E8 Modified Gravity from the Earth’s outskirts to the cosmos


    Fundamental physics has been challenged for decades by (1) the unification of General Relativity (GR) and of Quantum Physics (QP), and more recently by (2) the discovery of the acceleration of the expansion of the Universe. Known theories trying the reconcile GR and QP, e.g. string theory often introduce new scalar fields that could be detected through an associated fifth force. Similarly, the accelerated expansion of the Universe can be explained either by introducing a cosmological constant in Einstein’s equation, or alternatively by introducing extra fields that affect the Universe’s dynamics on cosmological scales or modify GR. However, the fifth force created by an extra field, if it affects the Universe on its larger scales, should also affect its dynamics on small scales, which contradicts past and current tests of GR. To avoid violating GR on smaller scales, screening mechanisms have been designed, that cancel the effect of the fifth force so that new theories are consistent with GR at the level of the current experimental constraints. One of the most stringent of these tests tackles putative violations of the equivalence principle which could occur in theories with certain types of screening, e.g. chameleons.

    bpc_microscope_p41481_vignetteMICROSCOPE, launched on April 26, 2016, will perform a test of the Weak Equivalence Principle by measuring the Eötvös parameter down to 10-15, two orders of magnitude lower than the best current constraints. As theories with an extra scalar field may violate the WEP, this mission will allow for new constraints on the presence of such scalar fields. In particular, the chameleon screening mechanism could be tested.

    The Lunar Laser Ranging Experiment and planetary ephemerids yield tight constraints on deviations from GR in the Solar System. In particular, it is possible to constrain other screening mechanisms such as the Vainshtein and K-mouflage ones as they affect the orbits of planets and interplanetary probes.

    Cosmological surveys bring complementary constraints, as Modified Gravity (MG) affects structure formation. For instance, massive galaxy cluster counts and measurements of the matter power spectrum can discriminate against LCDM and MG models; therefore, making it possible to constrain different screening mechanisms.


    The project aims to constrain (or investigate how to constrain) modifications to General Relativity, with an emphasis on screening mechanisms, on three complementary scales. We then aim to focus on the following three axes of research:

    1. Earth orbit scale: constrain the chameleon mechanism with MICROSCOPE.
    2. Solar System scale: development of an instrumental concept to experimentally constrain MG and screening mechanisms.
    3. Cosmological scales: constrain MG and screening mechanisms thanks to their effects on structure formation.

    WP leader BERGE Joel ONERA Research engineer, ONERA
    WP co-leader PIRES Sandrine AIM Research engineer, CEA
    WP co-leader BAGHI Quentin ONERA/OCA Postdoc, OCA (former ONERA PhD)
    WP member BRAX Philippe IPhT Research engineer, CEA
    WP member CHRISTOPHE Bruno ONERA Research engineer, ONERA
    WP member HARDY Emilie ONERA Research engineer, ONERA
    WP member KILBINGER Martin AIM Research engineer, CEA
    WP member LIORZOU Françoise ONERA Research engineer, ONERA
    WP member PIERRE Marguerite AIM Research engineer, CEA
    WP member RODRIGUES Manuel ONERA Research engineer, ONERA
    WP member UZAN Jean-Philippe IAP DR, CNRS
    WP member VALAGEAS Patrick IPhT Research engineer, CEA


    We followed the 2016 Science Committee’s advice and descoped our project, now focused on tests of gravity at small scale, and the development of the corresponding data analysis methods. Therefore, we regrouped on the two topics: MICROSCOPE data analysis and ISLAND concept. We present our work below.


    MICROSCOPE and gravity at Earth scale


    MICROSCOPE was launched on April 25, 2016, and has since delivered high-quality data. Data analysis is ongoing, and first results on the measurement of the Weak Equivalence Principle (WEP) have been submitted for publication (Touboul et al). Following this first publication, we will submit new constraints on modified gravity, where we focus on the dilaton, as well as on f(R) theories and the chameleon mechanism (Bergé et al, in prep).


    We used MICROSCOPE data to derive new constraints on the dilaton coupling constants, as well as on f(R) theories. Unfortunately, since the first MICROSCOPE results are confidential until their official publication, we cannot report on our results here.


    Gravity on Solar System scales: ISLAND concept


    ISLAND (Inverse Square Law And Newtonian Dynamics Space Experiment) aims to constrain deviations from the gravitational inverse square law (ISL) at submilliter scales and on scales of dozens of Astronomical Units (AU), the largest scales reachable by a man-made instrument in the Solar System. The submilliter scales will be tested with an electrostatic torsion pendulum, based on the Eöt-Wash on-ground torsion pendulum: a circular attractor plate is rotating under a circular detector plate, both of which having cylindrical holes that act as gravitational attractors. The twist of the detector can be estimated electrostatically, and can be directly linked to the gravitational torque exerted by the attractor. Any deviation from the ISL can then be directly measured.

    We are currently upgrading our model to allow for more general geometries, which will allow us to make more realistic and better motivated predictions.


    MICROSCOPE will provide data until the spring 2018. We then expect data analysis to take until late 2019. It will be focused on two main aspects:

    • Constraining fundamental physics involves performing detailed simulations and physics analyses.
    • Optimizing the characterization of the data involves data analysis methodology.


  • Pires S., Bergé , Baghi Q., Touboul P., Métris G., “Dealing with missing data in the MICROSCOPE space mission: An adaptation of inpainting to handle colored-noise data”, 2016, Phys. Rev. D 94, 123015

    Bergé , Brax P., Métris G., Pernot-Borras M., Touboul P., Uzan J.P., “MICROSCOPE first constraints on the violation of the weak equivalence principle by a light scalar dilaton”, to be submitted to Phys. Rev. Letters

    Bergé , Brax P., Métris G., Pernot-Borras M., Touboul P., Uzan J.P., “MICROSCOPE’s Local Constraints on Chameleon Screening and f(R) Models”, in preparation

    Bergé , Baghi Q., Massey R., “Exponential shapelets: basis functions for fundamental physics, space geodesy and observational cosmology data analysis”, in preparation

    Bergé , “The Inverse Square Law And Newtonian Dynamics space explorer (ISLAND)”, in Proceedings of the 52nd Rencontres de Moriond

    Bergé , Baghi Q., Hardy E., Métris G., Serron L., Carle P., Chhun R., Guidotti P.Y., Huynh P.H., Inchauspé H., Lala S., Robert A., Rodrigues M., Touboul P., Travert J.M., “Validation of the MICROSCOPE data analysis and in-flight calibration: mock data blind analysis”, to be submitted to Phys. Rev. D

    Baghi Q. et al., “In-orbit estimation of the dynamic differential sensitivity in MICROSCOPE mission: a calibration using glitches”, in preparation

    Pierre Touboul et al. MICROSCOPE Mission: First Results of a Space Test of the Equivalence Principle, Phys. Rev. Lett. 119, 231101 – Published 4 December 2017, https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.119.231101

    Bergé J., Touboul P., Rodrigues M., Liorzou F., « MICROSCOPE : five months after launch », Journal of Physics: Conference Series, Volume 840, Issue 1, article id. 012028 (2017)