Cosmology with Rayleigh Scattering

Home , Rayleigh scattering

Beyond Cosmic Variance with the next generation of CMB surveys

Benjamin Beringue with Daan Meerburg, Nick Battaglia, Joel Meyers

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Outline :

• Motivation

• Distortions induced by Rayleigh Scattering

• Detectability with the next generation of CMB surveys

• Impact on cosmological parameters

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With the next generation of CMB surveys promising to be Cosmic Variance limited up to ℓ~5000, there is a strong need to look beyond the primary CMB signal to further constrain Λ�� and its extensions.

• Spectral distortions

• Secondary anisotropies : CMB lensing, tSZ, kSZ, patchy reionisation

• Rayleigh Scattering !

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Rayleigh Scattering refers to the scattering of electromagnetic waves off particles which size is much smaller than the wavelength of the radiation.

• Observed on earth when solar photons scatter off neutral species in the atmosphere.

1.2

1.0 • During recombination (at � ~ 1100),

neutral species (mainly Hydrogen 0.8 and Helium) are formed, off which

CMB photons can scatter. 0.6

0.4 • After recombination, densities will Fraction of free electrons 0.2 dilute, making Rayleigh Scattering Fraction of neutral hydrogen less and less efficient. Last scattering surface 0.0 2500 2000 1500 1000 500 Redshift 03/09/2019 Cosmo19 - Aachen 4 Cosmology with Rayleigh Scattering

Rayleigh Scattering cross section depends on the frequency of the incoming photon :

� 638 � 1299667 � � � = � + + + … � 243 � 236196 �

[Lewis 2013 :1307.8148] [Alipour et al. 2014 :1410.6484] Having this additional scattering source increases the comoving optical depth around recombination and makes it frequency dependent.

�̇ = �� → �̇ � = �� + � � + 0.1 � �(�)

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This frequency dependent increase of the comoving opacity results in :

1088 • A shift of the visibility function : � = �̇� 1086

• An increase of Silk Damping 1084

• A frequency-dependent sound horizon 1082

1080 4 • A frequency dependent polarization amplitude Peak of the visibility function Rayleigh Scattering ⌫ Rayleigh Scattering ⌫4 & ⌫6 1078 Thomson Scattering

100 200 300 400 500 600 700 800 900 ⌫ [GHz]

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At the power spectrum level, Rayleigh Scattering induces :

0.03 0.15

0.02 • A damping of small scales fluctuations both 0.10 in temperature and E-mode polarization. 0.01 0.05

• A boost on large 0.00scale E-mode polarization 0.00

• A shift in the location-0.01 of the acoustic peaks. -0.05

-0.02 Fractional di↵erence in TT spectra -0.10 Fractional di↵erence in TT spectra Fractional di↵erence in TE spectra Fractional di↵erence in TE spectra Fractional di↵erence in EE spectra Fractional di↵erence in EE spectra

101 102 103 101 102 103

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Rayleigh Scattering can either be considered as a distortion of the primary CMB or as a separate signal with a unique spectral signature and correlation with the CMB.

, , , If we write : �ℓ � = �ℓ + Δ�ℓ + Δ�ℓ + � , with � = �, �, �

[Lewis 2013 :1307.8148] The power spectrum reads :

�ℓ �, � , 1 , , 1 , , �� ,, = �ℓ + � �ℓ + � �ℓ + � �ℓ + � �ℓ + �ℓ + … � � �

Primary CMB � � �� cross spectra � cross spectra � auto spectra

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Outline :

• Motivation

• Distortions induced by Rayleigh Scattering

• Detectability with the next generation of CMB surveys

• Impact on cosmological parameters

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The next generation of CMB surveys will be ground based : Simons Observatory, CCAT-prime, CMB-S4. SO LAT CCAT LAT

With atmosphere Without atmosphere With atmosphere Without atmosphere 0.0150 0.6 0.012 145 GHz 225 GHz 225 GHz 0.0125 280 GHz 0.5 0.010 0.3 280 GHz 350 GHz 0.0100 0.4 0.008 0.2 0.0075 0.006 0.3

0.004 0.0050 0.2 0.1 S/N per mode 0.002 S/N per0 mode .0025 0.1

0.000 0.0 0.0000 0.0

80 200 0.20 0.30

0.25 0.15 60 150 0.20

0.10 40 0.15 100

0.10 0.05 20 50 0.05 Cumulative S/N Cumulative S/N

0.00 0 0.00 0 0 1000 2000 3000 4000 0 1000 2000 3000 4000 0 1000 2000 3000 4000 0 1000 2000 3000 4000 ` ` ` `

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PICO

268 GHz 25 In a more distant future, space 321 GHz 20 385 GHz missions which would target B- 462 GHz 15 555 GHz S/N mode polarization would 10 provide an ideal set-up to further 5 observe and characterize 0 Rayleigh Scattering without atmospheric nuisance. 400000

300000

200000

100000 Cumulative S/N 0 0 250 500 750 1000 1250 1500 1750 2000 `

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Outline :

• Motivation

• Distortions induced by Rayleigh Scattering

• Detectability with the next generation of CMB surveys

• Impact on cosmological parameters

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The value of Λ��(+ its extentions) parameters change the shape of the CMB power spectra. Having a precise measurement of these spectra leads to tighter and tighter constraints on parameters values.

Similarly, the shape of the Rayleigh Scattering cross and auto spectra will also depend on the value of cosmological parameters.

Detecting and including Rayleigh Scattering in a cosmological analysis could therefore improve the constraints on key cosmological parameters while the primary CMB will have reached its cosmic variance limit.

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When Rayleigh Scattering is included in a Fisher analysis, constraints on some parameters reduces below the Cosmic Variance Limit. (Preliminary)

Assumptions :

- PICO (21 frequency channels) on 70% of the sky from ℓ = 2 to ℓ = 3000 in temperature, ℓ = 5000 in polarization.

- Lensed spectra, including lensing reconstruction information

- No foregrounds

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(Ne↵ ) Primary CMB only The number of relativistic species 0.030 PICO : Primary CMB only PICO : Rayleigh Scattering � is a key target for the next generation of CMB surveys. 0.028 11% Rayleigh Scattering provides an ) 0.026 ⇡ e ↵ N improvement that would require a ( 0.025 non trivial effort with the primary 0.024 CMB. 6.9 0.022 ⇥

0.020 12.00 10.00 8.00 6.87 6.00 4.00 2.00 1.00 0.00 Relative integration time or number of detectors

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In all this work we have neglected foregrounds contamination, but removing them is a challenging problem. However there are a few aspects of Rayleigh Scattering that plays in our favour :

• The spectral signature is well known and unique across the sky (�, �, …) Suitable for a blind method such as an ILC (internal Linear Combination)

• The cross correlation with the Primary CMB is a unique feature. Would need to explicitly de-project the CMB to get avoid residuals

• Rayleigh Scattering is easy to include in a Boltzmann code like CAMB.

Would be possible to include in a likelihood.

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Conclusion

• Rayleigh Scattering is a weak yet robustly predicted signal in the sky .

• Its first detection could be achieved with the next generation of CMB surveys.

• Future space missions could use this signal to further constrain Λ��

• Rayleigh Scattering gives us a rather simple path to beat cosmic variance and keep using the CMB for cosmic inference.

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Thank you very much for your attention !

(Keep an eye on the arXiv in the next few months !)

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