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

Cosmological constant? New scalar field? Modification of gravity?

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)

“Chameleon” particles

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

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

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

The Chameleon

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)

Massive Scalar Field

The Chameleon

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)

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

The Galileon

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)

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

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)

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

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)

Hunting for dark energy

Fifth Force and Parallel Plate Experiments

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

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)

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

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

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)

Coupling to Photons

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

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  

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

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

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)

Electroweak Precision Observables

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

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

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

Corrections to Electroweak Processes

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

Atomic Precision Measurements

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

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

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

Conclusions

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

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?

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

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

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

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

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 1992. Maksymyk, Burgess, London 1994)

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

Higgs Production

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

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

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

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