# Laboratory constraints on chameleon dark energy and power-law fields

###### Abstract

We report results from the GammeV Chameleon Afterglow Search—a search for chameleon particles created via photon/chameleon oscillations within a magnetic field. This experiment is sensitive to a wide class of chameleon power-law models and dark energy models not previously explored. These results exclude five orders of magnitude in the coupling of chameleons to photons covering a range of four orders of magnitude in chameleon effective mass and, for individual chameleon models, exclude between 4 and 12 orders of magnitude in chameleon couplings to matter.

###### pacs:

95.36.+x, 95.35.+d, 14.80.Va, 98.80.-kIntroduction: A wealth of observational evidence indicates that the universe is undergoing a phase of accelerated expansion, for which a promising class of explanations is scalar field “dark energy” with negative pressure Caldwell_Dave_Steinhardt_1998 . Such a field is expected to couple to Standard Model particles with gravitational strength and would mediate a new “fifth” force, but fifth forces are excluded by experiments from solar system to submillimeter scales. Three known ways to hide dark energy-mediated fifth forces include: weak or pseudoscalar couplings between dark energy and matter Frieman_Hill_Stebbins_Waga_1995 ; effectively weak couplings locally Dvali_Gabadadze_Porrati_2000 ; and an effectively large field mass locally, as in chameleon theories Khoury_Weltman_2004a ; Khoury_Weltman_2004b ; Brax_etal_2004 .

Chameleons are scalar (or pseudoscalar) fields with a nonlinear potential and a coupling to the local energy density. They evade fifth force constraints by increasing their effective mass in high-density regions of the universe, while remaining light on cosmological scales. Gravity experiments in the lab Adelberger_etal_2009 and in space Khoury_Weltman_2004a ; Khoury_Weltman_2004b can exclude chameleons with gravitational strength matter couplings, but strongly coupled chameleons evade these constraints Mota_Shaw_2006 ; Mota_Shaw_2007 . Casimir force experiments rule out strongly coupled chameleons Brax_etal_2007c , but are ineffective for a large class of potentials commonly used to model dark energy. Collider data exclude extremely strongly coupled chameleons Brax_etal_2009 . In this Letter, we place new constraints on chameleon couplings with a search focused on photon/chameleon interactions.

Photon-coupled chameleons may be detected through laser experiments Chou_etal_2009 or excitations in radio frequency cavities Rybka_etal_2010 . In laser experiments, photons travelling through a vacuum chamber immersed in a magnetic field oscillate into chameleons. They are then trapped through the chameleon mechanism by the dense walls and windows of the chamber since their higher effective mass within those materials creates an impenetrably large potential barrier Chou_etal_2009 ; Ahlers_etal_2008 ; Gies_Mota_Shaw_2008 . After a population of chameleons is produced, the laser is turned off and a photodetector exposed in order to observe the photon afterglow as trapped chameleons oscillate back to photons. The original GammeV experiment included a search for this afterglow and set limits on photon/chameleon couplings below collider constraints for a limited set of dark energy models Chou_etal_2009 . The experiment presented here, the GammeV Chameleon Afterglow Search (CHASE), bridges the gap between GammeV and collider constraints, improves sensitivity to both matter and photon couplings to chameleons, and probes a broad class of chameleon models.

Chameleon Models: We consider actions of the form

(1) | |||||

where the reduced Planck mass GeV, the Lagrangian for matter fields , and and are dimensionless chameleon couplings to photons and matter respectively (often expressed as and ). We assume universal matter couplings.

The dynamics of the scalar field are governed by an effective potential that depends on a scalar field potential , the background density of nonrelativistic matter, and the electromagnetic field Lagrangian density (for pseudoscalars ):

(2) |

A simple, well-studied class of chameleon models has a potential of the form Brax_etal_2004

(3) |

where is a real number and eV is the mass scale of the dark energy density and is a dimensionless constant. While the constant term in this potential causes cosmic acceleration that is indistinguishable from a cosmological constant when using standard techniques of cosmological surveys, the local dynamics from the power-law term can be probed in laboratory experiments.

Following the derivations in Raffelt_Stodolsky_1988 ; Upadhye_Steffen_Weltman_2010 the conversion probability between photons and chameleons is

(4) |

Here, is the particle energy, is the effective chameleon mass in the background fields, is the distance travelled through the magnetic field, and is the particle direction.

When a superposed photon/chameleon wavefunction strikes an opaque surface of the vacuum chamber, there is a model-dependent phase shift between the two components and a reduction in photon amplitude due to absorption. A glass window, however, performs a quantum measurement—photons are transmitted while chameleons reflect. Surface roughness and small misalignments of the windows cause the velocities of trapped chameleons to become isotropic. The decay rate of a chameleon to a photon , is found by averaging over initial directions and positions. The observable afterglow rate per chameleon is found by averaging over only trajectories that allow a photon to reach the detector. Once the experimental geometry is specified, these rates can be computed numerically Upadhye_Steffen_Weltman_2010 .

A single parameter is useful to describe the chameleon effect and to determine whether a particle will be trapped inside the chamber. If the chameleon mass in the chamber is dominated by the matter coupling, then where Upadhye_Steffen_Weltman_2010 . The largest value of with integer is for ; theory (), has . Here, we do not consider since their potentials are either unbounded from below or do not exhibit the chameleon effect.

Apparatus: The design of the CHASE apparatus is shown in Fig. 1. In addition to the windows at the ends of the vacuum chamber, we centered two 2.5 cm diameter BK7 glass windows in the 6.3 cm diameter cold bore of a Tevatron dipole magnet. These windows divide the magnetic field into three partitions of lengths 1.0 m, 0.3 m, and 4.7 m. The shorter partition lengths provide sensitivity to larger-mass chameleons and were chosen to minimize the number of regions of mass insensitivity that occur when the partition lengths are simultaneous multiples of the photon/chameleon oscillation length (see Eq. 4).

For a fixed magnetic field there are limits to the smallest and largest detectable —small produce small afterglow signals while with large the chameleon population will decay before the detector can be exposed. For CHASE, we implement an automated transition between filling the cavity and observing an afterglow. This requires turning off the laser, closing the laser-side gate valve, removing the mirror that deflects the laser into the power meter, and opening the PMT-side gate valve. Our sensitivity to large is further improved by operating at a variety of lower magnetic fields, which lengthen the decay time of the chameleon population and provide overlapping regions of sensitivity. A mechanical shutter (chopper) modulates any afterglow signal allowing real-time measurement of the PMT dark rate and improving sensitivity to low afterglow rates (small ).

To maximize our sensitivity to different chameleon models, the CHASE vacuum system uses ion pumps and cryogenic pumping on the cold ( K) bore of the magnet. This design leaves no port through which chameleons can be exhausted to the room and allows CHASE to probe as low as . This sensitivity is primarily due: 1) to the large matter density ratio between the walls of the vacuum chamber and its interior and 2) the large masses probed by the shortest partition of the magnetic field.

Data: We collected data in 14 configurations—seven vertically-oriented, dipole magnetic field values (0.050, 0.090, 0.20, 0.45, 1.0, 2.2, and 5.0 Telsa) and both vertical and horizontal polarizations of the electric field of the laser photons. The magnetic field was determined from field vs. current calibrations that are precise to better than 1%. We repeated measurements at 5.0T for a total of 16 science “runs”.

A 5.1cm diameter lens focuses the photons coming from the apparatus onto the photocathode of our Hamamatsu H7422P-40 PMT. The factory measured quantum efficiency of the PMT is 0.45 with a typical collection efficiency of 0.70. The threshold on the PMT descriminator is set to record 97% of the single photoelectrons while rejecting noise. We estimate our optical transport efficiency through the lens, the PMT-side vacuum window, and the windows in the magnet bore to be 0.96 by assigning an equal loss of 0.99 (based upon factory specifications) to each of the four elements. Thus, our photon detection efficiency is . Since a chameleon afterglow signal requires two factors of Eq. (4)—one to produce a chameleon and another to regenerate a photon—our sensitivity to scales only as the fourth root of , and a modest uncertainty (estimated to be smaller than 20%) has only a effect on .

A single science run consists of shining a frequency-doubled Continuum Surelite I-20 Nd:YAG laser with 20 Hz of 5 ns pulses through the cavity for ten minutes, then exposing the PMT to the apparatus for 14 minutes while cycling the shutter open and closed in second intervals each. At the highest magnetic field the filling and observation stages are extended to 5 hours and 45 minutes respectively to improve our sensitivity to low . The average input laser power is 3.5 Watts with Watt fluctuations (which also have negligible effect on our sensitivity). Before and after each science run, there is a 15 minute calibration run which we use to measure three quantities: the excess photon rate coming from the apparatus (due in part to discharge from the ion pumps), random fluctuations of that excess, and its run-to-run variation. Our data acquisition system saturates at approximately 300 Hz while the typical counting rate with the shutter-closed is Hz. We see an excess rate of Hz with the shutter open. The shutter-open data has Hz of variation beyond Poisson fluctuations of 1.34 Hz. At most Hz of this variation could be attributed to run-to-run changes in the mean offset.

Vacuum pressure measurements are taken before and after the observation stage using two ion gauges (one at either end of the magnet). We turn these gauges off during observation since, when on, we observe hundreds of photons per second from them. Frequent measurements of the residual gases show 87% H, 4% HO, and N and CO (28 amu) combine for 9%. Using the factory calibration of the gauges for the various gas species, we find that our vacuum pressure was always better than torr at 3.5K (a density of g/cm compared with g/cm for the glass windows).

Following the operation of the laser, we observe a decaying rate of photons dubbed “orange glow”. While its cause is unknown, its properties distinguish it from a scalar or pseudoscalar chameleon signal. First, the orange glow is isolated to the red and orange parts, rather than the expected 532nm green, of the electromagnetic spectrum (found using a series of 40nm-wide filters placed in front of the PMT). Second, it is independent of both the strength of the magnetic field and the laser polarization. Finally, the amplitude of the orange glow depends upon the temperature of the magnet bore. Virtually disappearing at room temperature, it increases until reaching several hundred Hz in amplitude at temperatures near 4 K.

A series of independent “orange glow runs” similar to the nominal science run show that the temporal shape of the orange glow is reproducible and, following a steep drop of a few tens of seconds, is well fit by an exponential with an initial amplitude and decay time of Hz and sec respectively.^{1}^{1}1While we suspect that the orange glow is of conventional origin, such as impurities in the glass windows or on the vacuum chamber surfaces, exotic physics such as kinetic mixing with a spin-1 chameleon Nelson_Walsh_2008 or chameleon induced atomic transitions Brax_Burrage_2010 have not been excluded. We eliminate the fast decaying components of the orange glow by ignoring the initial seconds of data from each science run. This cut limits our sensitivity to large photon couplings in each run to (data at lower magnetic fields compensates for this limitation).

Analysis: For the CHASE geometry, the rates and are computed in Upadhye_Steffen_Weltman_2010 . We extend those calculations to greater using a Monte Carlo simulation. We account for the absorption of photon amplitude and the differences in the induced phase shift between the and polarizations at each reflection from the stainless steel surfaces. We measured the amplitude reflectivity of the magnet bore material (averaged over all incident angles) to be by placing samples into an integrating sphere illuminated with 532nm laser light. Given these rates, the population of chameleons in the vacuum chamber is found by integrating

(5) |

where is the rate that laser photons stream through the chamber. Afterglow photons emerge and hit the PMT at a rate .

For a given , each chameleon model—specified by its mass in the vacuum chamber, its photon coupling , and the chameleon potential —has a characteristic afterglow signal. We compute this signal as a function of the magnetic field and the chameleon model parameters. From the raw data binned to the sec shutter cycle (e.g., Fig. 2) we subtract the 1.15 Hz excess rate from the ion pumps and the mean dark rate measured with the shutter-closed data for that run. Statistical fluctuations including the observed excess are included in the uncertainty of each datum. Data for all science runs with a given laser polarization and all orange glow runs (which have ) are simultaneously analyzed using the Profile Likelihood method rolk2005 . As nuisance parameters we include a common, exponentially decaying signal, which eliminates the long-decay tail of the orange glow, and each run is allowed an independent constant offset constrained by the possible 0.40 Hz run-to-run variations in the ion pump glow. We compare the for the chameleon model with that for the model where no chameleon is present. Any chameleon model whose is greater by is excluded to confidence.

Results: Analysis of our data shows no evidence for a photon-coupled chameleon. Figure 3 shows all of the residuals in the science data for the no chameleon model. The mean and RMS of these residuals are and Hz for pseudoscalar couplings ( with 471 degrees of freedom (DOF)) and and Hz for scalar couplings ( with 472 DOF). Fig. 4 shows parameters excluded to confidence for scalars and pseudoscalars assuming dependence on to be negligible and . These constraints reach four significant milestones. First, they bridge the nearly three order of magnitude gap between bounds on from GammeV and from colliders Brax_etal_2009 . Second, they exclude a range of spanning four orders of magnitude at masses around the dark energy scale ( eV). Third, they rule out photon couplings roughly an order of magnitude below previous limits in this mass range where for scalar and for pseudoscalar chameleons. Finally, they are sensitive to chameleon dark energy models and chameleon power-law models where , including .

Figure 5 shows CHASE constraints (at 95%) for select potentials given by Eq. (3). These limits truncate at low by the requirement that chameleons reflect from the chamber walls, at high by destructive interference at large (see Fig. 4), and at low by undetectably small signals. Not surprisingly, theories with the largest are excluded over the greatest range of . These constraints complement those from torsion pendula, which probe , and are consistent with constraints from Casimir force measurements for Brax_etal_2007c . CHASE data exclude chameleons spanning five orders of magnitude in photon coupling and over 12 orders of magnitude in matter coupling for individual models. They probe a wide range of chameleon models, and give significantly improved constraints for cosmologially interesting chameleon dark energy models.

## Acknowledgements:

We thank the staff of the Fermilab Technical Division Test and Instrumentation Department, the Fermilab Particle Physics Division mechanical design and electrical engineering groups, and the vacuum experts of the Fermilab Accelerator Division. This work is supported by the U.S. Department of Energy under contract No. DE-AC02-07CH11359 as well as by the Kavli Institute for Cosmological Physics under NSF contract PHY-0114422.

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