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 UPenn March 2012 2 / 26

Outline

1 Motivations 2 Review of µ-distortion 3 A new window on primordial non-Gaussianity 4 Remarks

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 3 / 26

The golden age of cosmology

We are living in the golden age of

• bservational cosmology: COBE

goes to Stockholm, WMAP, ACT & SPT measured the CMB with 1% accuracy. now Planck and a horde of ground and ballon based experiments

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 4 / 26

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 UPenn March 2012 5 / 26

The non-linear regime of structure formation

Small superhorizon primordial perturbations → linear evolution Homogeneous background → no mix of different scales Perturbations re-enter the horizon → grow with time Large perturbations evolve in a complicated non-linear way → erase primordial information Linear regime: Large scale structures k < O(Mpc−1) or look back in time

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 6 / 26

The cosmic microwave background

A snapshot of the universe at 370, 000 years, z ≃ 1100 Small perturbations δρ/ρ ∼ 10−5 → linearly related to primordial perturbations For l 2000 or k > O(0.2 Mpc−1) erased by diffusing damping! Can we access smaller scales?

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 7 / 26

The CMB/LSS window

• 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 0.2 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 UPenn March 2012 8 / 26

Outline

1 Motivations 2 Review of µ-distortion 3 A new window on primordial non-Gaussianity 4 Remarks

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 9 / 26

The µ-era

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 (almost) conserved. 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 UPenn March 2012 10 / 26

µ-distorted spectrum

For µ > 0 the spectrum n(ν) = ν2 eν/kBT+µ − 1 looks like

0.5 1.0 2.0 5.0 ΝkT nΝ

Distinctive ν dependence.

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 11 / 26

Perturbations during the µ-era

Perturbations during the µ-era 5 × 104 z 2 × 106 Dissipation of acoustic modes due to diffusion damping

[Silk ’72] .

Scale invariant power spectrum ns ∼ 1 µ ≃ 2.4 × 10−8 Adiabatic cooling → Bose-Eistein condensation

[Khatri, Chluba Sunyaev ’11,’12]

µBE ≃ −3 × 10−9 Non-standard physics e.g. decays of massive particles, . . .

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 12 / 26

Dissipation of acoustic modes

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

• scillate and dissipate

δγ ∼ Rk cos(kt) e−k2/k2

D

Shear viscosity and heat conduction damp the oscillations

[Silk, Kaiser, Weinberg]

kD ≃ z3/2 4 × 10−6 Mpc−1 Now we can only see k < kD(zL) ≃ 0.2 × Mpc−1 µ-distortion can see 50 < kMpc−1 < 104

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

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 13 / 26

Power dissipated in the µera

Analytical estimate of µ

[Hu et al. 94’, Khatri Chluba & Sunyaev ’11]

Energy in acoustic waves with relativistic correction δE ∼ ρ c2

s

1 + c2

s

δ2

γ

• i

f

Bose-Einstein spectrum with E → E + δE and fixed N µ ≃ 1.4 δE > 0 Linear integral probe of the power spectrum µ ∝

• d log k∆2

R(k)

zL

Μ

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

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 14 / 26

µ(ˆ n) constraints the small-scale power spectrum

The averaged µ-distortion over the whole sky (monopole)

[Hu et al. ’94, Khatri Chluba Sunyaev ’11’12]

µ(x) ≃ 9 4

• d log k ∆2

R(k)

• e−2k2/k2

D

i

f ,

Integral measure of the power spectrum at small scales For ns = 1 µ ∼ 2 × 10−8

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 15 / 26

Relating µ to R2 at small scales

Dissipation is smeared over a volume k−3

s

Nature takes the average for us Small cosmic variance!

[EP & Zaldarriaga ’12]

Final analytical estimate µ(x) ≃ 9 2 d3k1d3k2 (2π)6 R( k1)R( k2)ei

k+· xW

k+ ks

• ×cos (k1t) cos (k2t)p
• e−(k2

1+k2 2)/k2 D

i

f

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 16 / 26

Outline

1 Motivations 2 Review of µ-distortion 3 A new window on primordial non-Gaussianity 4 Remarks

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 17 / 26

Primordial non-Gaussianity

For a Gaussian random variable δ2n+1 = 0 , δ2n ∝ δ2n Using rotational and translational invariance R3 ≡ (2π)3fNLF(k1, k2, k3)δ3(k1 + k2 + k3) Scale invariance: only k1/k3 and k2/k3 fNL gives the size F(k1, k2, k3) (normalized) gives the shape.

Out[1320]=

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 18 / 26

Squeezed limit

Squeezed limit k3 ≪ k1 ∼ k2. Short-scale power modulated by long scales lim

kL≪kSR(kS)2R(kL) ∼ 1

k6

S

• A

kS kL >3 + B kS kL 3,2 + C kS kL 1 Microphysical inflationary models: A = 0 ⇒ instability B = 0 ⇒ multi-field (more than one clock), e.g. curvaton, quasi-single-field, local template

[Maldacena ’02, Creminelli Zaldarriaga ’04]

C = 0 ⇒ single or multi-field, e.g. small speed of sound, equilateral template

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 19 / 26

Local non-Gaussianity

Local model peaks in the squeezed limit k3 ≪ k1 ∼ k2 Distinguishes between broad classes of models R(k1)R(k2)R(k3) ∼ ∆2

R

k3

1

∆2

R

k3

2

+ 2perm′s Local in position space, e.g.

[Komatsu Spergel ’01]

R(x) = RG(x) + floc

NL

• RG(x)2 − RG(x)2
• Enrico Pajer

(Princeton) New window on primordial NG UPenn March 2012 20 / 26

µT cross correlation Μy Μx

µ ∼ R2 and T ∼ R ⇒ µT ∼ R3 µT probe the primordial bispectrum in the squeezed limit floc

NL

Straightforward computation µT ∼ 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 UPenn March 2012 21 / 26

µµ Gaussian self correlation

µµ ∼ R4 receives both a Gaussian and a non-Gaussian

• contributions. The Gaussian is

Cµµ

l,Gauss

∼ 6 × 10−17 ∆4

R(kD,f)

∆4

R(kp)

ksr−2

L

k3

D,f

• 1.5 × 10−28

µ fluctuations are uncorrelated at distances ∆x ≫ 1/ks 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 UPenn March 2012 22 / 26

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

It probes different scales than those of T anisotropy

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 23 / 26

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)

Because of Silk damping one can not do better than 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 UPenn March 2012 24 / 26

Outline

1 Motivations 2 Review of µ-distortion 3 A new window on primordial non-Gaussianity 4 Remarks

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 25 / 26

Outlook and Summary

How would a dedicated experiment look and perform? Foregrounds? How do the acoustic peaks look like in CµT

l

and Cµµ

l,NG

Probe other properties beyond Gaussianity? µ-distortion probes small, otherwise inaccessible scales µT is a direct and clean probe of the primordial bispectrum in the squeezed limit, floc

NL

µµ is a direct and clean probe of the primordial trispectrum τNL Cosmic variance is very small, allowing for a large margin of improvement

Enrico Pajer (Princeton) New window on primordial NG UPenn March 2012 26 / 26