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C.Shelpe, D. Seery and D.Shaw PRD70(04)123518, PRL 99(07)121103; PRD76(07)085010; PRD76(07)124034; 0902.2320 +unpublished Outline Introduction to chameleon theories Chameleon cosmology
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with P.Brax, C van deBruck,
C.Burrage, J. Khoury, A.Weltman,D.Mota, C.Shelpe,
D. Seery and D.Shaw
Consider scalar field
potential dominated for
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.
Effective field theories with gravity and scalars
deviation from Newton’s law
The distance between branes in the Randall-Sundrum model:
Deviations from Newton’s law
Far away branes small deviations
constant coupling constant
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..
When coupled to matter, scalar fields have a matter dependent effective potential:
Constant coupling to matter
Khoury & Weltman (2004)
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)
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!
R. S. Decca et al., PRD 75 (2007)
S. K. Lamoreaux, PRL 78 (1997)
S. K. Lamoreaux
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.
Chameleon can also couple to standard model particles. Would we see corrections in precision tests? Remember, chameleon mass small in expt vacuum pipe.
The coupling involves two unknown coupling functions (gauge invariance):
At one loop the relevant vertices are:
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
The self energy can be easily calculated:
The self energy parameters all involve quadratic divergences
The quadratic divergences cancel in the precision tests:
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.
Stronger bound from optics! M greater than 1 million GeV!
Higher order corrections all suppressed
(Raffelt, Stodolsky 1987)
(Csáki, Kaloper, Terning 2001)
(Steffen et al. 2006)