On modifying gravity as an alternative to dark matter

1. On modifying gravity as an alternative to dark matter Pedro G. Ferreira University of Oxford

2. Collaborators: C. Boehm (Annecy) C. Bonvin (Geneve) D. Mota (Heidelberg) C. Skordis (Perimeter Institute) G. Starkman (Case Western Reserve) T. Zlosnik (Oxford) C. Zunckel (Oxford) J. Zuntz (Oxford)

3. Roadmap • The problem with gravity. • Preaching to the converted: Dark Matter. • An alternative approach: Modified Gravity. • How to build a theory. • Isn’t this dark matter? • Dark Matter versus Modified Gravity • Conclusions.

4. NGC 3198 Keplerian

5. Galaxy Clusters Luminous potential energy ≠ Luminous kinetic energy

6. A Brief History of the Universe Density contrast in baryons: Gravitational collapse Silk Damping Acoustic waves

8. Dark Matter If then: and: potential energy of dark matter = kinetic energy of luminous matter and: sourced by dark matter through recombination

10. Simple and “predictive” • Cross sections of order the weak scale, masses between Gev and Tev. LHC !

11. The Bullet Cluster Displaced potential wells Clowe et al, 2006

12. Another “Bullet” Cluster

13. Is there an alternative? Milgrom, 83 Newton OK Constant

14. All with the same Sanders et al

15. Fixed offset of Tully-Fisher

16. A modified theory of gravity Rewrite as: Need a relativistic theory to make it truly predictive

17. Newtonian Gravity Einstein-Hilbert Geodesic Spacetime metric

18. Simplest approach: modify the Einstein-Hilbert action • Sakharov (1967)- quantum corrections of the Einstein-Hilbert action; low energy string theory • Higher derivatives of the metric. • Need it to change at low curvature • New degrees of freedom (frozen modes become dynamical)- new fields.

19. Keep Einstein Hilbert action Geodesic Gravity Common metric

20. Keep Einstein Hilbert action Geodesic Gravity Different metrics

21. “Bimetric” theories Use two different metrics “Physical” in Geodesic equations “Geometric” metric in Einstein equations Dirac, Jordan, Brans, Dicke Again! New degrees of freedom (new fields)

22. “Bimetric” theories Use two different metrics “Physical” in Geodesic equations “Geometric” metric in Einstein equations Bekenstein, 04 Time-like (“aether”) Again! New degrees of freedom (new fields)

23. Einstein-Hilbert, one metric and Aether field Extra degrees of freedom (the Aether) Zlosnik et al

24. How do we modify gravity? Take non-relativistic, weak field limit: Extra d.o.f. Modified gravity

25. Extra degrees of freedom … Is modified gravity simply a more contrived form of Dark Matter?

26. Cosmology of Bekenstein’s theory Skordis et al, 2006 BBN: Not Dark Matter

27. Perturbations: definitions Metric Scalar Field Extra d.o.f Vector Field

28. Perturbations New Source terms

29. Growth of sustains growth of structure

30. Important: There are models of modified gravity that can solve the dark matter problem on all scales without a substantial new contribution to the overall energy density.

31. All candidate theories violate Birkhoff’s Theorem Non- Newtonian Gravity Newtonian Gravity Starkman et al Local field is dependent on the global environment

32. Perturbations in extra degrees of freedom + Violations of Birkhoff’s theorem Local tests are complex Bekenstein’s theory-NO (Mavromatos et al) e.g. Bullet Cluster Einstein-Aether- YES (Dai et al)

33. “Antibullet” Cluster Abell 520 Peak of potential with no galaxies Mahdavi 2007

34. How can we test these theories? And how generic are these tests?

35. The Cosmic Microwave Background 3rd Peak is sensitive do dark matter

36. Remember: extra degrees of freedom drive gravity Pushes up peaks but … Boosts large scales as well

37. Distance to surface of last scatter The position of the peak Size of sound horizon at last scatter Position of CMB peak

38. Position of CMB peak is very well constrained: Need to fit peaks … … not generically true (Ferreira et al)

39. Is there a smoking gun for modified gravity ? Analogy with PPN approach: : deviations from Einstein Solar System Galaxies Clusters

40. on cosmological scales TeVeS Cross correlate ISW and galaxies Liguori et al And changes the growth of structure

41. What probes can we use? Galaxy Surveys Integrated Sachs-Wolfe in the CMB Weak lensing

42. Increase effect of modified gravity Cross correlate ISW and galaxies Caldwell et al

43. Zhang et al Cross correlate weak lensing and galaxies

44. ISW constraints from WMAP Analogous to the PPN parameterss Hu, 2008

45. Conclusions: • Does Einstein/Newton gravity break down in regions of very weak field? • Is there a consistent theory for this deviation from standard gravity? • How can we test it, i.e. how can we distinguish it from dark matter models?

46. There are now a range of relativistic theories: • All have some problems • All have extra degrees of freedom (just like dark matter) • Tests should be chosen wisely to disentangle extra degrees of freedom, modified gravity and non-”Birkoffianess”

47. More generally, searches for deviations in the PPN-like parameter, on cosmological scales. • A real opportunity with future surveys: satellites (Euclid, JDEM), groundbased (SKA, LSST, …).