Using a trapped quintessence model, a series of time-of-flight (TOF) experiments with a different frequency of probe light were designed and performed. The varying-frequency TOF (VFTOF) experiments demonstrated that the 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 µm in the current cosmic density ∼ 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 wavefunctions 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 to the order of ∼ 1 µm in the presence of dark matter and 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 was experimentally set up by the laser-irradiated background atoms in the ultrahigh vacuum chamber. The mass density of the source was altered by detuning the frequency of the probe laser light from the atomic resonance transition. The test atoms were prepared by the laser cooling technique and located initially above the probe light. When the test atoms were released from their initial positions, they were able to pass through the region of the source that generated the fifth force to be measured. Thus, if the scalar field existed, the corresponding fifth force might be sensed by the test atoms even if the interaction range was extremely short. By measuring the fall acceleration of the test atoms with the TOF method step-by-step in the detuning frequency domain of the probe light, we derived the dispersion curves of the measured acceleration versus the frequency detuning of the probe light. When the nonrelativistic matter density of the source increased due to the energy gained from the laser light, the test atoms were 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...

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The measured values for the cosmic expansion rate, the cosmic radius, the cosmic age, etc. vary with a direct or an indirect methodology. These discrepancies known as the cosmological crisis imply the existence of a new physical field. The coupling of matter to the field causes the ratio between a being measured mass of matter and a reference mass to vary with the field. Any experiment can only measure the relative ratio rather than the absolute mass of matter. Apparently, there are two representations in describing the field dependence of the ratio: the reference (being measured) mass varies with the field while the being measured (reference) mass does not. Therefore, the measured value of every quantity depends on the choice of the representations. A representation is selected based on the conscious or unconscious assumptions in an experiment. This new field can resolve the discrepancies as well as drive the late-time cosmic acceleration. The new closed cosmic model here can remove the tensions in the standard cold dark matter model with Λ being the cosmological constant.