Constraints on chameleon gravity from the measurement of the electrostatic stiffness of the $MICROSCOPE$ mission accelerometers

Constraints on chameleon gravity from the measurement of the electrostatic stiffness of the $M I C R O S C O P E$ mission accelerometers

Martin Pernot-Borràs, Joel Bergé, Philippe Brax, Jean-Philippe Uzan, Gilles Métris, Manuel Rodrigues, and Pierre Touboul

Phys. Rev. D 103, 064070 – Published 26 March 2021

Abstract

This article is dedicated to the use the MICROSCOPE mission’s data to test chameleon theory of gravity. We take advantage of the technical sessions aimed to characterize the electrostatic stiffness of MICROSCOPE’s instrument intrinsic to its capacitive measurement system. Any discrepancy between the expected and measured stiffness may result from unaccounted-for contributors, i.e., extra forces. This work considers the case of chameleon gravity as a possible contributor. It was previously shown that, in situations similar to these measurement sessions, a chameleon fifth force appears and acts as a stiffness for small displacements. The magnitude of this new component of the stiffness is computed over the chameleon’s parameter space. It allows us to derive constraints by excluding any force inconsistent with the MICROSCOPE data. As expected—since MICROSCOPE was not designed for the purpose of such an analysis—these new bounds are not competitive with state-of-the-art constraints, but they could be improved by a better estimation of all effects at play in these sessions. Hence, our work illustrates this novel technique as a new way of constraining fifth forces.

Received 2 February 2021
Accepted 9 March 2021

DOI:https://doi.org/10.1103/PhysRevD.103.064070

Physics Subject Headings (PhySH)

Alternative gravity theories Laboratory studies of gravity

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Martin Pernot-Borràs ^1,2,*, Joel Bergé^1,†, Philippe Brax³, Jean-Philippe Uzan^2,4,‡, Gilles Métris ⁵, Manuel Rodrigues ¹, and Pierre Touboul¹

¹DPHY, ONERA, Université Paris Saclay, F-92322 Châtillon, France
²Institut d’Astrophysique de Paris, CNRS UMR 7095, Université Pierre et Marie Curie–Paris VI, 98 bis Boulevard Arago, 75014 Paris, France
³Institut de Physique Théorique, Université Paris-Saclay, CEA, CNRS, F-91191 Gif-sur-Yvette Cedex, France
⁴Sorbonne Universités, Institut Lagrange de Paris, 98 bis, Boulevard Arago, 75014 Paris, France
⁵Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, IRD, Géoazur, 250 avenue Albert Einstein, F-06560 Valbonne, France

^*martin.pernot_borras@onera.fr
^†joel.berge@onera.fr
^‡uzan@iap.fr

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Vol. 103, Iss. 6 — 15 March 2021

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Images

Figure 1
Result of the comparison of the acceleration experienced by a test mass in planar and cylindrical configurations in different regimes of screening quantified by $\frac{e}{2 λ_{c}}$ , where $e$ is the thickness of the cylinder and $λ_{c}$ the Compton wavelength of the field associated with it.
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Figure 2
Scaling of the chameleon fifth force as a function of the displacement in the range $δ = 1 \dots 10 μ m$ for different sets of parameters ( $Λ, β)$ assuming $n = 1$ . The force is expressed in newtons. $Λ$ are chosen in the range $10^{- 1} - 3 \times 10^{2} eV$ and $β$ in the range $6 - 10^{7}$ . This shows that $\log F = \log k_{chameleon} (Λ, β) + \log δ$ is a good approximation to the behavior of the force at small displacements. We use a log-log plot for convenience, but it is easily checked that the slope is unity so that linearity is confirmed.
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Figure 3
Evolution with the parameters $β$ and $Λ$ of the chameleonic stiffness $k_{chameleon}$ of the external test mass of the sensor unit SUEP from the MICROSCOPE mission for $n = 1$ . Its magnitude is shown by the background colors. This function is obtained by linearly interpolating the data points. These points are the result of the three numerical methods discussed in the main text that are here distinguished by different points of colors. This is represented in log scale for $β$ , $λ$ , and $k_{chameleon}$ . The uniform dark-blue region corresponds to parameters for which we are unable to compute the stiffness. The black line is the contour line at which the stiffness is equal to the measured $2 σ$ uncertainty on the discrepancy $Δ k_{MIC}$ in the MICROSCOPE experiment.
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Figure 4
Constraints on the chameleon model for $n = 1$ from the MICROSCOPE experiment using stiffness measurement sessions: The region excluded at $2 σ$ is above the four lines described in the legend. They correspond to the different test masses: IS1 (respectively, IS2) denotes the internal (respectively, external) test masses of the SUREF and SUEP sensor units. Their constraints are compared to the current constraints from other experiments denoted with the colored regions as presented in Refs. [12, 13]. They come from atomic interferometry (purple [14, 15, 20]), the Eöt-Wash group’s torsion balance experiments (green [16, 17]), Casimir effect measurements (yellow [18, 19]), astrophysics tests (blue [21, 22, 23]) and lensing (pink [24]), precision atomic tests (orange [25, 26]), microsphere (blue line [27]), and neutron interferometry (blue and red points [28, 29]). The horizontal dotted line denotes the energy scale of dark energy.
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