Could trapped quintessence account for the laser-detuning-dependent acceleration of cold atoms in varying-frequency time-of-flight experiments?

Using a trapped quintessence model, a series of time-of-flight (TOF) experiments with different frequencies of probe light are designed and performed. The varying-frequency TOF (VFTOF) experiments demonstrate that the free-fall acceleration of test atoms is dependent on the detuning of the probe light frequency with respect to the atomic transition frequency. In appropriately designed experiments, if the scalar field in the model accounts for the accelerated expansion of the Universe entirely, the field will result in an observable fifth force. Meanwhile, the trapped quintessence model still satisfies all experimental bounds on deviations from general relativity due to both the saturation effect and the short interaction range of the scalar field. The scalar saturates at a value corresponding to the cosmological constant when the microscopic nonrelativistic matter density is large enough. The interaction range of the scalar is inversely proportional to the square root of the microscopic nonrelativistic matter density. The interaction range has been estimated to be several mu m in the current cosmic density similar to 10(-27) kg/m(3). The Universe is assumed to be permeated with fuzzy dark matter, which means that the microscopic nonrelativistic matter density defined through the quantum wave functions of the ultralight particles can be used on the cosmic scale. In an almost completely empty space between atoms of a dilute atomic gas in an ultrahigh vacuum chamber, the interaction range of the scalar field may approach the order of similar to 1 mu m in the presence of dark matter; then, the scalar field might be detected in laboratories. Since the trapped quintessence model hypothesizes that the scalar strongly couples to nonrelativistic matter but cannot couple to radiation, the source for generating the fifth force is experimentally set up by the laser-irradiated background atoms in the ultrahigh vacuum chamber. The mass density of the source is altered by detuning the frequency of the probe laser light from the atomic resonance transition. The test atoms are prepared by the laser cooling technique and located initially above the probe light. When the test atoms are released from their initial positions, they are able to pass through the region of the source that generates the fifth force to be measured. Thus, if the scalar field exists, the corresponding fifth force might be sensed by the test atoms even if the interaction range is extremely short. By measuring the free- fall acceleration of the test atoms with the TOF method step by step in the detuning frequency domain of the probe light, we derive the dispersion curves of the measured acceleration versus the frequency detuning of the probe light. When the nonrelativistic matter density of the source increases due to the energy gained from the laser light, the test atoms are pulled to the center of the source, and vice versa. If the trapped quintessence model is correct, the observed detuning-dependent acceleration in the VFTOF scheme suggests a closed Universe, i.e., a positive spatial curvature of the Universe.