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Luca Amendola University of Heidelberg

Luca Amendola University of Heidelberg. The next ten years of dark energy research. Raphael, The School of Athens, Rome. Maps of the World. 1.6 billion yrs. Kosmas IV c. d.C . SDSS XXI c. d.C. Lighthouses in the dark. Supernovae Ia. Lighthouses in the dark. Heidelberg 2010.

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Luca Amendola University of Heidelberg

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

  2. Venice 2013

  3. Maps of the World 1.6 billion yrs Kosmas IV c. d.C. SDSS XXI c. d.C. Venice 2013

  4. Lighthouses in the dark Supernovae Ia Venice 2013

  5. Lighthouses in the dark Heidelberg 2010 Venice 2013

  6. Hubble diagram 1997 1998 2010 Venice 2013

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

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

  9. 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 Venice 2013

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

  11. Cosmological constant Lambda density Matter density Venice 2013

  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 CMB radiation matter DE BBN Shall we repeat our mistake and think that there is just a Λ ? Venice 2013

  14. An example of Modified Gravity: DGP (Dvali, Gabadadze, Porrati 2000) 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 brane gravity leakage Venice 2013

  15. Space-time geometry The most general (linear, scalar) metric at first-order background Full metric reconstruction at first order requires 3 functions perturbations Venice 2013

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

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

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

  19. Venice 2013 Classifying the unknown • Cosmological constant • Dark energy w=const • Dark energy w=w(z) • quintessence • scalar-tensor models • coupled quintessence • mass varying neutrinos • k-essence • Chaplygin gas • Cardassian • quartessence • quiessence • phantoms • f(R) • Gauss-Bonnet • anisotropic dark energy • brane dark energy • backreaction • void models • degravitation • TeVeS • oops....did I forget your model?

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

  21. Saõ Paulo 2013 A quintessential scalar field The most general 4D scalar field theory with second order equation of motion • 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

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

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

  25. Venice 2013 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

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

  27. Reconstruction of the metric massive particles respond to Ψ massless particles respond to Φ-Ψ Venice 2013

  28. Galaxy power spectrum δ = P(k) = Venice 2013

  29. Peculiar velocities r = cz/H0 . Venice 2013

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

  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 as function of redshift and scale! How to combine them to test the theory?

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

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

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

  35. Venice 2013 Combine lensing and galaxy clustering !

  36. Venice 2013 Euclid in a nutshell 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 SELECTED! Euclid satellite arXiv Red Book 1110.3193

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

  38. Euclid’s challenge C. Di Porto & L.A. 2010 Euclid error forecast Present error Growth of matter fluctuations Venice 2013

  39. Summary: Euclid’s challenge Euclid - Primary Science Goals IPMU Dark Energy Conference

  40. Cambridge University Press Venice 2013

  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 Line of sight angle Galaxy bias Present mass power spectrum Growth function

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

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

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

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