Luca Amendola Venice 2013 University of Heidelberg Raphael
Luca Amendola Venice 2013 University of Heidelberg Raphael, The School of Athens, Rome The next ten years of dark energy research
Venice 2013
Maps of the World 1. 6 billion yrs Kosmas IV c. d. C. Venice 2013 SDSS XXI c. d. C.
Lighthouses in the dark Supernovae Ia Venice 2013
Lighthouses in the dark Heidelberg 2010 Venice 2013
Hubble diagram 1997 1998 Venice 2013 2010
Bug or feature? Conclusion: SNIa are dimmer than expected in a matter universe ! Evolution in time: standard candles BUT: - Dependence on progenitors? - Contamination? - Environment? - Host galaxy? - Dust? - Lensing? - Unknowns? Ordinary matter Venice 2013
Cosmological explanation Local Hubble law There is however a simple cosmological solution Evolution in time: standard candles 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) now Venice 2013 time
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
Cosmological explanation Local Hubble law There is however a simple cosmological solution Evolution in time: standard candles Venice 2013 Global Hubble law
Lambda density Cosmological constant Matter density Venice 2013
Venice 2013
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 matter DE BBN Shall we repeat our mistake and think that there is just a Λ ? Venice 2013
An example of Modified Gravity: DGP (Dvali, Gabadadze, Porrati 2000) brane L = crossover scale: 5 D Minkowski bulk: infinite volume extra dimension gravity leakage • 5 D gravity dominates at low energy/late times/large scales • 4 D gravity recovered at high energy/early times/small scales Venice 2013
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
Two free functions At linear order we can write: § Poisson equation § zero anisotropic stress Venice 2013
Two free functions At linear order we can write: § modified Poisson equation § non-zero anisotropic stress Venice 2013
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
Classifying the unknown 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 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 Te. Ve. S oops. . did I forget your model? Venice 2013
The past ten years of dark energy models Venice 2013
A quintessential scalar field The most general 4 D scalar field theory with second order equation of motion ü First found by Horndeski in 1975 ü rediscovered by Deffayet et al. in 2011 ü no ghosts, no classical instabilities ü it modifies gravity! ü it includes f(R), Brans-Dicke, k-essence, Galileons, etc etc Saõ Paulo 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! Venice 2013
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. , ar. Xiv: 1210. 0439, 2012 Venice 2013
Modified Gravity at the linear level De Felice et al. 2011; L. A. et al. , ar. Xiv: 1210. 0439, 2012 Saõ Paulo 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 Venice 2013
Dark Force Limits on Yukawa coupling are strong but local! Schlamminger et al 2008 Venice 2013
Reconstruction of the metric massive particles respond to Ψ massless particles respond to Φ-Ψ Venice 2013
Galaxy power spectrum Venice 2013
Peculiar velocities r = cz/H 0 . Venice 2013
Weak lensing Dark matter halos Observer Venice 2013 Background sources
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 theory? Venice 2013
Model-independent ratios Redshift distortion/Amplitude Lensing/Redshift distortion rate Expansion rate Venice 2013
Testing the entire Horndeski Lagrangian A unique combination of model independent observables Observables Theory Venice 2013 L. A. et al. 1210. 0439
Horndeski Lagrangian: not too big to fail If this relation is falsified, the Horndeski theory is rejected L. A. et al. 1210. 0439 Venice 2013
Combine lensing and galaxy clustering ! Venice 2013
Euclid in a nutshell Euclid Surveys – Simultaneous (i) visible imaging (ii) NIR photometry (iii) NIR spectroscopy – 15, 000 square degrees ! D E – 100 million redshifts, 2 billion images – Median redshift z = 1 – PSF FWHM ~0. 18’’ – >900 peoples, >10 countries E S E L T C Euclid satellite Venice 2013 ar. Xiv Red Book 1110. 3193
History repeats itself… Sensitivity 1998 2011 Venice 2013 Hu, 1999
Euclid’s challenge C. Di Porto & L. A. 2010 Euclid error forecast Present error Growth of matter fluctuations Venice 2013
Euclid - Primary Science Summary: Euclid’s challenge Goals Issue Our Targets Dark Energy Measure the DE equation of state parameters w 0 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 modifiedgravity 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. 04 e. V 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. IPMU Dark Energy Conference
Venice 2013 Cambridge University Press
Standard rulers θ Rio de Janeiro 2013
Standard rulers Rio de Janeiro 2013
BAO ruler Charles L. Bennett Nature 440, 1126 -1131(27 April 2006) Rio de Janeiro 2013
Deconstructing the galaxy power spectrum Redshift distortion Galaxy clustering Line of sight angle Growth function Galaxy bias Rio de Janeiro 2013 Present mass power spectrum
Three linear observables: A, R, L μ=0 Amplitude A clustering μ=1 Redshift distortion R lensing L Rio de Janeiro 2013
The only model-independent ratios Redshift distortion/Amplitude Lensing/Redshift distortion rate Expansion rate How to combine them to test theory? Rio de Janeiro 2013
Theoretical behaviour Matter conservation equation or Rio de Janeiro 2013
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