1. Venice 2013 Luca Amendola University of Heidelberg The next ten years of dark energy research Raphael, The School of Athens, Rome

2. Venice 2013

3. Maps of the World Kosmas IV c. d.C. SDSS XXI c. d.C. 1.6 billion yrs

4. Lighthouses in the dark Supernovae Ia Venice 2013

5. Heidelberg 2010 Lighthouses in the dark Venice 2013

6. Hubble diagram 1997 1998 2010

7. Venice 2013 Bug or feature? Evolution in time: standard candles Conclusion: SNIa are dimmer than expected in a matter universe ! BUT: -Dependence on progenitors? -Contamination? -Environment? -Host galaxy? -Dust? -Lensing? -Unknowns? Ordinary matter

8. Venice 2013 Cosmological explanation Evolution in time: standard candles There is however a simple cosmological solution If H(z) in the past is smaller (i.e. acceleration), then r(z) is larger: larger distances (for a fixed redshift) make dimmer supernovae a(t) time Local Hubble law Global Hubble law now

9. Venice 2013 Cosmological constant acceleration, in GR, can only occur if pressure is large and negative Properties: dominant dark, weakly clustered with large negative pressure Einstein 1917

10. Venice 2013 Cosmological explanation Evolution in time: standard candles There is however a simple cosmological solution Local Hubble law Global Hubble law

11. Cosmological constant Venice 2013 Matter density Lambda density

12. Venice 2013

13. Time view We know so little about the evolution of the universe! We assumed for many years that there were just matter and radiation Venice 2013 matter DE radiation Shall we repeat our mistake and think that there is just a Λ ? BBN CMB

14. L = crossover scale: 5D gravity dominates at low energy/late times/large scales 4D gravity recovered at high energy/early times/small scales 5D Minkowski bulk: infinite volume extra dimension gravity leakage brane An example of Modified Gravity: DGP (Dvali, Gabadadze, Porrati 2000) Venice 2013

15. Space-time geometry The most general (linear, scalar) metric at first-order Full metric reconstruction at first order requires 3 functions background perturbations

16. Venice 2013 Two free functions At linear order we can write:  Poisson equation  zero anisotropic stress

17. Venice 2013 Two free functions  modified Poisson equation  non-zero anisotropic stress At linear order we can write:

18. Venice 2013 Modified Gravity at the linear level  scalar-tensor models  standard gravity  DGP  f(R) Lue et al. 2004; Koyama et al. 2006 Bean et al. 2006 Hu et al. 2006 Tsujikawa 2007  coupled Gauss-Bonnet see L. A., C. Charmousis, S. Davis 2006 Boisseau et al. 2000 Acquaviva et al. 2004 Schimd et al. 2004 L.A., Kunz &Sapone 2007

19. Venice 2013 Classifying the unknown 1. Cosmological constant 2. Dark energy w=const 3. Dark energy w=w(z) 4. quintessence 5. scalar-tensor models 6. coupled quintessence 7. mass varying neutrinos 8. k-essence 9. Chaplygin gas 10. Cardassian 11. quartessence 12. quiessence 13. phantoms 14. f(R) 15. Gauss-Bonnet 16. anisotropic dark energy 17. brane dark energy 18. backreaction 19. void models 20. degravitation 21. TeVeS 22. oops....did I forget your model?

20. Venice 2013 The past ten years of dark energy models

21. First found by Horndeski in 1975 rediscovered by Deffayet et al. in 2011 no ghosts, no classical instabilities it modifies gravity! it includes f(R), Brans-Dicke, k-essence, Galileons, etc etc etc The most general 4D scalar field theory with second order equation of motion A quintessential scalar field Saõ Paulo 2013

22. Venice 2013 The next ten years of DE research Combine observations of background, linear and non-linear perturbations to reconstruct as much as possible the Horndeski model … or, even better, rule it out!

23. Modified Gravity at the linear level Every Horndeski model is characterized at linear scales by the two observable functions De Felice et al. 2011; L.A. et al.,arXiv:1210.0439, 2012 Venice 2013

24. Modified Gravity at the linear level De Felice et al. 2011; L.A. et al.,arXiv:1210.0439, 2012 Saõ Paulo 2013

25. Generality of the Yukawa correction Every Horndeski model induces at linear level, on sub-Hubble scales, a Newton-Yukawa potential where both α and λ depend on space and time Every consistent modification of gravity based on a scalar field must generate this gravitational potential Venice 2013

26. Dark Force Schlamminger et al 2008 Limits on Yukawa coupling are strong but local! Venice 2013

27. Reconstruction of the metric massive particles respond to Ψ massless particles respond to Φ-Ψ

28. Venice 2013 Galaxy power spectrum

29. Venice 2013 Peculiar velocities. r = cz/H 0

30. Venice 2013 Observer Dark matter halos Background sources Weak lensing

31. Venice 2013 All you can ever get out of Cosmology Expansion rate Amplitude of the power spectrum Redshift distortion of the power spectrum Lensing How to combine them to test the theory? as function of redshift and scale!

32. Venice 2013 Model-independent ratios Redshift distortion/Amplitude Lensing/Redshift distortion Redshift distortion rate Expansion rate

33. Venice 2013 Testing the entire Horndeski Lagrangian A unique combination of model independent observables L.A. et al. 1210.0439 Observables Theory

34. Venice 2013 Horndeski Lagrangian: not too big to fail L.A. et al. 1210.0439 If this relation is falsified, the Horndeski theory is rejected

35. Venice 2013 Combine lensing and galaxy clustering !

36. Euclid Surveys –Simultaneous (i) visible imaging (ii) NIR photometry (iii) NIR spectroscopy –15,000 square degrees –100 million redshifts, 2 billion images –Median redshift z = 1 –PSF FWHM ~0.18’’ –>900 peoples, >10 countries Euclid in a nutshell Euclid satellite SELECTED! arXiv Red Book 1110.3193 Venice 2013

37. Sensitivity Hu, 1999 1998 2011 History repeats itself… Venice 2013

38. Euclid’s challenge Growth of matter fluctuations C. Di Porto & L.A. 2010 Euclid error forecast Present error

39. IPMU Dark Energy Conference Euclid - Primary Science Goals IssueOur Targets Dark Energy Measure the DE equation of state parameters w0 and wa to a precision of 2% and 10%, respectively, using both expansion history and structure growth. Test of General Relativity Distinguish General Relativity from the simplest modified- gravity theories, by measuring the growth factor exponent γ with a precision of 2% Dark Matter Test the Cold Dark Matter paradigm for structure formation, and measure the sum of the neutrino masses to a precision better than 0.04eV when combined with Planck. The seeds of cosmic structures Improve by a factor of 20 the determination of the initial condition parameters compared to Planck alone. Summary: Euclid’s challenge

40. Venice 2013 Cambridge University Press

41. Rio de Janeiro 2013 Standard rulers θ

42. Rio de Janeiro 2013 Standard rulers

43. Rio de Janeiro 2013 BAO ruler Charles L. Bennett Nature 440, 1126-1131(27 April 2006 )

44. Rio de Janeiro 2013 Deconstructing the galaxy power spectrum Redshift distortion Galaxy clustering Present mass power spectrum Galaxy bias Growth function Line of sight angle

45. Rio de Janeiro 2013 Three linear observables: A, R, L μ=0 Amplitude A μ=1 Redshift distortion R Lensing L clustering lensing

46. Rio de Janeiro 2013 The only model-independent ratios Redshift distortion/Amplitude Lensing/Redshift distortion Redshift distortion rate How to combine them to test the theory? Expansion rate

47. Rio de Janeiro 2013 Theoretical behaviour or Matter conservation equation