66: In fact we can do much better, sinc
- Page 67 and 68: the power spectrum can be defined a
- Page 69 and 70: with 3 − 2νχ ηχ. Using Eq. (
- Page 71 and 72: 8.1 The metric fluctuations The mat
- Page 73 and 74: Neglecting the terms − 2 Φ · X
- Page 75 and 76: for which the first-order perturbat
- Page 77 and 78: In components we have δT ij = δT0
- Page 79 and 80: Figure 15: In the reference unpertu
- Page 81 and 82: Φ = Φ − ξ 0′ − a′ a ξ0
- Page 83 and 84: is the comoving curvature perturbat
- Page 85 and 86: 8.9 Comments about gauge invariance
- Page 87 and 88: ackground solution and are therefor
- Page 89 and 90: to slow-roll parameters), that is
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which reproduces our previous findi
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we get Similarly, we obtain u µ =
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From (325) we find therefore −Ψ(
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where the ∗ stands for the value
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9.1 Gauge-invariant computation of
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∇ 2 H ΦGI = 4 π GN a 2 ΦGI H
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with nR − 1 = 3 − 2ν = 2η −
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perturbations ζφ and ζγ ζ ′
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∆ + ΦMD (τls) = − 4 SW 2 + 1
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Take for instance a model of chaoti
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The de Sitter algebra SO(1,4) has t
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which, for de Sitter space, they pr
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isocurvature mode associated with t
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that are not accessible to any coll
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our study of NG require going beyon
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• at second order 〈W (τ)〉 (2
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7.0 3.5 0 0.0 S local (1,x2,x3) 0.5
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S SR (k1, k2, k3) ∝ (ɛ − 2η)
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long-wavelength fluctuations ζL is
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defines the relative contribution o
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13.4.4 A test of multi-field models
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angular scales as density inhomogen
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to the higher-order statistics of t
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or ln ρ m = ln ρ 3/4 γ . (569) N
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where we have used the identity:
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Thus, we define the Fisher matrix F
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S(ℓ, k z τ0 , τ) = 0 dτ (τ0
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Figure 21: Signal-to-Noise ratio fo
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is the transformation for modes whi
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theory breaks down either when we g
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where in the second equality we hav
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function (sometimes called filter f
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universe so that ˙ Rm,i = HIRm,i,
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We thus obtain δL(π) 1.063 for t
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15.1 The computation of the halo ma
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S. We may refer to the evolution of
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so the two-point correlator is give
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16 The bias In order to make full u
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where ν = δc/S 1/2 = δc/σ(M) as
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and we follow them for a “time”
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can expand the three-point correlat
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Figure 26: The ratio between the ha
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ρ → n 1 + δn (1 + δℓ) (774)
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so that d ln ν/d ln M does not dep