After Planck: The road to observing 17 e-folds of inflation

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1 After Planck: The road to observing 17 e-folds of inflation Rishi Khatri with Rashid Sunyaev & Jens Chluba Silk damping: arxiv: Review: arxiv: Forecasts: arxiv:

2 We have reached the resolution limit for CMB anisotropies 10 4 l(l+1)c l /(2π) (µk 2 ) COBE 7 o Horizon size at recombination WMAP 0.2 o Planck 5 Silk damping SPT/ACT 1.5 Spectral distortions y-type i-type Un-damped µ-type Blackbody photosphere l

3 Going from 7 to 17 e-folds of inflation k 3 P(k) Cosmic Horizon CMB best fit + Ly-α COBE y limit y-type low redshift confusion 7 e-folds 7 e-folds 17.7 e-folds i-type µ-type Pixie COBE µ limit PRISM Blackbody Photosphere k Mpc -1

4 Brief history of the Universe

5 Brief history... Time 3 mins 19 yrs 70 days BBN 8 z ~ 3x10 + e /e Spectral annihilation 9 8 Distortions 10 > z > 10 y type Blackbody Photosphere Blackbody surface µ type i type x x x yrs billion years 3000 yrs 200 million yrs Recombination Redshift Last scattering surface 1100 Reionization

6 Planck spectrum I ν = 2hν3 c 2 1 e hν/(k BT ) 1 Relativistic invariant occupation number/phase space density n(ν) c2 2hν 3I ν n(x) = 1 e x 1, x = hν k B T

7 COBE-FIRAS confirmed blackbody spectrum of CMB at high precision Nobel prize for Planck 1918 Nobel Prize for Mather 2006 Fixsen et al. 1996

8 The CMB spectrum from COBE agrees with the Planck spectrum Fixsen et al. 1996, Fixsen & Mather 2002 I ν MJ/Sr, Error bars kj/sr Residuals kj/sr ν (GHz) K ν (GHz)

9 Compton scattering Compton Scattering γ P γ =(p, p ) e P e =(m e,0) e θ P e = γm e(1, v) γ P γ =(p, p ) p/p p/m e (1 cosθ)

10 Efficiency of energy exchange between electrons and photons Recoil: y γ = dtcσ T n e k B T γ m e c 2, T γ = 2.725(1 + z) Doppler effect: y e = dtcσ T n e k B T e m e c 2 In early Universe y γ y e y: Amplitude of distortion ( ) k B Te T γ y = dtcσ T n e m e c 2

11 Efficiency of energy exchange between electrons and photons Recoil: y γ = dtcσ T n e k B T γ m e c 2, T γ = 2.725(1 + z) No. of scatterings Doppler effect: y e = dtcσ T n e k B T e m e c 2 In early Universe y γ y e y: Amplitude of distortion ( ) k B Te T γ y = dtcσ T n e m e c 2

12 Efficiency of energy exchange between electrons and photons Recoil: y γ = dtcσ T n e k B T γ m e c 2, T γ = 2.725(1 + z) No. of scatterings Doppler effect: Energy transfer per scattering y e = dtcσ T n e k B T e m e c 2 In early Universe y γ y e y: Amplitude of distortion ( ) k B Te T γ y = dtcσ T n e m e c 2

13 y-type (Sunyaev-Zeldovich effect) from clusters/reionization y γ 1, T e 10 4 y = (τ reionization ) k BT e m e c 2 (0.1)( ) 10 7 e e e e e e e e e e Frequency (GHz) T=2.725K I ν (Wm 2 Hz 1 Sr 1 ) Blackbody y distortion x 10

14 y-type (Sunyaev-Zeldovich effect) from clusters/reionization n SZ = y T 4 T = y 1 n Pl T 2 T xe x ( ) (e x 1) 2 x ex + 1 e x 1 4 I sz = I sz I planck = 2hν3 c 2 n sz

15 Average y-distortion (Sunyaev-Zeldovich effect) limits (Zeldovich and Sunyaev 1969) COBE-FIRAS limit (95%): y (Fixsen et al. 1996) Frequency (GHz) I ν (Wm 2 Hz 1 Sr 1 ) Blackbody y distortion x 10

16 For y γ 1 equilibrium is established. T e and T γ converge to common value The photon spectrum relaxes to equilibrium Bose-Einstein distribution y γ (z) y-type i-type µ-type z Blackbody Photosphere

17 Bose-Einstein spectrum- Chemical potential (µ) n(x) = 1 e x+µ 1

18 Bose-Einstein spectrum- Chemical potential (µ) n(x) = 1 e x+µ 1 Given two constraints, energy density (E) and number density (N) of photons, T, µ uniquely determined.

19 Bose-Einstein spectrum- Chemical potential (µ) n(x) = 1 e x+µ 1 Given two constraints, energy density (E) and number density (N) of photons, T, µ uniquely determined. Idea behind analytic solutions: If we know rate of production of photons and energy injection rate, we can calculate the evolution/production of µ (and T)

20 µ-distortion: Bose-Einstein spectrum, y γ 1 COBE-FIRAS limit (95%): µ (Fixsen et al. 1996) 2 Frequency(GHz) I ν (10-22 Wm -2 ster -1 Hz -1 ) µ=5.6x10-5 Y= x=hν/kt

21 Intermediate-type distortions (Khatri and Sunyaev 2012b) Solve Kompaneets equation with initial condition of y type solution. n = 1 ( y γ x 2 x x4 n + n 2 + T ) e n, T e (n + n 2 T x T = )x 4 dx 4 nx 3 dx I ν (10-22 Wm -2 ster -1 Hz -1 ) y-type y γ =0.01 y γ =0.05 y γ =0.1 y γ =0.2 y γ =0.5 y γ =1 y γ =2 µ-type Observed Frequency (GHz) x 0 x max x min 1 10 x

22 Intermediate-type distortions... t=3 mins t=70 days t=19 years t=3000 years BBN 8 + z ~ 3x10 e /e annihilation 9 10 > z > 10 8 Blackbody Photosphere z=2x10 Blackbody surface Time µ Intermediate type z=2x10 z=1.5x10 y t=380,000 years CMB Last scattering surface t=200 million years Reionization z=1100 z=30 z=6 Redshift intermediate-type distortions: Numerically solve Kompaneets equation

23 Processes responsible for creation of CMB spectrum Compton γ e θ e Recoil=h ν(1 cos θ) mc 2 Dominant Electron accelerates Can emit photon γ γ Double Compton e θ γ γ e p+ few percent e p+ Bremsstrahlung γ Double Compton and bremsstrahlung create/absorb photons ( 1/x 2 ) Compton scattering distributes them over the whole spectrum

24 µ-type distortions... t=3 mins t=70 days t=19 years t=3000 years BBN 8 + z ~ 3x10 e /e annihilation 9 10 > z > 10 8 Blackbody Photosphere z=2x10 Blackbody surface Time µ Intermediate type z=2x10 z=1.5x10 y t=380,000 years CMB Last scattering surface t=200 million years Reionization z=1100 z=30 z=6 Redshift Compton + double Compton + bremsstrahlung Analytic solution: µ = 1.4 dq dz e T (z) dz (Sunyaev and Zeldovich 1970)

25 Solutions for T (Z) Old solutions (Sunyaev and Zeldovich 1970, Danese and de Zotti 1982) Extension of old solutions to include both double Compton and bremsstrahlung [ ( ) 1 + z 5 ( ) ] 1 + z 5/2 1/2 ( ) T (z) + + ε ln 1 + z 5/4 ( ) 1 + z 5/ z dc 1 + z br 1 + z ε 1 + z ε This solution has accuracy of 10%, z dc Numerical studies: Illarionov and Sunyaev 1975, Burigana, Danese, de Zotti 1991, Hu and Silk 1993, Chluba and Sunyaev 2012 New solution, accuracy 1% (Khatri and Sunyaev 2012a) [ ( ) 1 + z 5 ( ) ] 1 + z 5/2 1/2 ( ) T (z) ε ln 1 + z 5/4 ( ) 1 + z 5/ z dc 1 + z br 1 + z ε 1 + z ε [ ( ) 1 + z 3 ( ) ] 1 + z 1/2 + +, 1 + z dc 1 + z br

26 The general picture -(1+z)dQ/dz Last Scattering Surface y-type i-type µ-type Silk Damping, n s =0.96 Cooling/BEC (z) redshift Blackbody Surface Blackbody visibility e + e - ->γγ Blackbody Photosphere BBN

27 Silk damping Photon diffusion mixing of blackbodies T+dT Entropy T-dT (Diffusion scale)

28 Silk damping Photon diffusion mixing of blackbodies T+dT Entropy T-dT (Diffusion scale) Mixing of blackbodies gives y-type distortion Zeldovich, Illarionov & Sunyaev 1972, Chluba & Sunyaev 2004

29 Silk damping Photon diffusion mixing of blackbodies T+dT Entropy T-dT (Diffusion scale) Mixing of blackbodies gives y-type distortion Zeldovich, Illarionov & Sunyaev 1972, Chluba & Sunyaev 2004 ( < n Planck T + δt ) >=< T 1 hν > e k(t+δt/t) 1

30 Silk damping Photon diffusion mixing of blackbodies T+dT Entropy T-dT (Diffusion scale) Mixing of blackbodies gives y-type distortion Zeldovich, Illarionov & Sunyaev 1972, Chluba & Sunyaev 2004 (δt < n Planck >= 1 ) 2 (δt T n Pl T T T e + kt hν 1 ) 2 T 4 1 n Pl T T 2 T

31 Silk damping Photon diffusion mixing of blackbodies T+dT Entropy T-dT (Diffusion scale) Mixing of blackbodies gives y-type distortion Zeldovich, Illarionov & Sunyaev 1972, Chluba & Sunyaev 2004 (δt < n Planck >= 1 ) 2 (δt e + T n Pl kt hν 1 T T + 1 ) 2 2 T (δt ) ) 2 (δt = n Planck (T ) 2 T 2 T 2/3 1/3 Black body T 4 T n SZ 1 n Pl T 2 T Kompaneets operator/sz

32 SZ effect in CMB rest frame: Doppler boost CMB rest frame e

33 SZ effect in electron rest frame: Mixing of blackbodies in the dipole seen by the electron Electron rest frame e COBE DMR

34 Silk damping Photon diffusion mixing of blackbodies T+dT Entropy T-dT λ (Diffusion scale) Apply mixing of blackbodies result to CMB Chluba, Khatri and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012 T T d dt E E γ d k 2 distortion dt 2 dk 2π 2 P i(k) [ Θ Θ (l > 1 terms) ] = l( i) l (2l + 1)P l Θ l

35 Silk damping Photon diffusion mixing of blackbodies T+dT Entropy T-dT λ (Diffusion scale) Apply mixing of blackbodies result to CMB Chluba, Khatri and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012 d dt E E γ d k 2 distortion dt 2 dk 2π 2 P i(k) [ Θ Θ (l > 1 terms) ] z = 8 k D 10 4 Mpc 1

36 Silk damping Photon diffusion mixing of blackbodies T+dT Entropy T-dT λ (Diffusion scale) Apply mixing of blackbodies result to CMB Chluba, Khatri and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012 d dt E E γ d k 2 distortion dt 2 dk 2π 2 P i(k) [ Θ Θ (l > 1 terms) ] density Θ 0 cos(kr s )e k2 /k 2 D, velocity Θ1 sin(kr s )e k2 /k 2 D

37 Silk damping Photon diffusion mixing of blackbodies T+dT Entropy T-dT λ (Diffusion scale) Apply mixing of blackbodies result to CMB Chluba, Khatri and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012 d dt E E γ d k 2 distortion dt 2 dk 2π 2 P i(k) [ Θ Θ (l > 1 terms) ] density Θ 0 cos(kr s )e k2 /k 2 D, velocity Θ1 sin(kr s )e k2 /k 2 D Total energy in the standing wave is independent of time

38 The Silk damping scale k D Mpc Last scattering surface 8 Mpc -1 y-type 364 Mpc x10 4 i-type 1.1x10 4 Mpc x10 5 µ-type Blackbody photosphere 1.98x Redshift (z)

39 Silk damping (Khatri and Sunyaev 2012b) Add spectra for different k D (y γ ) with weights P i (k D ) n s =0.7 n s =1.0 n s =1.5 I ν (10-26 Wm -2 ster -1 Hz -1 ) PRISM sensitivity Frequency (GHz)

40 Pivot point k 0 = 42 Mpc 1 k 3 P(k) P ζ = (A ζ 2π 2 /k 3 )(k/k 0 ) n s dn s/dlnk(lnk/k 0 ) n ss =0.5 n ss =0.8 n ss =0.9 n ss =1.0 n ss =1.1 n ss =1.2 n ss =1.5 10A ζ,n ss =2 CMB best fit + Ly-α COBE y limit y-type low redshift confusion limited Intermediate -type Pixie COBE µ limit µ-type Weaker constraints Blackbody Photosphere k Mpc -1

41 Spectrum: Pixie will improve over the COBE precision by at least 3 orders of magnitude (Kogut et al. 2011)

42 New proposal to ESA for L class mission 10 times more sensitive than Pixie Polarized Radiation Imaging and Spectroscopy Mission PRISM Probing cosmic structures and radiation with the ultimate characterization of the microwave sky in intensity, polarization, and frequency spectrum

43 Please Sign Up to show your support for PRISM

44 Fisher matrix forecasts Model: I ν = tiν t + yiν y + Iν damping (n s,a ζ,dn s /dlnk). Marginalize over temperature (t) and SZ effect (y) I damping ν contains i-type and µ-type distortions

45 Fisher matrix forecasts (Khatri and Sunyaev 2013) Pixie-like experiments: (x,y) (Resolution GHz, δi(ν) = Wm 2 Sr 1 Hz 1 ) Pixie=(15,5) 1-σ Pixie 3 A ζ (k 0 =42 Mpc -1 ) PRISM Pixie n s (k 0 =42 Mpc -1 )

46 Importance of i-type distortions,degeneracies (Khatri and Sunyaev 2013) Information in the shape of i-type distortions breaks the A ζ n s degeneracy PRISM New physics: µ free A ζ (k 0 =42 Mpc -1 ) y free y fixed 1 µ only, no i-type n s (k 0 =42 Mpc -1 )

47 Running spectral index Fix the pivot point at k = 0.05 Mpc 1 Long lever arm: Main effect in the amplitude of distortion 8 6 dn s /dlnk= I ν (10-26 Wm -2 ster -1 Hz -1 ) PRISM sensitivity Frequency (GHz)

48 Fisher matrix forecasts with Planck+SPT+ACT+WMAP-pol (Khatri and Sunyaev 2013) Planck parameters, running spectrum, Pivot point k 0 = 0.05 (x,y) (Resolution GHz, δi(ν) = Wm 2 Sr 1 Hz 1 ) Pixie=(15,5) Fiducial model n s =0.955, dnd/dlnk= Planck+SPT+ACT+WMAP pol Pixie+ Pixie Fiducial model n s =0.958, dnd/dlnk=0.0 Planck+SPT+ACT+WMAP pol Pixie Pixie+ dns/dlnk PRISM dns/dlnk 0 PRISM n s (k 0 =0.05 Mpc -1 ) n s (k 0 =0.05 Mpc -1 )

Foregrounds Figure courtesy Jacques Delabrouille 10 6 8 10 CMB Delabrouille et al.

49 Foregrounds Figure courtesy Jacques Delabrouille CMB Delabrouille et al Best fit Planck sky model CIB Lagache et al Fixsen et al Data points: Penin at al. 2012,Lagache Sensitivity goal/cmb spectral features

50 Summary The shape of the µ and intermediate type distortions is rich in information

51 Summary The shape of the µ and intermediate type distortions is rich in information With spectral distortions we can extend our view of inflation from 6-7 e-folds at present to 17 e-folds

52 Summary The shape of the µ and intermediate type distortions is rich in information With spectral distortions we can extend our view of inflation from 6-7 e-folds at present to 17 e-folds Spectral distortions take us a little nearer to the end of inflation

53 Summary The shape of the µ and intermediate type distortions is rich in information With spectral distortions we can extend our view of inflation from 6-7 e-folds at present to 17 e-folds Spectral distortions take us a little nearer to the end of inflation µ-type and intermediate type distortions can be calculated very fast using analytic and pre-calculated cosmology-independent high precision numerical solutions (Green s functions). This allows us to explore the rich multidimensional parameter space

54 Summary The shape of the µ and intermediate type distortions is rich in information With spectral distortions we can extend our view of inflation from 6-7 e-folds at present to 17 e-folds Spectral distortions take us a little nearer to the end of inflation µ-type and intermediate type distortions can be calculated very fast using analytic and pre-calculated cosmology-independent high precision numerical solutions (Green s functions). This allows us to explore the rich multidimensional parameter space i-type distortions are quite powerful in removing degeneracies between power spectrum parameters. The extra information comes from the shape of the i-type distortion

55 Summary continued With intermediate-type distortions we can distinguish between different mechanisms of energy injection which have different redshift dependence

56 Summary continued With intermediate-type distortions we can distinguish between different mechanisms of energy injection which have different redshift dependence There is more... Cosmological recombination spectrum gives measurement of primordial helium Kurt,Zeldovich,Sunyaev,Peebles,Dubrovich,Chluba,Rubino-Martin

57 Summary continued With intermediate-type distortions we can distinguish between different mechanisms of energy injection which have different redshift dependence There is more... Cosmological recombination spectrum gives measurement of primordial helium Kurt,Zeldovich,Sunyaev,Peebles,Dubrovich,Chluba,Rubino-Martin Resonant scattering on C,N,O and other ions during and after reionization makes the optical depth to the last scattering surface frequency dependent Basu, Hernandez-Monteagudo, and Sunyaev 2004

58 Summary continued With intermediate-type distortions we can distinguish between different mechanisms of energy injection which have different redshift dependence There is more... Cosmological recombination spectrum gives measurement of primordial helium Kurt,Zeldovich,Sunyaev,Peebles,Dubrovich,Chluba,Rubino-Martin Resonant scattering on C,N,O and other ions during and after reionization makes the optical depth to the last scattering surface frequency dependent Basu, Hernandez-Monteagudo, and Sunyaev 2004 Sunyaev-Zeldovich effect from hot electrons during reionization/whim can give a measurement of average electron temperature, find missing baryons Zeldovich & Sunyaev 1969, Hu, Scott, Silk 1994, Cen and Ostriker 1999,2006,

59 Summary continued With intermediate-type distortions we can distinguish between different mechanisms of energy injection which have different redshift dependence There is more... Cosmological recombination spectrum gives measurement of primordial helium Kurt,Zeldovich,Sunyaev,Peebles,Dubrovich,Chluba,Rubino-Martin Resonant scattering on C,N,O and other ions during and after reionization makes the optical depth to the last scattering surface frequency dependent Basu, Hernandez-Monteagudo, and Sunyaev 2004 Sunyaev-Zeldovich effect from hot electrons during reionization/whim can give a measurement of average electron temperature, find missing baryons Zeldovich & Sunyaev 1969, Hu, Scott, Silk 1994, Cen and Ostriker 1999,2006, Primordial non-gaussianity on extremely small scales Pajer and Zaldarriaga 2012, Ganc and Komatsu 2012

60 Summary continued Silk damping: dq dz (1 + z)(3n s 5)/2 (Chluba, Khatri and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012)

61 Summary continued Silk damping: dq dz (1 + z)(3n s 5)/2 (Chluba, Khatri and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012) Adiabatic cooling: Opposite sign to Silk damping with n s = 1 (Chluba and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012b)

62 Summary continued Silk damping: dq dz (1 + z)(3n s 5)/2 (Chluba, Khatri and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012) Adiabatic cooling: Opposite sign to Silk damping with n s = 1 (Chluba and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012b) ( ) 1+zdecay 2 dz e 1+z (1+z) 4 (Hu and Silk 1993, Chluba and Sunyaev 2012, Khatri and Sunyaev 2012a, 2012b) Particle decay: dq

63 Summary continued Silk damping: dq dz (1 + z)(3n s 5)/2 (Chluba, Khatri and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012) Adiabatic cooling: Opposite sign to Silk damping with n s = 1 (Chluba and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012b) ( ) 1+zdecay 2 dz e 1+z (1+z) 4 (Hu and Silk 1993, Chluba and Sunyaev 2012, Khatri and Sunyaev 2012a, 2012b) Particle decay: dq Cosmic strings: dq dz constant Tashiro, Sabancilar, Vachaspati 2012

64 Summary continued Silk damping: dq dz (1 + z)(3n s 5)/2 (Chluba, Khatri and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012) Adiabatic cooling: Opposite sign to Silk damping with n s = 1 (Chluba and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012b) ( ) 1+zdecay 2 dz e 1+z (1+z) 4 (Hu and Silk 1993, Chluba and Sunyaev 2012, Khatri and Sunyaev 2012a, 2012b) Particle decay: dq Cosmic strings: dq dz constant Tashiro, Sabancilar, Vachaspati 2012 Primordial magnetic fields : (1 + z) (3n+7)/2, n is the spectral index of magnetic field power spectrum (Jedamzik, Katalinic, and Olinto 2000)

65 Summary continued Silk damping: dq dz (1 + z)(3n s 5)/2 (Chluba, Khatri and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012) Adiabatic cooling: Opposite sign to Silk damping with n s = 1 (Chluba and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012b) ( ) 1+zdecay 2 dz e 1+z (1+z) 4 (Hu and Silk 1993, Chluba and Sunyaev 2012, Khatri and Sunyaev 2012a, 2012b) Particle decay: dq Cosmic strings: dq dz constant Tashiro, Sabancilar, Vachaspati 2012 Primordial magnetic fields : (1 + z) (3n+7)/2, n is the spectral index of magnetic field power spectrum (Jedamzik, Katalinic, and Olinto 2000) Black holes: Depends on the mass function Tashiro and Sugiyama 2008, Carr et al. 2010

66 Summary continued Silk damping: dq dz (1 + z)(3n s 5)/2 (Chluba, Khatri and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012) Adiabatic cooling: Opposite sign to Silk damping with n s = 1 (Chluba and Sunyaev 2012, Khatri, Sunyaev and Chluba 2012b) ( ) 1+zdecay 2 dz e 1+z (1+z) 4 (Hu and Silk 1993, Chluba and Sunyaev 2012, Khatri and Sunyaev 2012a, 2012b) Particle decay: dq Cosmic strings: dq dz constant Tashiro, Sabancilar, Vachaspati 2012 Primordial magnetic fields : (1 + z) (3n+7)/2, n is the spectral index of magnetic field power spectrum (Jedamzik, Katalinic, and Olinto 2000) Black holes: Depends on the mass function Tashiro and Sugiyama 2008, Carr et al Quantum wave function collapse: dq (1 + z) 4 Lochan, Das and Bassi 2012 dz

67 There is still a long road ahead for CMB cosmology CMB spectrum is very rich in information about the early Universe, late time Universe and fundamental physics

68 There is still a long road ahead for CMB cosmology CMB spectrum is very rich in information about the early Universe, late time Universe and fundamental physics This information is accessible and within reach of experiments in not too far future: Pixie, PRISM

69 Public code/pre-calculated numerical solutions Example Mathematica code + high precision pre-calculated numerical solutions for i-type distortions available at Fortran version soon.

70 Algorithm for fast solution, 1% level accuracy (Khatri and Sunyaev 2012b, arxiv: ) Calculate µ type distortion using the analytic solution, integrating up to the redshift when y γ = 2. n µ type = 1.4n µ z(yγ =2) dq dz e T (1)

71 Algorithm for fast solution, 1% level accuracy (Khatri and Sunyaev 2012b, arxiv: ) Calculate µ type distortion using the analytic solution, integrating up to the redshift when y γ = 2. n µ type = 1.4n µ z(yγ =2) dq dz e T (1) Calculate intermediate type distortions by adding up pre-calculated numerical solutions (Green s functions) in δy γ bins. n i type = 1 dq Q num (y i γ )δy i γ n(y i γ ) (2) dy γ khatri/idistort.html i

72 Algorithm for fast solution, 1% level accuracy (Khatri and Sunyaev 2012b, arxiv: ) Calculate µ type distortion using the analytic solution, integrating up to the redshift when y γ = 2. n µ type = 1.4n µ z(yγ =2) dq dz e T (1) Calculate intermediate type distortions by adding up pre-calculated numerical solutions (Green s functions) in δy γ bins. n i type = 1 dq Q num (y i γ )δy i γ n(y i γ ) (2) dy γ khatri/idistort.html Add rest of the energy to y-type distortions. i n y type = 0.25n y z=0 z(y γ =0.01) dq dz (3)

73 Accuracy of new solutions is better than 1% 0.1 1e-08 µ(x e ) 0.01 µ/µ 1e-09 Numerical SZ1970 Improved Error: SZ1970 Improved x e

74 y+µ cannot fully mimic i-type distortion µ type and intermediate-type distortions are not independent. For Silk damping, intermediate-type distortions must contain about the same amount of energy as µ-type distortions. 10 Observed Frequency (GHz) Total Y+µ fit I ν (10-25 Wm -2 ster -1 Hz -1 ) Residual x

75 Blackbody photosphere E/E e-05 1e-06 1e-07 1e-08 1e-09 1e-10 1e-11 FIRAS Pixie µ-distortion Blackbody Surface µ final /µ initial 1e-06 1e-08 1e-10 Blackbody Photosphere 1e-12 1e+06 1e+07 1e-12 energy injection redshift (z i ) µ final /µ initial

76 y γ = 0 zinj dt k Bσ T n e m e c T γ y γ 1 = µ, y γ 1 = y y γ (z inj ) y-type intermediate-type µ-type Blackbody Photosphere z inj

77 Intermediate-type distortions (Khatri and Sunyaev 2012b) Solve Kompaneets equation with initial condition of y type solution. n = 1 ( y γ x 2 x x4 n + n 2 + T ) e n, T e (n + n 2 T x T = )x 4 dx 4 nx 3 dx

78 Intermediate-type distortions (Khatri and Sunyaev 2012b) Solve Kompaneets equation with initial condition of y type solution. n = 1 ( y γ x 2 x x4 n + n 2 + T ) e n, T e (n + n 2 T x T = )x 4 dx 4 nx 3 dx I ν (10-22 Wm -2 ster -1 Hz -1 ) y-type µ-type Observed Frequency (GHz) x 0 x max x min 1 10 x

79 Sensitivity of Pixie like Experiment, resolution 15 GHz W m Hz Sr Signal Physics/parameters 26 y distortion from 5x10 Find missing baryons reionization/whim reionization temperature Richness Amplitude of i+ µ type distortion from Silk damping H recombination spectrum Shape of i type distortion Detect helium feature in recombination spectrum 26 1x x x10 Amplitude of primordial power spectrum on 100 pc 100kpc scales Baryon density Shape of primordial power spectrum Detect primordial helium Amplitude of Signal Precise measurement of He features 28 1x10 Measure primordial helium baryon density etc. with some precision (10 20%?)

Polarization from Rayleigh scattering

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