a viable candidate for dark energy?

1. Luca Amendola INAF/Osservatorio Astronomico di Roma a viable candidate for dark energy? Is higher-order gravity • Collaboration: D. Polarski, S. Tsujikawa, R. Gannouji, C. Charmousis, S. Davis, E. Magliaro • Firenze GGI 2006

2. Observations are converging… …to an unexpected universe

3. What do we know about cosmicexpansion ? Nucleosynthesis (z~109) CMB (z~1000) Standard candles (z~1) Perturbations (z~0-1000)

4. Four hypotheses on dark energy A) Lambda & friends B) scalar field C) modified gravity D) non-linear effect

5. Two classes of models A) Lambda & friends B) scalar field C) modified gravity D) non-linear effect 1) Models which are almost impossible to rule out 2) Models which are easy to rule out

6. Lambda & friends A) Lambda & friends B) scalar field C) modified gravity D) non-linear effect

7. Scalar field A) Lambda & friends B) scalar field C) modified gravity D) non-linear effect

8. An ultra-light scalar field • It is more general • Scalars are predicted by fundamental theories Observational requirements: Slow evolution Light mass V()  Compton wavelength = Hubble length

9. The coupling • But beside the potential there can be also a coupling…

10. Dark energy as scalar gravity T(m)= CT(m) T= -CT(m) coupled conservation laws : First basic property: C2/G = scalar-to-tensor ratio

11. Dark energyasscalar gravity Jordan frame Einstein frame

12. An extra gravity Newtonian limit: the scalar interaction generates an attractive extra-gravity in real space Yukawa term

13. How about local gravity constraints ? α λ

14. The fourfold way out NO DE uninteresting Chameleon models Coupled DE.... Make mφvery large Make βvery small Make them density dependent Make them species dependent

15. A species-dependent interaction T(cdm)= CT(cdm) T= -CT(cdm) T(bar)= 0 T(rad)= 0

16. Two qualitatively different cases:weak coupling strong coupling 

17. Weak coupling: density trends today No coupling mat rad = 0 a ~ tp p = 2/3 MDE: field coupling rad mat = /9 a ~ tp p = 6/(42+9) MDE: field MDE kinetic phase, indep. of potential!

18. Deceleration and acceleration Assume V(f) = f-a today mat rad Dominated by potential energy α Dominated by kinetic energy β field The equation of state w=p/r depends on bduring fMDE and on aduring tracking: we = 4b2/9: past value (decelerated) wf = -2/(a+2): present value (accelerated)

19. cl) WMAP and thecoupling  Planck:  Scalar force 100 times weaker than gravity

20. Modified 3D gravity A) Lambda & friends B) scalar field C) modified gravity D) non-linear effect Higher order gravity ! Simplest case: Capozziello,Turner, Carroll, Odintsov… L.A., S. Capozziello, F. Occhionero, 1992

21. Modified N-dim gravity Simplest case:

22. Faces of the same physics Extra-dim. degrees of freedom Higher order gravity Coupled scalar field Scalar-tensor gravity

23. The simplest higher-order gravity is in fact a scalar-tensor model in the Jordan frame and a coupled dark energy model in the Einstein Frame

24. General higher order gravity In Einstein Frame Coupled dark energy with a strong coupling !

25. Is this already ruled out by local gravity? is a scalar-tensor theory with Brans-Dicke parameter ω=0 or β=1/2 Therefore if and f(R) is not yet ruled out see eg. Nojiri & Odintsov 2003; Brookfield et al. 2006

26. The simplest case In Einstein Frame

27. R+1/R model:the φMDE today mat rad field rad mat field MDE Jordan F: Caution: Plots in the Einstein frame!

28. R+1/R model:the φMDE More exactly today mat rad During this phase, field rad mat and therefore field MDE Caution: Plots in the Einstein frame!

29. R+Rn model L.A., S. Tsujikawa, D. Polarski 2006

30. Distance to last scattering in R+Rn model

31. A view from the Jordan Frame Plots by R. Gannouji, U. of Montpellier

32. How far can we extend this? An autonomous dynamical system

33. Analytical results: critical points For all f(R) theories: The wrong matter era (the t1/2 behavior) exists always The good matter era (the t2/3 behavior)exists only if m(-1)=0 This immediately rules out many cases:

34. Gallery of Failed Cosmologies Plots by R. Gannouji, U. of Montpellier

35. Numerical results a) Dark energy domination is always preceded by the wrong matter era (if any), except... b) …when the acceleration is driven by a Lambda term as in

36. General f(R, Ricci, Riemann) we find that an exact matter era exists only for very special combination of parameters so probably most of these models are ruled out.

37. Back to second order gravity Is this the most general second-order scalar-tensor theory ? No! This is a Coupled Gauss Bonnet model. Can we put constraints on it without specifying the potential/couplings? Yes, if the scalar field is a DE field

38. Coupled Gauss-Bonnet Everything depends on Observable deviations from linearized Newtonian gravity

39. Coupled Gauss-Bonnet Observable deviations from linearized Newtonian gravity in the slow-rolling and small-coupling limit

40. Observing a Gauss-Bonnet term Direct observables Growth of matter fluctuations ISW effect L.A., C. Charmousis,S. Davis, astro-ph/0506306

41. Searching for a perfect dark energy model Quanto a figure perfette o nobili, credo che per murare le quadre sieno più perfette che le sferiche, ma per ruzzolare o condurre i carri stimo più perfette le tonde che le triangolari. (Il Saggiatore, 1623) As to the perfection or nobility of geometric figures, I think that for works in masonry square figures are more perfect than spherical ones, but to roll or drive a carriage I consider the circular figures more perfect than the triangular ones. (Il Saggiatore, 1623)

42. An ultra-light scalar field Hubble size Galactic size Adopting a PGB potential Abundance Mass L.A. & R. Barbieri 2005