## Space test of the Equivalence Principle: first results of the MICROSCOPE mission

### Space test of the Equivalence Principle: first results of the MICROSCOPE mission

 Authors: P. Touboul, G. Metris, M. Rodrigues, Y. André, Q. Baghi, J. Bergé, D. Boulanger, S. Bremer, R. Chhun, B. Christophe, V. Cipolla, T. Damour, P. Danto, H. Dittus, P. Fayet, B. Foulon, P.-Y. Guidotti, E. Hardy, P.-A. Huynh, C. Lämmerzahl, V. Lebat, F. Liorzou, M. List, I. Panel, S. Pires, B. Pouilloux, P. Prieur, S. Reynaud, B. Rievers, A. Robert, H. Selig, L. Serron, T. Sumner, P. Viesser Journal: Classical and Quantum Gravity Year: 2019 Download: ADS | arXiv

## Abstract

The Weak Equivalence Principle (WEP), stating that two bodies of different compositions and/or mass fall at the same rate in a gravitational field (universality of free fall), is at the very foundation of General Relativity. The MICROSCOPE mission aims to test its validity to a precision of 10^-15, two orders of magnitude better than current on-ground tests, by using two masses of different compositions (titanium and platinum alloys) on a quasi-circular trajectory around the Earth. This is realised by measuring the accelerations inferred from the forces required to maintain the two masses exactly in the same orbit. Any significant difference between the measured accelerations, occurring at a defined frequency, would correspond to the detection of a violation of the WEP, or to the discovery of a tiny new type of force added to gravity. MICROSCOPE's first results show no hint for such a difference, expressed in terms of Eötvös parameter δ =  [-1 +/- 9(stat) +/- 9 (syst)] x 10^-15 (both 1σ uncertainties) for a titanium and platinum pair of materials. This result was obtained on a session with 120 orbital revolutions representing 7% of the current available data acquired during the whole mission. The quadratic combination of 1σ uncertainties leads to a current limit on δ of about 1.3 x 10^-14.

## pmclib

 Authors: K. Benabed, M. Kilbinger et al. Language: C Download: github/pmclib Description: Population Monte-Carlo (PMC) sampling code, for fast end efficient parallel iterative importance sampling to compute integrals over the posterior including the Bayesian evidence. Notes: Requires gsl and fftw libraries. A MPI C compiler is recommended.

## MGCNN

 Authors: F. Lalande, A. Peel Language: Python 3 Download: mgcnn.tar.gz Description: A Convolutional Neural Network (CNN) architecture for classifying standard and modified gravity (MG) cosmological models based on the weak-lensing convergence maps they produce.

## Introduction

This repository contains the code and data used to produce the results in A. Peel et al. (2018), arXiv:1810.11030.

The Convolutional Neural Network (CNN) is implemented in Keras using TensorFlow as backend. Since the DUSTGRAIN-pathfinder simulations are not yet public, we are not able to include the original convergence maps obtained from the various cosmological runs. We do provide, however, the wavelet PDF datacubes derived for the four models as described in the paper: one standard LCDM and three modified gravity f(R) models.

## Requirements

• Python 3
• numpy
• Keras with Tensorflow as backend
• scikit-learn

## Usage

\$ python3 train_mgcnn.py -n0

The three options for the noise flag "-n" are (0, 1, 2), which correspond to noise standard deviations of sigma = (0, 0.35, 0.70) added to the original convergence maps. Additional options are "-i" and "-e" for the number of training iterations and epochs, respectively.

Confusion matrices and evaluation metrics (loss function and validation accuracy) are saved as numpy arrays in the generated output/ directory after each iteration.

## pyGMCALab

 Authors: J. Bobin, J.Rapin, C.Chenot, C.Kervazo Language: Python Download: Python Description: A toolbox for solving Blind Source Separation problems. Notes:

## GMCALab

GMCALab is a Python toolboxes that focus on solving Blind Source Separation problems from multichannel/multispectral/hyperspectral data. In essence, multichannel data provide different observations of the same physical phenomena (e.g. multiple wavelengths, ), which are modeled as a linear combination of unknown elementary components or sources:

where $\mathbf{Y}$ is the data matrix, $\mathbf{S}$ is the source matrix, and $\mathbf{A}$ is the mixing matrix. The goal of blind source separation is to retrieve $\mathbf{A}$ and $\mathbf{S}$ from the knwoledge of the data only.

Generalized Morphological Component Analysis, a.k.a. GMCA, is a BSS method that enforces the sparsity of the sought-after sources:

Please check out the project's GitHub page.

It is worth noting that GMCA provides a very generic framework that has been extended to tackle different matrix factorization problems:

• Non-negative matrix factorization with nGMCA
• Separation of partially correlated sources with AMCA
• The decomposition of hyperspectral data with HypGMCA (available soon)
• The analysis of multichannel data in the presence of outliers with rAMCA at this location (updated the 14/06/16).
• Robust BSS in transformed domains with tr-rGMCA .

We are now developping a python-based toolbox coined pyGMCALab, which is available at this location.

## LGMCA

 Authors: J. Bobin Language: IDL Download: IDL Description: The scripts required to compute the CMB map from WMAP and Planck data Notes:

## LGMCA

Local-generalised morphological component analysis is an extension to GMCA. Similarly to GMCA it is a Blind Source Separation method which enforces sparsity. The novel aspect of LGMCA, however is that the mixing matrix changes across pixels allowing LMCA to deal with emissions sources which vary spatially.

Running LGMCA on the WMAP9 temperature products requires the main script and a selection of mandatory files, algorithm parameters and map parameters.

## CosmoPmc

 Authors: M. Kilbinger et al. Language: C Download: github/CosmoPMC Description: A Monte-Carlo sampling code to explore the likelihood of various cosmological probes. Notes: Requires gsl and fftw libraries, and the software packages pmclib and nicaea. A MPI c compiler is recommended.

## MSVST-lab

 Authors: J. Fadili Language: Matlab Download: Homepage Description: A code for sparse representation-based image deconvolution with Poisson noise. Notes:

## GMCALab

 Authors: J. Bobin Language: Matlab and Python Download: Python | Matlab Description: A toolbox for solving Blind Source Separation problems. Notes:

## GMCALab

GMCALab is a set of Matlab toolboxes that focus on solving Blind Source Separation problems from multichannel/multispectral/hyperspectral data. In essence, multichannel data provide different observations of the same physical phenomena (e.g. multiple wavelengths, ), which are modeled as a linear combination of unknown elementary components or sources:

where $\mathbf{Y}$ is the data matrix, $\mathbf{S}$ is the source matrix, and $\mathbf{A}$ is the mixing matrix. The goal of blind source separation is to retrieve $\mathbf{A}$ and $\mathbf{S}$ from the knwoledge of the data only.

Generalized Morphological Component Analysis, a.k.a. GMCA, is a BSS method that enforces the sparsity of the sought-after sources:

A lightweight Matlab/Octave version of the GMCALab toolbox is available at this location. Illustrations are provide here.

Please check out the project's GitHub page.

It is worth noting that GMCA provides a very generic framework that has been extended to tackle different matrix factorization problems:

• Non-negative matrix factorization with nGMCA
• Separation of partially correlated sources with AMCA
• The decomposition of hyperspectral data with HypGMCA (available soon)
• The analysis of multichannel data in the presence of outliers with rAMCA at this location (updated the 14/06/16).
• Robust BSS in transformed domains with tr-rGMCA .

We are now developping a python-based toolbox coined pyGMCALab, which is available at this location.