Phys. Rev. Lett. 129, 131302 (2022) - Searching for Chameleon Dark Energy with Mechanical Systems

Searching for Chameleon Dark Energy with Mechanical Systems

J. Betz, J. Manley, E. M. Wright, D. Grin, and S. Singh

Phys. Rev. Lett. 129, 131302 – Published 23 September 2022

Abstract

A light scalar field framework of dark energy, sometimes referred to as quintessence, introduces a fifth force between normal matter objects. Screening mechanisms, such as the chameleon model, allow the scalar field to be almost massless on cosmological scales while simultaneously evading laboratory constraints. We explore the ability of existing mechanical systems to directly detect the fifth force associated with chameleons in an astrophysically viable regime where it could be dark energy. We provide analytical expressions for the weakest accessible chameleon model parameters in terms of experimentally tunable variables and apply our analysis to two mechanical systems: levitated microspheres and torsion balances, showing that the current generation of these experiments have the sensitivity to rule out a significant portion of the proposed chameleon parameter space. We also indicate regions of theoretically well-motivated chameleon parameter space to guide future experimental work.

Received 10 February 2022
Revised 20 July 2022
Accepted 29 August 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.131302

Physics Subject Headings (PhySH)

Dark energy Experimental studies of gravity Optics & lasers

Gravitation, Cosmology & AstrophysicsInterdisciplinary PhysicsParticles & FieldsAtomic, Molecular & Optical

Authors & Affiliations

J. Betz ¹, J. Manley ², E. M. Wright ³, D. Grin⁴, and S. Singh^2,1,*

¹Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
²Department of Electrical and Computer Engineering, University of Delaware, Newark, Delaware 19716, USA
³Wyant College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
⁴Department of Physics and Astronomy, Haverford College, Haverford, Pennsylvania 19041, USA

^*swatis@udel.edu

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Vol. 129, Iss. 13 — 23 September 2022

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Figure 1
Schematic of mechanical systems considered here to detect the chameleon mediated force between matter. In both cases, $M_{1}$ is the gold source mass, while $M_{2}$ is the mechanically compliant test mass. We consider (a) torsion balance and (b) optically levitated microspheres as sensors of chameleon DE. The blue curves show the two-body chameleon field profile. The levitated microsphere is enlarged to show detail.
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Figure 2
Projected constraints from levitated microspheres (blue) and torsion balances (orange) as chameleon dark energy detectors, where the chameleon self-coupling is fixed at $Λ = Λ_{DE}$ . In this plot, we consider a microsphere system with $R_{1} = 5 μ m$ , $s = 0.5 mm$ , and $F_{\min} = 10^{- 21} N$ , and a torsion balance system with $R_{1} = 0.1 mm$ , $s = 0.6 mm$ , and $F_{\min} = 4 \times 10^{- 18} N$ . For both systems, the solid (dashed) black line corresponds to source a mass with $R_{1} = 1 mm$ (0.1 mm). The multiplicative ansatz and force expression are used to generate the torsion balance curves in the region where the additive ansatz breaks down. Existing constraints from Ref. [16], which include results from Refs. [24, 26, 30, 32], are shown in gray. See Ref. [42] for a qualitative description of chameleon constraint plots.
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Figure 3
Projected constraints from levitated microspheres (blue) and torsion balances (orange) as chameleon dark energy detectors, where the power-law index is fixed at $n = 1$ . In this plot, we consider a microsphere system with $R_{2} = 5 μ m$ , $s = 3 mm$ , and $F_{\min} = 10^{- 21} N$ , and a torsion balance system with $R_{2} = 1 mm$ , $s = 6 mm$ , and $F_{\min} = 10^{- 16} N$ . For torsion balances, the dashed (dotted) black line corresponds to a source mass with $R_{1} = 7 mm$ (5 cm). The multiplicative ansatz and force expression are used to generate the torsion balance curves in the region where the additive ansatz breaks down. For microspheres, the solid (dashed) black line corresponds to a source mass with $R_{1} = 3 mm$ (7 mm). The horizontal black dashed line indicates the dark energy scale $Λ = Λ_{DE}$ . Existing constraints from Ref. [16], which include results from Refs. [30, 32], are shown in gray.
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Figure 4
The parameter space for both $n = 1$ and $n > 1$ chameleon models considered here is limited by cosmological [11, 53, 55] as well as quantum field theory analyses [56]. The green regions indicate where the chameleon model has safe cosmological evolution and small quantum corrections and should be the aim of future experimental searches. Existing and projected constraints from Figs. 2 and 3 are also shown. See Ref. [42] for region definitions.
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Physical Review Letters

Searching for Chameleon Dark Energy with Mechanical Systems

J. Betz, J. Manley, E. M. Wright, D. Grin, and S. Singh

Phys. Rev. Lett. 129, 131302 – Published 23 September 2022

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