1. Dark Energy Hunting Clare Burrage University of Nottingham
with Philippe Brax, Anne-Christine Davis, David Seery, Douglas Shaw, Amanda Weltman

2. Cosmological constant? New scalar field?
Modification of gravity?

3. Dark Energy
The acceleration of the expansion of the universe is explained by a (slowly rolling) scalar field
Mass
Interaction range
New light scalar fields mediate long range fifth forces
(Mota, Shaw 2007)

4. “Chameleon” particles

5. Outline Screening Mechanisms Hunting for Dark Energy The Chameleon
The Symmetron
The Galileon
Hunting for Dark Energy
Parallel Plate Experiments
Astrophysical Observations
Particle Colliders
Atomic Precision Measurements

6. Scalar Forces
We will be interested in scalar fields that couple to the trace of the energy-momentum tensor of matter
The fifth force mediated by this scalar field is given by

7. Canonical Scalar Field
For a canonical, linearly coupled scalar field
Inside a region of constant density
Outside a spherical object

8. The Chameleon

9. The Chameleon
The chameleon is a scalar field with non minimal couplings to matter
This gives rise to an effective potential
Need self-interaction terms in the potential
The mass of the field depends on the local density
(Khoury, Weltman 2004)

10. Massive Scalar Field

11. The Chameleon

12. The Chameleon
The scalar force is suppressed when the scalar potential well is shallower than the gravitational one
The force is only surpressed when the object is big enough
(Khoury, Weltman 2004)

13. The Symmetron Potential Coupling to matter Force:
Low Density High Density
Force:
(Hinterbichler, Khoury 2010)

14. The Galileon

15. The Galileon Model Galileon model
Respects the symmetry
Equations of motion are second order in derivatives
In four dimensions only five possible operators
Galileon action
(Nicolis, Rattazzi, Trincherini. 2008)

16. The Galileon Model Finite set of operators allowed
(Nicolis, Rattazzi, Trincherini. 2008)

17. The Vainshtein Effect
Spherically symmetric, static equations of motion, near an object of mass M
Force can be made substantially weaker than gravity if non-linearities become important
Writing
The equation of motion becomes
(Nicolis, Rattazzi, Trincherini. 2008)

18. The Vainshtein Effect
The scalar force is suppressed within a screening radius
All gravitational tests must be done inside this radius

19. Screening Mechanisims: Summary
Non-linear terms dominate in regions of high density
This changes
The mass (chameleon)
The coupling strength (symmetron)
The kinetic terms (Galileon)
Chameleon arises in f(R) gravity
Galileon shown to arise from
DGP
Probe brane world scenarios
Massive gravity
(Navarro, Van Acoleyen. 2006)
(de Rham, Gabadadze. 2008)
(de Rham, Tolley. 2010)
(Dvali, Gabadadze, Porrati. 2000)

20. Hunting for dark energy

21. Fifth Force and Parallel Plate Experiments

22. Eöt-Wash Looks for deviations from Newtonian gravitational potential
Area of overlap changes as the plates are rotated
Null experiment: No force if only Newtonian gravity present

23. Eöt-Wash: The Chameleon
Only weak constraints on the chameleon
Force due to thin shell object only weakly depends on coupling strength
(Mota, Shaw. 2007)

24. Eöt-Wash: The Galileon
Have to expand around the background due to the Earth
No Vainshtein mechanism in a 1D system
Bounds on torque from beyond standard model physics constrains
In the simplest case

25. Other Fifth Force tests of the Galileon
Lunar Laser Ranging
Bounds on the precession of the perihelion of the moon
In massive gravity

26. Casimir Experiments
Casimir force arises between two uncharged plates in a vacuum due to the quantisation of the electromagnetic field
Constrains form of chameleon potential, but not coupling
Current experimental set-ups not suitable to look for Galileons
(Brax, van de Bruck, Davis, Mota Shaw. 2007)

27. Coupling to Photons

28. Scalar Fields Couple to Gauge Bosons
Conformally coupled scalar fields
No coupling to kinetic terms of gauge bosons at tree level
The Standard Model is not conformally invariant
The conformal anomaly means that a coupling to photons will always be generated

29. Bounds on the Coupling to Photons
The interaction
Leads to mixing in magnetic fields
A photon travelling through a magnetic field can convert into dark energy (Raffelt & Stodolsky 1988)
Photon number is not conserved
Polarization of light is changed B  

30. Mixing in Magnetic fields
So far no detection of scalar fields mixing with photons
Best constraints come from observations where the photons have travelled a long way through vacuum
Can use magnetic fields of Galaxies and Galaxy clusters
Approximate these as made up of uniform domains

31. Starlight Polarization
Look for correlations in the noise in low frequency measurements
Best constraints from WUPPE Milky Way starlight polarization observations (Anderson 1996)

32. Luminosity of Active Galactic Nuclei
When the mixing is strong, on average 1/3 of photons are converted to scalars
The probability distribution is highly skewed
Observed correlations between X-ray and optical luminosities of AGN can be used to constrain this effect
2009: possible signal in COMBO-17, ROSAT observations (CB, Davis, Shaw 2009)
2010: Analysis of new data set from Sloan/Xmm-Newton shows no effect (Pettinari, Crittenden 2010)

33. Electroweak Precision Observables

34. Scalar fields at Colliders
All fermions and bosons entitled to radiate into scalar fields
May introduce large corrections to currently observable interactions
Focus on Electroweak sector
Also a correction to QCD processes, but calculations more difficult

35. Scalar fields at Colliders
Effective Lagrangian
Contributes
New processes - scalar in final state
Corrections to SM processes - scalar only in intermediate state

36. Scalar Bremsstrahlung
Contribution to the width of Z decay
Decay rate:
Width of the Z
Prediction from the standard model
Known from observation
Dark Energy correction negligible if

37. Corrections to Electroweak Processes

38. Electroweak precision observables
Constraints on scalar couplings from EW precision observables at LEP
Measurements of
Coupling constants
Boson masses
Mixing angles
Decay rates
Cross sections
Combine to constrain oblique corrections to the EW sector

39. Atomic Precision Measurements

40. Atomic precision measurements
Perturations of the scalar fields are sourced by
Nuclear electric field
Density of the atomic nucleus
Fermion masses are scalar field dependent
Leads to a perturbed Schrodinger equation

41. Atomic precision measurements
Perturbs atomic energy levels
1 sigma uncertainty on the 1s to 2s transition in hydrogen of order
Constrains:

42. Atomic precision measurements
Lamb shift is the splitting between the 2s and 2p energy levels due to QED effects
The electronic Lamb Shift bounds
Current bounds mean that a new scalar field cannot explain the anomalous Lamb shift of muonic hydrogen E 2p 2s 1s 1 2
QED
QED + Dark Energy

43. Conclusions

44. Dark Energy Hunting
If the acceleration expansion of the universe is caused by a scalar field it must couple to matter
For linear theories gravitational strength couplings are excluded by fifth force experiments
Therefore theories must be non-linear
Non-linear theories could be detected in vacuum
Casimir experiments
Astrophysical observations
Particle colliders
Atomic precision measurements

45. Future Prospects Corrections to precision measurements of muonium?
Dark energy production in stars?
Corrections to Higgs physics?
What role does dark energy play in the early universe?
Is there a general formulation for scalar fields with screening mechanisms?

47. Scalar Fields Couple to Gauge Bosons
Start with a coupling only to fermions
Conformal rescaling of the metric
Canonically normalised spinors are related by
This makes the measure of the path integral scalar field dependent
The Jacobian is not invariant under rescaling

48. Scalar Fields Couple to Gauge Bosons
Computing the Jacobian
Leading to a term in the Lagrangian
Quantisation and conformal rescaling do not commute!

49. The Vainshtein Effect
A perturbation around the spherically symmetric background
Within the Vainshtein radius renormalisations from the background alter coefficient of the kinetic term eg
Canonically normalising
The coupling strength is suppressed

50. Corrections to Electroweak Processes
Leading order scalar effects occur as oblique corrections

51. Electroweak precision observables
Six parameters to describe oblique corrections
S measures the difference between wavefunction renormalisation of Z and photon
T measures additional isospin breaking at zero momentum (difference between charged and neutral current interactions)
U measures difference between W and Z wavefunction renormalisations
V measures the difference between Z wavefunction renormalisation on shell and at zero momentum
W measures the difference between W wavefunction renormalisation on shell and at zero momentum
X measures additional mixing between Z and photon (not present for conformally coupled scalars)
(Peskin, Takeuchi Maksymyk, Burgess, London 1994)

52. Electroweak precision observables
The vacuum polarization for each boson is
These are sensitive to the cut off scale
Leads to Log divergences in S,T,U,V,W

53. Higgs Production

54. Higgs Production
Can the scalar give large corrections to Higgs production cross sections?
Focus on production mechanisms with gauge bosons

55. Higgs Production Enhancement of Higgs production rate
New oblique parameter
Higgs vacuum polarisation

56. Higgs Production Oblique parameter
Leads to corrections to Higgs production
Gluon-gluon fusion corrections possibly enhanced (work in progress)

57. Scalar Fields Couple to Gauge Bosons
Conformally coupled scalar fields
No coupling to kinetic terms of gauge bosons at tree level
If there are additional heavy, charged fermions in the theory
In the low energy theory this looks like a contact interaction between gauge bosons and dark energy