A new window on primordial non-Gaussianity based on 1201.5375 with M. Zaldarriaga Enrico Pajer Princeton University 2.0 � R � k � 2 � 10 9 1.5 Μ CMB � LSS 1.0 10 � 4 0.01 1 100 10 4 k Mpc
Summary We know little about primordial perturbations outside the range 10 − 4 � k Mpc � 1 µ -type spectral distortion of the CMB is a unique probe of small scales 50 � k Mpc � 10 4 [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 f loc NL Fisher forecast with current technology ∆ f loc NL � 10 3 Beat cosmic variance with an enormous number of modes Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 2 / 14
Primordial perturbations 1 H ? radiation matter dark E Log a 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? 2.00 1.00 0.50 outside CMB � LSS � R � k � 2 � 10 9 0.20 ? horizon Gaussian 0.10 0.05 Scale � inv 0.02 10 � 7 10 � 5 0.001 0.1 10 1000 k Mpc 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 z i ≃ 2 × 10 6 double Compton scattering ( e − + γ → e − + 2 γ ) is very efficient. Perfect thermodynamical equilibrium, Planck spectrum n ( ν ) = ( e ν/k B T − 1) − 1 Between z i and z f ∼ 5 × 10 4 only elastic Compton scattering ( e − + γ → e − + γ ) is efficient. Photon number is effectively frozen. Bose-Einstein spectrum with chemical potential µ 1 n ( ν ) = e ν/k B T + µ − 1 After z f 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 1 n ( ν ) = e ν/k B T + µ − 1 looks like n � Ν � Ν � kT 0.5 1.0 2.0 5.0 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 � k Mpc � 10 4 Perturbations of the adiabatic mode R re-enter the horizon and oscillate and dissipate δ γ ∼ R k cos( kt ) e − k 2 /k 2 D Damping of k < k D ∼ z 3 / 2 erases primordial perturbations and injects δE into photons For z i < z < z f µ -distortion is created 1 . 4 δE = µ ∼ R 2 z i � R � k � 2 � 10 9 � R � k � 2 � 10 9 z L z L z f z f 1 z i 1 1 1 Out[90]= Μ 10 � 4 0.01 1 100 10 4 10 � 4 0.01 1 100 10 4 k Mpc k Mpc 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 � δ 2 n +1 � = 0 , � δ 2 n � ∝ � δ 2 � n Non-vanishing odd correlation → non-Gaussianity δ ≪ 1 → � δ 3 � 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 ( k 1 ) R ( k 2 ) R ( k 3 ) � ≡ (2 π ) 3 f NL F ( k 1 , k 2 , k 3 ) δ 3 ( k 1 + k 2 + k 3 ) Interesting limit k 3 ≪ k 1 ∼ k 2 f loc NL distinguishes between single and multifield inflation F loc ∼ ∆ 2 ∆ 2 + 2perm ′ s R R k 3 k 3 1 2 Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 9 / 14
µT cross correlation Spherical harmonics: n ) → a µ lm , a T µ (ˆ n ) , T (ˆ lm µT gives the primordial Μ � y � Μ � x � bispectrum in the very squeezed limit f loc NL Straightforward computation 50 ∆ 4 NL b ≃ 3 × 10 − 16 R ( k p ) � a µ lm � ≡ C µT lm a T l ( l + 1) f loc l ( l + 1) f loc ≃ NL b l b ∼ ∆ 2 R ( k D ) / ∆ 2 R ( k p ), 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 k s r − 2 6 × 10 − 17 ∆ 4 R ( k D,f ) � a µ lm a µ lm � ≡ C µµ L ∼ l, Gauss ∆ 4 k 3 R ( k p ) D,f 1 . 5 × 10 − 28 � White noise, l -independent Very small cosmic variance! Suppressed by N − 1 / 2 modes with k 3 D,f ∼ 10 12 N modes ∼ k s r − 2 L Enrico Pajer (Princeton) New window on primordial NG Princeton, Feb 2012 11 / 14
Fisher matrix forecast NL from C µT Signal to noise for f loc l � S C µT C µT � 2 � l l = C µµ,N N 2 l +1 C TT 1 l l l A figure of merit PIXIE [Chuss et al. ’11] � √ � � 4 π × 10 − 8 S log l max 10 − 3 b f loc ≃ 80 . NL w − 1 / 2 N µ NL � 10 3 with current technology i.e. ∆ f loc 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 ∝ N 1 / 2 modes ∼ l max log 1 / 2 ( l max ) Diffusion damping ⇒ l max � 2000. Ideal experiment ∆ f loc NL � 3 For µT there are many more modes. Nature beats down cosmic variance for us � k 3 S N ∝ N 1 / 2 D,f ∼ 10 6 modes ∼ k s r − 2 L Ideal experiment ∆ f loc 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, f loc 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
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