Non-Gaussian bubbles in the sky T ) - - PowerPoint PPT Presentation

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Non-Gaussian bubbles in the sky T ) - - PowerPoint PPT Presentation

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Non-Gaussian bubbles in the sky T ) 2 2 T ) 3 ( T ( , ) / ( T/ f NL ( , ) 3

slide-1
SLIDE 1

Non-Gaussian bubbles in the sky

  • fNL(θ, φ) ≡ 3
  • (δT(θ, φ)/ ¯

T)3 (δT/ ¯ T)22

Y TP

YUKAWA INSTITUTE FOR THEORETICAL PHYSICS

slide-2
SLIDE 2

Non-Gaussian bubbles in the sky

  • fNL(θ, φ) ≡ 3
  • (δT(θ, φ)/ ¯

T)3 (δT/ ¯ T)22

Y TP

YUKAWA INSTITUTE FOR THEORETICAL PHYSICS

slide-3
SLIDE 3

Intr troducti tions

3

slide-4
SLIDE 4
  • Motivation

!

http://journalofcosmology.com

  • !
  • !
slide-5
SLIDE 5

!

  • Bubbles in the sky

!

  • !
  • φ(x) = φL(x) + fNL
  • φ2

L(x) −

  • φ2

L

slide-6
SLIDE 6

Toy Model Toy Model

6

slide-7
SLIDE 7

Three scalar fields

  • !

! !

slide-8
SLIDE 8

Bubble nucleation during slow-roll inflation

!

  • !
slide-9
SLIDE 9

Curvaton evolution in the universe with a bubble

V (eff)

int

(φ; x) := Vint(¯ σ(x), φ) !

  • V(φ)= m2

2 φ2+Vint(σ, φ)

  • !
  • !
  • Vint(σ, φ) = λ(σ)φ3

(λ(σF) = 0)

slide-10
SLIDE 10

Meth thod

10

slide-11
SLIDE 11

How to calculate 3pt function
 in the universe with a bubble

  • !
  • φ3(x)
  • =
  • P
  • φ3(x) exp
  • − i
  • C1+C2

dt

  • d3x√−gV (eff)

int

(φ(x); x)

  • !
slide-12
SLIDE 12

From curvaton fluctuation to δT

!

  • δT(θ, ϕ)
  • δT 3(θ, ϕ)
  • !

ζ(x)

  • φ(x)
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SLIDE 13

Result t and Conclusion

13

slide-14
SLIDE 14

Result

! |∆fNL| ∼ O(5)

  • fNL(θ, φ) ≡ 1

5

  • (δT(θ, φ)/ ¯

T)3 (δT/ ¯ T)22

fNL(θ, φ) ≡ 3

  • (δT(θ, φ)/ ¯

T)3 (δT/ ¯ T)22

slide-15
SLIDE 15

Conclusions

!

  • !
  • !
slide-16
SLIDE 16

Ap Append endix ix

16

slide-17
SLIDE 17

el parameters

! !

m/H = 0.3, HRW = 0.2π H/φ0 = 0.001 λ = 0.005,

005, rφ = 0.1, |x0| = r∗ = 2, Hte = 50.

  • LI = −√−g λHδ (χ − HRW) δφ3,
  • ¯

σ(χ) = σT for 0 χ < HRW, σF for HRW < χ π.

!

  • !

f (cen)

NL

≈ 3×10−4 λ r3

φ sin3(

HRW) A4

ζ exp

  • ( m

H )2Hte

  • H

m

  • 6H

φ0

  • 3

.

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SLIDE 18

Graphical description of in-in formalism with bubble

18

t t

C C

x

Σt Σt

Re Im

×

i /2

  • i /2

C C’

  • δφ(x1)δφ(x2) · · · δφ(xN)
  • · · ·
  • =
  • Pδφ(x1)δφ(x2) · · · δφ(xN)ei

R

C×Σt dtd3xLI

  • Pei

R

C×Σt dtd3xLI

  • ,
  • !

R-region C-region L-region E-region reheating bubble nucleation bubble wall

slide-19
SLIDE 19

ˆ) ≈ 40r3

φ

81ζ22 δφ3(|x0 + r∗ ˆ n|, t∗) φ3

te

  • curvaton mechanism and


<δφ3> to fNL

!

  • ζ2 = A2

ζ ≡ 6.25 × 10−10

ζ = (1 − rφ)ζr + rφζφ

ζφ = 1 3 δρφ ρφ

  • te

= 1 3

  • 2 δφ

φ0 + δφ2 φ2

  • te

,

!

  • !

can be written in terms of the cu (δT/T)(ˆ n) = (1/5) ζ(x0 + r∗ ˆ n, t∗),

  • fNL(n) ≡ 3
  • (δT(n)/ ¯

T)3 (δT/ ¯ T)22