1. CMB lensing and cosmic acceleration Viviana Acquaviva SISSA, Trieste

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

3. small deflection angles  WEAK LENSING source lenslensplaneα unlensedimage lensedimage deflectionangle Einstein equations geodesic equation

4. why lensing for dark energy? CMB light from LSS us z 1000 ~ 10 r/H 0 -1 ~ 2 ~ 10 DE lensing selection effect OVERLAPPING OVERLAPPING

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

6. Temperature power spectrum - - - unlensed lensed

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 1.Formal extension of lensing framework to generalized theories of gravity to generalized theories of gravity 2. Study of lensed B signal in different models VA, Baccigalupi and Perrotta 2004 RP: V(  ) = M 4+  /   (aka IPL) RP: V(  ) = M 4+  /   (aka IPL) Ratra & Peebles 2000 SUGRA: V(  ) = M 4+  /   e 4  (  /Mpl) 2 SUGRA: V(  ) = M 4+  /   e 4  (  /Mpl) 2 Brax & Martin 2000 VA & Baccigalupi 2005

10. technicalities  lensed correlation functions are obtained by a convolution with a gaussian of arguments: background expansion W = (χ LS – χ)/χ LS evolution of gravitational potential P ψ (k,χ) ≠ T 2 (k,0) g 2 (χ) no analytical fit is available Zaldarriaga & Seljak 1998 Ψ  generalized gauge-invariant variable accounting for all the fluctuating components lensing of the spectra performed in the main integration routine (all k,z needed!) integration routine (all k,z needed!)

11. RESULTS FOR THE QUINTESSENCE MODELS no anisotropic stress basically geometry effects tracking behaviour  main dependence is on α w 0 = - 0.9 tuned to get G eff = G 0 SAME PRIMORDIAL NORMALIZATION SUGRA IPL SUGRA IPL

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

13. TTpowerspectrum EEpowerspectrum only slight projection effect SUGRA IPL SUGRA IPL

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

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

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

17. PARAMETERS 1. w 0 = -1 2. w ∞ = -1 3. n s = 0.96 4. h 0 = 0.72 5. τ = 0.11 6. Ω b h 2 = 0.022 7. Ω m h 2 = 0.11 8. A = 1 1. w 0 = -0.9 2. w ∞ = -0.4 3. n s = 0.96 4. h 0 = 0.72 5. τ = 0.11 6. Ω b h 2 = 0.023 7. Ω m h 2 = 0.12 8. A = 1 SUGRA ΛCDM EBEX-like experiment

18. ΛCDM RESULTS SUGRA RESULTS 0.1 few ·10 -2 3·10 -3 6·10 -2 3·10 -3 8·10 -5 7·10 -4 3·10 -3 5 ·10 -2 few·10 -2 2·10 -3 2·10 -2 3·10 -3 7·10 -5 5·10 -4 5.0·10 -3 w0w0w0w0 w’ nsnsnsns h0h0h0h0 τ Ωbh2Ωbh2Ωbh2Ωbh2 Ωmh2Ωmh2Ωmh2Ωmh2 A √ (F -1 ) ii

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)