1. Investigating dark energy with CMB lensing Viviana Acquaviva, SISSA, Trieste Lensing collaborators in SISSA: C. Baccigalupi, S. Leach, F. Perrotta, F. Stivoli

2. ACCELERATION Vacuum energy unknownphysics? Quintessence GR modifications

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

4. lensing is quadratic in the cosmological perturbations: hard life if we are dominated by primary anisotropies due to power redistribution lensing generates late B-modes at l > 100 why CMB for dark energy? observed imagesource emission re-mapping lensing equation source lens plane α unlensed image lensed image deflection angle

5. Temperature power spectrum

6. E modes of polarization power spectrum

7. Cross-correlation power spectrum

8. B modes of polarization

9. Dark Energy dynamics tracer Dark Energy dynamics tracer No dependence on the present era No dependence on the present era (complementar to local universe constraints) (complementar to local universe constraints) CMB observable almost entirely born almost entirely born via gravitational lensing at the epoch at the epoch of the onset of acceleration

10. GRAVITY THEORIES GENERALIZATION modifications of dynamics time-varyinggravitationalcoupling R /16 π G  f / 2κ anisotropic stress Ф ≠  corrections to  due to fluctuations δφ, δR V.A., C. Baccigalupi & F. Perrotta 2004

11. IPL: V(  ) = M 4+  /   Ratra & Peebles 1988 SUGRA: V(  ) = M 4+  /   e 4  (  /Mpl) 2 Brax & Martin 2000 RESULTS FOR QUINTESSENCE MODELS no anisotropic stress  basically geometry effects tracking behaviour  main dependence is on α w 0 = - 0.9 SAME PRIMORDIAL AND PRESENT NORMALIZATION

12. Technicalities  a description of the lensed power spectra is given in terms of convolution in the l-space with a gaussian function GEOMETRY: lensing kernel κ(θ) PERTURBATION GROWTH: transfer function T Δ Zaldarriaga & Seljak 1998

13. Lensing kernel Perturbation growth factor different amount of dark energy at z ~ 1  significant deviation same trend

14. SUGRA and IPL: Temperature power spectrum only slight projection effect SUGRA IPL

15. COMPARISON OF B-MODES SPECTRA effect is due to B-modes sensitivity to DE equation of state DERIVATIVE! 30% difference in amplitude at peak VA & Baccigalupi 2005

16. 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

17. 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

18. PARAMETERS w 0 = -1 w ∞ = -1 w 0 = -0.82 w ∞ = -0.24 SUGRA ΛCDM n s = 0.96 h 0 = 0.72 τ = 0.11 Ω b h 2 = 0.022 Ω m h 2 = 0.123 A = 1 sky coverage (how many data points) Planck: 0.66, ground-based: usually < few % sensitivity per pixel (how good are data) for CMB B modes: EBex 4%, PolarBear 10% FWHM of beam (what extent can we measure to) Planck: l ~ 1000, EBex: l ~ 1400, PolarBear: l ~ 2700

19. 7d-5 0.001 0.01 ΛCDM RESULTS SUGRA RESULTS 0.19 0.39 w0w0w0w0 w∞w∞w∞w∞ nsnsnsns h0h0h0h0 τ Ωbh2Ωbh2Ωbh2Ωbh2 Ωmh2Ωmh2Ωmh2Ωmh2 A √ (F -1 ) ii f sky = 0.2, noise = PolarBear, FWHM = 5’ 0.005 0.003 0.06 0.031 0.003 0.02 0.005 7d-5 8d-4 0.01

20. 1d-4 9d-4 6d-3 ΛCDM RESULTS SUGRA RESULTS 0.17 0.40 w0w0w0w0 w∞w∞w∞w∞ nsnsnsns h0h0h0h0 τ Ωbh2Ωbh2Ωbh2Ωbh2 Ωmh2Ωmh2Ωmh2Ωmh2 A √ (F -1 ) ii f sky = 0.66, noise = PolarBear, FWHM = 10’ 0.003 0.07 0.04 0.03 0.003 0.02 0.003 1d-4 6d-4 6d-3

21. CMB light from LSS us z 1000 ~ 10 r/H 0 -1 ~ 2 ~ 10 Dark Energy ΛCDM lensing selection effect OVERLAPPING OVERLAPPING

22. CMB light from LSS us z 1000 ~ 10 r/H 0 -1 ~ 2 ~ 10 Dark Energy SUGRA lensing selection effectMORE OVERLAPPING OVERLAPPING

23. WORK IN PROGRESS study of complementarity with other dark energy investigation methods (SNe, cosmic shear) investigation methods (SNe, cosmic shear) Refregier 2003 Yeche et al 2005

24. WORK IN PROGRESS Better understanding of lensing non-gaussianity issue Lensed map by S. Leach, SISSA, using A. Lewis’ LensPix code

25. WORK IN PROGRESS Better understanding of lensing non-gaussianity issue Lensed map by S. Leach, SISSA, using A. Lewis’ LensPix code

26. WORK IN PROGRESS Better understanding of lensing non-gaussianity issue REDUCEDSTATISTICALSIGNIFICANCE Smith, Hu & Kaplinghat 2004 PROPER INCLUSION OF NON GAUSSIANITY (HIGHER QUALITY DATA) Smith, Challinor & Rocha 2005 ANALYSIS OF POSSIBLE DEGENERACIES WITH NEUTRINO MASSES Kaplinghat, Knox and Song 2003 DISCRIMINATION THROUGH DEFLECTING FIELD RECONSTRUCTION

27. WORK IN PROGRESS Analysis of modified gravity models (scalar-tensor theories, DGP, Extended Quintessence) (scalar-tensor theories, DGP, Extended Quintessence) need for sensitivity to expansion history perturbation growth Lue et al 2004

28. MORE FUTURE DIRECTIONS Use of more sophisticated techniques (MCMC) in order to refine predictions (MCMC) in order to refine predictions of available precision of available precision Analysis of principal components of dark energy (are there better parametrizations?) (are there better parametrizations?) Better understanding of the foregrounds (not yet well known for B polarization) (not yet well known for B polarization) Impact on other cosmological parameters determination determination

29. 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  Our computational machinery allows us to predict the lensing effect in 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  There are a lot of connected future directions still to be fully exploited

30. 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  Our computational machinery allows us to predict the lensing effect in 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  There are a lot of connected future directions still to be fully exploited

31. 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  Our computational machinery allows us to predict the lensing effect in 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  There are a lot of connected future directions still to be fully exploited

32. 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  Our computational machinery allows us to predict the lensing effect in 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  There are a lot of connected future directions still to be fully exploited

33. 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  Our computational machinery allows us to predict the lensing effect in 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  There are a lot of connected future directions still to be fully exploited

34. 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  Our computational machinery allows us to predict the lensing effect in 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  There are a lot of connected future directions still to be fully exploited