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### The Chameleon A.C.Davis

with P.Brax, C van deBruck,

C.Burrage, J. Khoury, A.Weltman,D.Mota, C.Shelpe,

D. Seery and D.Shaw

PRD70(04)123518,

PRL 99(07)121103;

PRD76(07)085010;

PRD76(07)124034;

0902.2320 +unpublished

Outline

- Introduction to chameleon theories
- Chameleon cosmology
- Photon Coupling and PVLAS
- Predictions + Casimir Force
- Electroweak physics --Implications for LHC
- Possible detection in AGNs + polarised starlight
- Conclusions

Dark Energy?

Like during primordial inflation, scalar fields can trigger the late acceleration of the universe.

An attractive possibility: runaway behaviour.

The mass of the field now is of order of the Hubble rate. Almost massless.

Do Scalars Couple to Matter?

Effective field theories with gravity and scalars

deviation from Newton’s law

The radion

The distance between branes in the Randall-Sundrum model:

where

Deviations from Newton’s law

Far away branes small deviations

close branes

constant coupling constant

Experimental consequences?

Long lived scalar fields which couple with ordinary matter lead to the presence of a new Yukawa interaction:

This new force would have gravitational effects on the motion of planets, the laboratory tests of gravity etc..

The Chameleon Mechanism

When coupled to matter, scalar fields have a matter dependent effective potential:

Chameleon field: field with a matter dependent mass

- A way to reconcile gravity tests and cosmology:
- Nearly massless field on cosmological scales
- Massive field in the atmosphere
- Allow large gravitational coupling constant of order one or more
- Possible non-trivial effects in the solar system (satellite experiments)

Gravity Tests

- Fifth force experiments
- Equivalence principle

The thin-shell property

- The chameleon force produced by a massive body is due only to a thin shell near the surface
- Thin shell
- deviations from Newton’s law
- Thick shell
- deviations from Newton’s law

Khoury & Weltman (2004)

Scalar Optics

- The PVLAS experiment originally claimed to have observed a signal for the birefrigence (ellipticity) and the dichroism (rotation) of a polarised laser beam going through a static magnetic field.
- Effect claimed to be larger than induced by higher order terms in the QED Lagrangian (one loop) or gaseous effects (Cotton-Mouton effect)
- The phenomenon can be interpreted as a result of the mixing between photons and scalars.
- More precisely: a coupling between 2 photons and a scalar can induce two effects:

Rotation: a photon can be transformed in a scalar.

Ellipticity: a photon can be transformed into a scalar and then regenerated as a photon (delay)

PVLAS: Alas!

- New runs looking for experimental artifacts have contradicted the 2000-2005 experimental results.
- No rotation signal observed at 2.3 T and 5.5 T
- No ellipticity signal at 2.3 T and a large positive signal at 5.5 T
- Ellipticity incompatible with a traditional scalar/axion interpretation ( scaling).

PVLAS vs CAST

- Putative PVLAS experimental results could be seen as a result of the coupling:
- Limits on mass of scalar quite stringent:
- No contradiction with CAST experiments on scalar emitted from the sun
- What if ?

CHAMELEON ?

Universality of coupling:

- Large gravitational coupling:
- No contradiction with gravity tests, variation of constants, cosmology, astrophysics bounds….
- No deviation from gravity in satellite experiments…. Small objects have a thin shell.

Chameleon Optics

- Chameleons never leave the cavity (outside mass too large, no tunnelling)
- Chameleons do not reflect simultaneously with photons.
- Chameleons propagate slower in the no-field zone within the cavity

Because the chameleon is reflected rather than escaping and their reflection is decoherent with photons we expect

- ellipticity > rotation

in chameleon theories. This is because, for a large number of passes in the chamber the ellipticity builds up but due to the decoherence the rotation doesn’t. At present we are in agreement with current experiments, but this could be tested soon!

Can fit the new data with various values of n and M:

- We know that these parameters lead to a full compatibility with gravity tests, cosmology, CAST….
- GammeV could see an `afterglow’

Casimir Force Experiments

R. S. Decca et al., PRD 75 (2007)

S. K. Lamoreaux, PRL 78 (1997)

- Measure force between
- Two parallel plates
- Difficult to keep plates parallel
- A plate and a sphere
- Harder to calculate analytically.
- No physical shield is used.
- Electrostatic forces calibrated for by controlling electric potential between plates.

Chameleons & Casimir

- We consider two potentials:
- We find that currently:

New experiments

S. K. Lamoreaux

- Two new experiments currently under construction have real prospect of detecting chameleons.
- Los Alamos experiment
- Sphere and plate
- Could detect chameleon force ifwithout a detailed knowledge of the thermal force.

Chameleons??

Next generation of Casimir force measurement experiments have the precision to detect almost all chameleon dark energy models with

Generally a good model for the thermal Casimir force is required although some models can be detected without it.

Coupling to Electro-Weak Sector

Chameleon can also couple to standard model particles. Would we see corrections in precision tests? Remember, chameleon mass small in expt vacuum pipe.

- Dark energy scalar like Higgs scalar: highly sensitive to high energy physics (UV completion)
- As Higgs mass taken to infinity, should recover divergences of SM without Higgs: quadratic divergences of self-energy. Higgs mass acts as a loose cut-off so in principle (Veltman param):
- Unfortunately it turns out that
- In principle same type of dependence for any scalar field:
- Large corrections O(1)??

Effective Action and Couplings

The coupling involves two unknown coupling functions (gauge invariance):

At one loop the relevant vertices are:

Self-Energy Corrections I

The corrected propagator becomes:

Measurements at low energy and the Z and W poles imply ten independent quantities. Three have to be fixed experimentally. One is not detectable hence six electroweak parameters: STUVWX

Self-Energy Corrections II

The self energy can be easily calculated:

The self energy parameters all involve quadratic divergences

For instance:

The quadratic divergences cancel in the precision tests:

DarkEnergy Screening

Vacuum Polarisation sensitive to the UV region of phase space where the difference between the W and Z masses is negligible

Gauge invariance implies the existence of only two coupling functions with no difference between the W and Z bosons in the massless limit (compared to the UV region)

No difference between the different particle vacuum polarisations, hence no effects on the precision tests.

Experimental Constraints

Stronger bound from optics! M greater than 1 million GeV!

mass

Inverse Coupling

Rainbows, Daisies and Bridges

Higher order corrections all suppressed

ALPs and Dark Energy

- Consider scalars and pseudoscalars coupling to photons through the terms
- Such particles have been proposed as Dark Energy candidates:
- Coupled Quintessence (Amendola 1999)
- Chameleon Dark Energy (Khoury, Weltman 2004, Brax, Davis, van de Bruck 2007 )
- Axionic Dark Energy (Carroll 1998, Kim, Nilles 2003)
- ...

ALPs and Dark Energy

- We consider fields with
- Pseudoscalars: limits from observations of neutrino burst from SN 1987A (Ellis, Olive 1987)
- Scalars: limits from fifth force

experiments

- Chameleons: limits from the structure of starlight polarisation

Photon-ALP Mixing

- Mixing when photons propagate through background magnetic fields
- Probability of mixing
- Mixing with only one photon polarisation state
- Also induces polarisation
- Strong Mixing limit:

(Raffelt, Stodolsky 1987)

Astrophysical Photon-ALP Mixing

- Magnetic fields known to exist in galaxies/galaxy clusters
- These magnetic fields made up of a large number of magnetic domains
- field in each domain of equal strength but randomly oriented
- ALP mixing changes astrophysical observations
- Non-conservation of photon number alters luminosity
- Creation of polarisation

Strong Mixing in Galaxy Clusters

- Galaxy cluster:
- Magnetic field strength
- Magnetic coherence length
- Electron density
- Plasma frequency
- Typical no. domains traversed
- Strong mixing if
- Requires

Effects of Strong Mixing on Luminosity

- After passing through many domains power is, on average, split equally between ALP and two polarisations of the photon
- Average luminosity suppression = 2/3
- Difficult to use this to constrain mixing because knowledge of initial luminosities is poor
- Single source:
- If ; averaged over many paths

(Csáki, Kaloper, Terning 2001)

Active Galactic Nuclei

- Strong correlation between 2 keV X-ray luminosity and optical luminosity (~5eV)
- Use observations of 77 AGN from COMBO-17 and ROSAT surveys (z=0.061-2.54)
- Likelihood ratio
- r14 Assuming initial polarisation
- r>11 Allowing all polarisations
- Is this really a preference for ALPsm? Or just an indication of more structure in the scatter?

(Steffen et al. 2006)

Fingerprints

- 105 bootstrap resamplings (with replacement) of the data - all samples 77 data points
- Compute the central moments of the data
- is the standard deviation
- is the skewness of the data
- …
- Compare this with simulations of the best fit Gaussian and ALPsm models

Conclusions I

- Chameleons automatically explain the observed acceleration of the universe.
- The could be detected by PVLAS experiments, evade the CAST bound and predict ellipticity>rotation.
- Casimir force experiments can test for chameleons.
- The next generation of experiments could detect them or rule them out as dark energy candidates.

Conclusions II

- Their coupling to matter is screened in precision tests of the electroweak physics due to UV sensitivity or vacuum polarisation and gauge invariance.
- Scatter in astrophysical luminosity relations can be used to study the mixing with photons in magnetic fields. Applied to AGN this shows strong evidence for chameleons/ALP strong mixing over Gaussian scatter.

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