# Dark Matter Axions, Non-Newtonian Gravity and Constraints on Them from Recent Measurements of the Casimir Force in the Micrometer Separation Range

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## Abstract

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## 1. Introduction

## 2. Effective Potentials Due to Exchange of Pseudoscalar and Scalar Particles

## 3. Measurements of the Casimir Force in the Micrometer Separation Range

## 4. Constraints on Axionlike Particles

## 5. Constraints on Non-Newtonian Gravity

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The strongest constraints on the coupling constant of axionlike particles to nucleons obtained from different experiments. Lines labeled “gr${}_{1}$” and “gr${}_{2}$” are found from the Cavendish-type experiments and from measuring the minimum gravitational forces, respectively. Lines labeled “new” and “H${}_{2}$” follow from the recent experiment on measuring the Casimir force in the micrometer separation range and from the experiment using a beam of molecular hydrogen. Line 1 and the dashed line are obtained from measuring the effective Casimir pressure and from the experiment nullifying the Casimir force. The regions above each line are excluded, and those below are allowed.

**Figure 2.**The strongest constraints on the interaction constant and interaction range of the Yukawa-type interaction obtained from different experiments. Lines 1, 2 and 3 are found from measuring the effective Casimir pressure between two parallel plates, and normal and lateral Casimir forces between the sinusoidally corrugated surfaces of a sphere and a plate, respectively. The line labeled “n” is found from the experiments on neutron scattering. The lines labeled “new” and 4 follow from the experiment measuring the Casimir force in the micrometer separation range and from the experiment using a torsion pendulum. The line labeled “gr” and the dashed line are obtained from the Cavendish-type experiments and from the experiment nullifying the Casimir force. The regions above each line are excluded, and those below each line are allowed.

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**MDPI and ACS Style**

Klimchitskaya, G.L.; Mostepanenko, V.M.
Dark Matter Axions, Non-Newtonian Gravity and Constraints on Them from Recent Measurements of the Casimir Force in the Micrometer Separation Range. *Universe* **2021**, *7*, 343.
https://doi.org/10.3390/universe7090343

**AMA Style**

Klimchitskaya GL, Mostepanenko VM.
Dark Matter Axions, Non-Newtonian Gravity and Constraints on Them from Recent Measurements of the Casimir Force in the Micrometer Separation Range. *Universe*. 2021; 7(9):343.
https://doi.org/10.3390/universe7090343

**Chicago/Turabian Style**

Klimchitskaya, Galina L., and Vladimir M. Mostepanenko.
2021. "Dark Matter Axions, Non-Newtonian Gravity and Constraints on Them from Recent Measurements of the Casimir Force in the Micrometer Separation Range" *Universe* 7, no. 9: 343.
https://doi.org/10.3390/universe7090343