CMB lensing and cosmic acceleration

1. CMB lensingand cosmic acceleration Viviana Acquaviva SISSA, Trieste

2. Outline • Physics of lensing • From CMB to dark energy • Results and forecasts

3. lens plane unlensed image source α lensed image deflection angle lens geodesic equation Einstein equations small deflection angles  WEAK LENSING

4. lensing selection effect CMB light from LSS DE OVERLAPPING  z 1000 ~ 1 0 why lensing for dark energy? us r/H0-1 ~ 2 ~ 1 0

5. source emission observed image lensing is quadratic in the cosmological perturbations ! lensing generates UNBIASED B-modes at l > 100 ! there is a CMB observation in the DE-related redshift window hard life if we are dominated by primary anisotropies CMB lensing phenomenology re-mapping

6. - - unlensed • lensed Temperature power spectrum

7. B polarization modes power spectrum reionization primordial GW lensing

8. B polarization modes power spectrum unbiased observable, tracking DE at lensing epoch

9. plan of our work • Formal extension of lensing framework • to generalized theories of gravity VA, Baccigalupi and Perrotta 2004 2. Study of lensed B signal in different models RP: V() = M4+/ (aka IPL) Ratra & Peebles 2000 SUGRA: V() = M4+/ e4(/Mpl)2 Brax & Martin 2000 VA & Baccigalupi 2005

10. evolution of gravitational potential background expansion W = (χLS – χ)/χLS Ψ generalized gauge-invariant variable accounting for all the fluctuating components Pψ(k,χ) ≠ T2(k,0) g2(χ) lensing of the spectra performed in the main integration routine (all k,z needed!) no analytical fit is available technicalities  lensed correlation functions are obtained by a convolution with a gaussian of arguments: Zaldarriaga & Seljak 1998

11. SUGRA IPL SUGRA IPL RESULTS FOR THE QUINTESSENCE MODELS no anisotropic stress basically geometry effects tracking behaviour  main dependence is on α w0 = - 0.9 tuned to get Geff = G0 SAME PRIMORDIAL NORMALIZATION

12. SUGRA IPL SUGRA IPL SUGRA IPL Lensing kernel different amount of dark energy at z ~ 1  significant deviation Perturbation growth factor

13. SUGRA IPL SUGRA IPL TT power spectrum only slight projection effect EE power spectrum

14. COMPARISON OF B-MODES SPECTRA IPL SUGRA 30% difference in amplitude at peak effect is due to B-modes sensitivity to DE equation of state DERIVATIVE!

15. GETTING MORE QUANTITATIVE: A FISHER MATRIX ANALYSIS ESTIMATOR OF ACHIEVABLE PRECISION set of parameters αi single spectrum four spectra F-1ij gives marginalized 1-σ error on parameters

16. dark energy parametrization: Chevallier & Polarski 2001, Linder & Huterer 2005 fixing primordial normalization one has only projection effects on TT,TE,EE spectra B spectrum  amplitude changes!  (sensitivity to dynamics at lower redshifts)

17. w0 = -1 w∞= -1 ns = 0.96 h0 = 0.72 τ = 0.11 Ωbh2= 0.022 Ωm h2 = 0.11 A = 1 PARAMETERS ΛCDM SUGRA • w0 = -0.9 • w∞= -0.4 • ns = 0.96 • h0 = 0.72 • τ = 0.11 • Ωbh2= 0.023 • Ωm h2= 0.12 • A = 1 EBEX-like experiment

18. √(F-1)ii 0.1 ΛCDM RESULTS few ·10-2 w0 3·10-3 6·10-2 w’ 3·10-3 5 ·10-2 ns 8·10-5 h0 few·10-2 7·10-4 τ 3·10-3 Ωbh2 2·10-3 2·10-2 Ωmh2 3·10-3 A 7·10-5 SUGRA RESULTS 5·10-4 √(F-1)ii 5.0·10-3

19. CONCLUSIONS AND FURTHER THOUGHTS • We can extract valuable information from the lensed CMB spectra • The B-modes are the most faithful tracer of the dark energy behaviour at intermediate redshifts and can discriminate among models • We have a computational machine allowing us to predict the lensed spectra of a wide range of models • We expect to be able to rule out or select models thanks to the next generation of CMB polarization-devoted experiments (EBEX, CMBpol, PolarBEar)

20. CONCLUSIONS AND FURTHER THOUGHTS • We can extract valuable information from the lensed CMB spectra • The B-modes are the most faithful tracer of the dark energy behaviour at intermediate redshifts and can discriminate among models • We have a computational machine allowing us to predict the lensed spectra of a wide range of models • We expect to be able to rule out or select models thanks to the next generation of CMB polarization-devoted experiments (EBEX, CMBpol, PolarBEar)

21. CONCLUSIONS AND FURTHER THOUGHTS • We can extract valuable information from the lensed CMB spectra • The B-modes are the most faithful tracer of the dark energy behaviour at intermediate redshifts and can discriminate among models • We have a computational machine allowing us to predict the lensed spectra of a wide range of models • We expect to be able to rule out or select models thanks to the next generation of CMB polarization-devoted experiments (EBEX, CMBpol, PolarBEar)

22. CONCLUSIONS AND FURTHER THOUGHTS • We can extract valuable information from the lensed CMB spectra • The B-modes are the most faithful tracer of the dark energy behaviour at intermediate redshifts and can discriminate among models • We have a computational machine allowing us to predict the lensed spectra of a wide range of models • We expect to be able to rule out or select models thanks to the next generation of CMB polarization-devoted experiments (EBEX, CMBpol, PolarBEar)

23. CONCLUSIONS AND FURTHER THOUGHTS • We can extract valuable information from the lensed CMB spectra • The B-modes are the most faithful tracer of the dark energy behaviour at intermediate redshifts and can discriminate among models • We have a computational machine allowing us to predict the lensed spectra of a wide range of models • We expect to be able to rule out or select models thanks to the next generation of CMB polarization-devoted experiments (EBEX, CMBpol, PolarBEar)