Constraining the chameleon model with the HUST-2020 torsion pendulum experiment

The chameleon model was proposed as a promising candidate for the dark energy screening mechanism. It is not straightforward to detect the fifth force mediated by the chameleon scalar field in a high-density environment, such as those in a ground-based laboratory. Nevertheless, short-range gravitational experiments such as the torsion pendulum experiment can provide strong constraints on the chameleon model. In this work, we constrain the chameleon model from a precise test of the inverse-square law at Huazhong University of Science and Technology. In particular, we take full advantage of the regular flat-plate structure of the test and attraction mass, which gives rise to accurate modeling for the chameleon force and torque. The derived analytical results on the chameleon torque are shown to agree well with those by numerical calculations. Subsequently, based on the experimental data, the parameter space of the chameleon model is analyzed, and the results are presented in terms of a more stringent constraint on the model parameters.

Figure 1

The diagram of the HUST-2020 torsion pendulum experiment [46]. The blue and yellow structures are tungsten plates, while the yellow ones represent the compensation mass. The white ones are glass plates, and the light orange one is shielding foil.

Figure 2

Sketch of the chameleon field distribution in the HUST-2020 experiment. (a) The densities of the test mass (tungsten) and attraction mass (glass) are different, and (b) the densities of the test mass (tungsten) and attraction mass (tungsten) are the same.

Figure 3

Upper panel: numerical and approximately analytical calculation results of chameleon torque. Here, we take the coupling constant $\beta =1$ and the experimental resolution of the torque is ${\tau }_{mea}=2.0\times {10}^{-17}\mathrm{N}·\mathrm{m}$. Lower panel: relative difference.

Figure 4

Sketch of the three-plate structure. The left plate is the test mass, the right plate is the attraction mass, and the intermediate thin plate is the shielding foil. The solid blue line is the field profile with some chameleon parameters.

Figure 5

Shielding foil suppression factor $f_{\sup }$ of the chameleon force. The red points represent the result of the numerical computation, and the blue solid line is the fitting curve.

Figure 6

The constraints on the chameleon model with the HUST-2020 experimental data. (a)–(c) represent the parameter constraints on the chameleon model with inverse power-law potential $V(\varphi )={\mathrm{\Lambda }}_0^4+{\mathrm{\Lambda }}^{4+n}/{\varphi }^n$. (d) indicates the constraint on the quartic chameleon with $V(\varphi )=\frac{\lambda }{4!}{\varphi }^4$. Here, $1/\beta =M/M_{\mathrm{Pl}}$ with $M$ being the energy scaled by the Planck mass. As a dimensionless coupling constant, $\beta$ describes the coupling strength between the chameleon field and matters.

Figure 7

The laboratory experiment constrains on the chameleon model with $n=1$. The blue shaded region indicates the current best constraint results from the atom interferometer [33]. The yellow shaded region indicates the region is excluded by the Eöt-Wash experiment with the torque resolution $0.01\mathrm{fN}·\mathrm{m}$ [49]. The light yellow region indicates the region is excluded by the HUST-2020 experiment.

Figure 8

Left: the function graph of $y=\frac{{(2m_{\mathrm{eff}}{d}_A)}^2}{12}x$ and $y=x^3-\frac{9}{4}{x}^2-\frac{0-18}{12}x-\frac{1}{4}$ with a special value of $m_{\mathrm{eff}}{d}_L$. Right: the function relation graph between each root and $m_{\mathrm{eff}}{d}_A$.