A new window on primordial non-Gaussianity based on 1201.5375 with - - PowerPoint PPT Presentation

A new window on primordial non-Gaussianity

based on 1201.5375 with M. Zaldarriaga

Enrico Pajer Princeton University CMBLSS

Μ

104 0.01 1 100 104 1.0 2.0 1.5 k Mpc Rk2109

Summary

We know little about primordial perturbations outside the range 10−4 kMpc 1 µ-type spectral distortion of the CMB is a unique probe of small scales 50 kMpc 104

[Sunyaev, Zel’dovich, Silk, Peebles, Hu, Danese, de Zotti, Chluba, . . . ]

The monopole µ(ˆ n) probes the small-scale power spectrum µT cross correlation probes the primordial bispectrum in the squeezed limit floc

NL

Fisher forecast with current technology ∆floc

NL 103

Beat cosmic variance with an enormous number of modes

Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 2 / 14

Primordial perturbations

? radiation matter dark E Log a 1 H Primordial superhorizon perturbations seed the structures in our universe They teach us about the earlier stage

Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 3 / 14

Primordial perturbations: What do we know?

• utside

horizon CMBLSS Gaussian Scaleinv

?

107 105 0.001 0.1 10 1000 0.02 0.05 0.10 0.20 0.50 1.00 2.00 k Mpc Rk2109

k 10−4 Mpc−1 are still outside our horizon k 0.15 Mpc−1 (l 2000) have been erased by Silk damping k O(1) Mpc−1 are now contaminated by gravitational non-linearities

Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 4 / 14

Photon thermodynamics before decoupling

Before zi ≃ 2 × 106 double Compton scattering (e− + γ → e− + 2γ) is very efficient. Perfect thermodynamical equilibrium, Planck spectrum n(ν) = (eν/kBT − 1)−1 Between zi and zf ∼ 5 × 104 only elastic Compton scattering (e− + γ → e− + γ) is efficient. Photon number is effectively frozen. Bose-Einstein spectrum with chemical potential µ n(ν) = 1 eν/kBT+µ − 1 After zf also elastic Compton scattering is not efficient, e.g. y-type distortion.

Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 5 / 14

µ-distorted spectrum

For µ > 0 the spectrum n(ν) = 1 eν/kBT+µ − 1 looks like

0.5 1.0 2.0 5.0 ΝkT nΝ

The distortion has a different ν dependence from y-distortion.

Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 6 / 14

µ-distortion probes 50 kMpc 104

Perturbations of the adiabatic mode R re-enter the horizon and

• scillate and dissipate

δγ ∼ Rk cos(kt) e−k2/k2

D

Damping of k < kD ∼ z3/2 erases primordial perturbations and injects δE into photons For zi < z < zf µ-distortion is created 1.4δE = µ ∼ R2

Out[90]=

zL zf zi 104 0.01 1 100 104 1 1 k Mpc Rk2109 zL

Μ

zf zi 104 0.01 1 100 104 1 1 k Mpc Rk2109

Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 7 / 14

Primordial non-Gaussianity

It is hard to tell by eye For a Gaussian random variable δ2n+1 = 0 , δ2n ∝ δ2n Non-vanishing odd correlation → non-Gaussianity δ ≪ 1 → δ3 is the most sensitive

Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 8 / 14

Symmetries, sizes and shapes

Conservation of momentum + rotational invariance + scale invariance R(k1)R(k2)R(k3) ≡ (2π)3fNLF (k1, k2, k3) δ3(k1 + k2 + k3) Interesting limit k3 ≪ k1 ∼ k2 floc

NL distinguishes between single and multifield inflation

F loc ∼ ∆2

R

k3

1

∆2

R

k3

2

+ 2perm′s

Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 9 / 14

µT cross correlation

Spherical harmonics: µ(ˆ n), T(ˆ n) → aµ

lm, aT lm

µT gives the primordial bispectrum in the very squeezed limit floc

NL

Μy Μx

Straightforward computation aµ

lmaT lm ≡ CµT l

≃ 50 ∆4

R(kp)

l(l + 1) floc

NL b ≃ 3 × 10−16

l(l + 1) floc

NL b

b ∼ ∆2

R(kD)/∆2 R(kp), if scale invariant b ∼ 1.

Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 10 / 14

µµ Gaussian self correlation

µµ receives both a Gaussian and a non-Gaussian contributions. The Gaussian is aµ

lmaµ lm ≡ Cµµ l,Gauss

∼ 6 × 10−17 ∆4

R(kD,f)

∆4

R(kp)

ksr−2

L

k3

D,f

• 1.5 × 10−28

White noise, l-independent Very small cosmic variance! Suppressed by N−1/2

modes with

Nmodes ∼ k3

D,f

ksr−2

L

∼ 1012

Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 11 / 14

Fisher matrix forecast

Signal to noise for floc

NL from CµT l

S N 2 =

• l

CµT

l

CµT

l 1 2l+1CTT l

Cµµ,N

l

A figure of merit PIXIE

[Chuss et al. ’11]

S N ≃ 10−3 b floc

NL

√ 4π × 10−8 w−1/2

µ

log lmax 80 . i.e. ∆floc

NL 103 with current technology

Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 12 / 14

How well can we do?

Nature puts a lower bound on the noise, i.e. cosmic variance We can beat it only having more modes by N−1/2

modes

For the TTT bispectrum S N ∝ N1/2

modes ∼ lmax log1/2(lmax)

Diffusion damping ⇒ lmax 2000. Ideal experiment ∆floc

NL 3

For µT there are many more modes. Nature beats down cosmic variance for us S N ∝ N1/2

modes ∼

• k3

D,f

ksr−2

L

∼ 106 Ideal experiment ∆floc

NL 10−3

Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 13 / 14

Conclusions

µ-distortion probes small, other wise unaccesible scales µT is a direct and clean probe of the primordial bispectrum in the squeezed limit, floc

NL

Cosmic variance is very small, allowing in principle for a large margin of improvement How would a dedicated experiment look and perform? Foregrounds? Numerical analysis is needed for detail predictions

Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 14 / 14