| Dark energy is a mysterious energy driving the accelerating expansion of the Universe,and investigating the nature and composition of dark energy is one of the great challenges to modern science.One of the simplest explanations for dark energy is the cosmological constant.Although it is almost consistent with all observations,the difficulties in its theoretical interpretation drive theorists to further explore alternative dark energy models.The two dark energy models of the chameleon and the symmetron with screening mechanisms are the main subjects of this paper.The chameleon model is based on the mass of the scalar field depending on the local background density,and the symmetron model is based on the coupling between the scalar field and matter depending on the local background density.Success in theory requires experimental tests.Due to the strong screening effect of the chameleon and symmetron models in the high-density environment of the Earth,the test of this type of model mainly comes from astronomical observations.In recent years,with the establishment of ultra-high vacuum chambers and the introduction of high-sensitivity measuring instruments,the use of laboratory experiments to detect dark energy has continued to emerge.Although many efforts have been made to test dark energy theories,it is not yet possible to provide a definitive conclusion on the validity of these theories.Therefore,both theoretical research and experimental tests of dark energy are of great scientific significance,which will help promote human research on the evolution of the universe and its accelerating expansion.This paper attempts to solve some dark energy problems by building a bridge between the precise gravity experiment and the dark energy theory.It is mainly based on the data of the torsion pendulum experiment（HUST-2020）of Huazhong University of Science and Technology which tested the inverse square law at submillimeter range to constrain the chameleon and symmetron models.The most important part of the theoretical analysis is the solution of the field profile and the torque.The key experimental components of the HUST-2020 torsion pendulum experiment are all regular flat-plate structures,it is conducive to model the experimental geometry structure as a plate model,which is convenient to solve the field profile between plates.The main framework of this experiment is the test mass,the attraction mass,and the electrostatic shielding foil inserted between them to reduce electrostatic disturbance.Therefore,it can be modeled as a three-plate model.Considering that it is too complex to solve the field profile of the three-plate model directly,we simplify it by first calculating the field profile between the two plates of the test mass and the attraction mass,and then the influence of the electrostatic shielding foil.Based on this idea,the primary research contents and results of this paper are as follows:（1）Calculation of the field profile between two plates.For the chameleon model,we develop an approximate analytical method to solve the chameleon field profile and torque,and the results show that the analytical calculation is in good agreement with the numerical calculation.For the symmetron model,we use the numerical method to calculate the field profile and determine the symmetron torque.（2）Analysis of the effect of the electrostatic shielding foil.We calculate the effect of the electrostatic shielding foil on each of the two models.Especially for the symmetron model,we find that the influence of the electrostatic shielding foil on the symmetron torque difference is an enhancement effect in certain ranges of the mass scale M,which is helpful for designing a torsion pendulum experiment to test the symmetron model in the future.（3）The results of constraining the model parameters.For the chameleon model,we give the constraint of the model parameters with different values of n.Among them,the strongest constraint for the chameleon model in this experiment is n=1,and the strongest constraint ofΛisΛ>8.07×10-4e V,which excludes a wider range of model parameter spaces than the best constrained by the torsion pendulum experiment.For the symmetron model,the results show that the experiment is extremely sensitive to the me V symmetron model.In particular,at the dark energy scaleμ=2.4×10-3e V,the constraint at M=1.3 Te V is improved by about 10 times the previous constraints on the torsion pendulum experiment. |
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