GAUGE: the GrAnd Unification and Gravity Explorer
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Abstract
The GAUGE (GrAnd Unification and Gravity Explorer) mission proposes to use a dragfree spacecraft platform onto which a number of experiments are attached. They are designed to address a number of key issues at the interface between gravity and unification with the other forces of nature. The equivalence principle is to be probed with both a highprecision test using classical macroscopic test bodies, and, to lower precision, using microscopic test bodies via coldatom interferometry. These two equivalence principle tests will explore stringdilaton theories and the effect of space–time fluctuations respectively. The macroscopic test bodies will also be used for intermediaterange inversesquare law and an axionlike spincoupling search. The microscopic test bodies offer the prospect of extending the range of tests to also include shortrange inversesquare law and spincoupling measurements as well as looking for evidence of quantum decoherence due to space–time fluctuations at the Planck scale.
Keywords
Fundamental physics Space mission Equivalence principle Mass–spin coupling Atom interferometry1 Introduction

A test of stringdilaton theories using a high precision macroscopic equivalence principle experiment, MEPE

A test of the effect of quantum space–time fluctuations in a microscopic equivalence principle experiment, QSTEP

A 1/r ^{2} test at intermediate ranges, IRISL

An intermediate range axionlike mass–spin coupling search, IRSC

Measurement of quantum decoherence from space–time fluctuations at the Planck scale, QDE
2 Scientific objectives
GAUGE proposes new tests of general relativity (GR) in Earthorbit that will include the Einstein equivalence principle (EEP), the inverse square law, spincoupling and the quantum vacuum. This will be done using a combination of macroscopic test masses and matter wave interferometry in a dragfree spacecraft.
2.1 The equivalence principle
2.2 Inverse square law
The inverse square law can be checked with both classical and quantum detectors on GAUGE. GAUGE will use pairs of masses to measure force changes as one of the masses is moved. The inverse square law is welltested for planetary astrophysical distances but not for distances of microns or less. Models that go beyond the SM such as string theory and supersymmetry aiming at unification have, as a natural consequence, new long range forces with strengths comparable or weaker than gravity. GAUGE will be able to look for violations of Newton’s law confirming new long range forces on both intermediate (∼20 cm) and possible short range (∼10 μm).
2.3 Spin coupling
2.4 Quantum vacuum
2.4.1 Violation of equivalence principle at the atomic level
2.4.2 Quantum vacuum atom wave decoherence
The physics of the vacuum is amongst the most fundamental issues of quantum field theory and GR. The existence of zero point energy is an essential feature of quantum field theory [31]. EM vacuum energy has already seen experimental confirmation through the Casimir effect [32], Lamb shift [33] and spontaneous emission [34]. Recent measurement of the Planckian spectral density of Josephson noise in superconducting circuits [35] confirms the physical reality of EM zero point energy and its ability to interact with the macroscopic world. According to the uncertainty principle, all field components in the SM (and possibly beyond) show a minimum level of fluctuation even at absolute zero temperature, giving rise to zero point energy in vacuum. The role of vacuum energy in cosmology is a subject of intense debate [31, 36, 37]. Does vacuum energy gravitate? The Planckian spectrum for zero point energy is Lorentz invariant but has no UV cutoff, resulting in a formally divergent energy density. The only natural UV cutoff frequency seems to be the Planck frequency but if this value is used the resulting finite vacuum energy density would provide a ‘cosmological constant’ 10^{120} times above the observational limit, measured to be a fraction of the critical density of the Universe. This is the well known cosmological constant problem [31, 38, 39]. A UV cutoff imposed on the Planckian spectrum will lead to Lorentz invariance. Could a signature of this be detectable [29]? The lack of experimental guidance on the gravitational nature of vacuum energy and its role in cosmology has led to many theoretical speculations including quintessence, braneworld and holographic approaches [31, 38]. Quantum field theory in curved spacetime and semiclassical gravity are useful theoretical tools in estimating gravitational effects on quantum fields and their backreactions [40]. It has important applications in, e.g. black hole radiation and evaporation [41]. However, semiclassical gravity has been shown to contradict certain experiments [42]. Theoretically, it fails to capture quantum fluctuations of spacetime and would lead to a perfectly homogeneous and isotropic universe even in the presence of fluctuating quantum matter fields [43]. Stochastic gravity [28] is probably a better approximation to quantum gravity but so far has been subject to few experimental tests. The ubiquity of vacuum energy makes all quantum systems into open systems [44]. For example, EM zero point energy may affect electron diffusion in metals [45]. Furthermore, decoherence of free electrons in vacuum by EM zero point energy has been a subject of intense investigations [46, 47]. Due to the weakness of gravitational coupling, the gravitational analogue of the Casimir effect is inconceivable. However, quantum decoherence due to gravitational vacuum fluctuations does not require modifying the boundary conditions of gravity and could be tested using matter wave interferometry under ultra quiet conditions. A number of models exploring quantum and stochastic gravitational decoherence have recently been considered [48, 49, 50, 51]. These phenomenological models predict decoherence in terms of the loss of visibility in matter wave interferometry of the form
This section has discussed a range of experiments targeting a number of different scientific goals. The main underlying theme has been at the interface between gravity and quantum mechanics. Any discovery in this regime could lead to fundamental new insights into quantumgravity or other new forces of nature [52] and would be of profound importance.
3 Proposed payload instrument complement
3.1 Overview of all payload elements

Macroscopic testmasses (LTP) used as source masses for an inverse square law test (IRISL) and as measurement masses for a spincoupling measurement (IRSC)

An atom interferometer used for both a microscopic equivalence principle test (QSTEP) and a quantum decoherence study (QDE)

Three macroscopic test mass pairs housed within a cryogenic science module (CSM) used for a highprecision equivalence principle test (MEPE)

A polarisable spinsource within the CSM to drive spinmass coupling forces to be measured by both the LTP test masses and the test mass pairs within the CSM

An option to supplement the atom interferometry with atom lasers which would enable both shortrange inverse square law and spincoupling tests (SRISL, SRSC)
3.2 The LISA test package
The LISA Test Package (LTP) should be replicated in full. The only change required for GAUGE is to reorientate the optical bench along the spacecraft axis. In all other respects it should have the same performance parameters as it does for LISA Pathfinder.
3.3 Atom interferometry, QSTEP
For GAUGE the sensitive axis of QSTEP must be perpendicular to the symmetry axis of the satellite which points in sun direction. Hence, during one orbit the measurement axis will twice align with the Earth direction and twice with the tangent to the orbit path. An equivalence principle violation signal will be modulated once per orbit whereas a modulation due to the gravity gradient will be twice per orbit.

In the central vacuum chamber where the atoms are probed the required vacuum level of order 10^{ − 9} mbar will be maintained by a small ion getter pump and additional getter materials. All lasers are fibre coupled to the beam expander telescopes which are close connected to the chamber. The detection unit contains calibrated photodiodes and a CCD camera for spatially resolved detection. The whole device will be thermally decoupled from the LPSM. Thermal stability of the physics package is achieved by a combination of passive isolation (multilayer insulation, conductive decoupling with titanium mounts), and active temperature control by heaters. Extensive use of CFRP gives superior stiffness and minimises mass and thermal distortions. This vacuum chamber has to be placed in the central tube of the LPSM right below the LTP test mass housing as shown in Fig. 2.

The lasers and modulation units required to cool, prepare and detect the atoms can be placed in one of the free outer compartments of the LPSM. The light is delivered to the central vacuum chamber using optical fibres.

Raman laser systems will generate the laser light pulses. Two prestabilised lasers will be phaselocked to highly stable microwave frequency reference sources. These units can be placed outside of the inner cylinder with fibreoptic feeds.

Computer control will autonomously run measurements, calibrations and control phases. In addition, a preprocessing of raw data will be performed. This control unit will be combined with the LPSM onboard computer.
3.4 Inverse squarelaw experiments

Metrology, in particular the absolute separation between the centres of mass

Absolute calibration of force sensors (if nonnull experiment)

Density inhomogeneities present in the interacting bodies

The presence of an external, wellknown modulated Earth gravity gradient that can be used for absolute calibration of separation ratios

The flexibility to use freefloating test masses alternatively as source and test masses, which can be used to calibrate stiffness ratios of force sensors

A high force sensitivity, masses that are separated by distances much larger than their dimensions can be used, thus minimising density inhomogeneity problems
3.5 Spincoupling experiments
3.6 Macroscopic equivalence principle experiment
4 Basic spacecraft key factors

Provision of standard services (Power, Telemetry, etc.) to all payload instruments

Physical accommodation of all payload instrument control electronics

Provision of a dragfree environment, either standalone using the LTP or in conjunction with sensors within the other experiments

Physical accommodation of GAUGE Atom Interferometer

Use of the LTP test masses as part of an inverse square law (ISL) experiment

Provision of cryogenic environment

Accommodation of the macroscopic equivalence principle proofmasses

Accommodation of the spin source for the spincoupling experiment

Accommodation of a dedicated test mass pair for the ISL experiment

Provision of dragfree components, either standalone or in conjunction with the LTP, including provision of cold gas for possible thrust control
LISA Pathfinder Science Module Design for GAUGE
The science module benefits from the heritage of LISA Pathfinder, due to launch in 2009. LPSM consists of an octagonal structure with a fixed solar array mounted to the upper panel. Volume for the room temperature payload including the LTP and the Atom Interferometer is provided within the central cylinder. In addition the LPSM accommodates all service module equipments required for the mission. Wherever possible LISA Pathfinder systems have been baselined. The electrical system and AOCS equipments are identical to those of LPF. The structure only differs in that the lower interface from the central cylinder is to the CSM rather than a propulsion module.
Cryogenic Science Module for GAUGE
Some experiments on GAUGE benefit from operating elements in the CSM in conjunction with elements in LPSM. A key requirement, is that vibrational noise be kept to an absolute minimum. This, together with the need for LEO, precludes the use of active cryocoolers based on Stirling compressors and mechanical JouleThompson systems (too noisy) or cryocoolers based on sorption coolers and radiative cooling (insufficient performance in LEO). Consequently, the design is based on a passive LHe dewar, sized to ensure sufficient lifetime. This has the benefit that He boiloff gas can be used by the dragfree system, as successfully demonstrated by GPB. There is a tradeoff between capacity and lifetime on the one hand, and mass on the other. An additional constraint is set by available launch fairing volume (VEGA). The most relevant dewar heritage comes from GPB and STEP [56]. GPB employed a 2500 l dewar and had a lifetime of approximately 14 months, whereas the baseline STEP dewar has 230 l and is designed for total lifetime (including margin) of approximately 8 months. For GAUGE, different experiments relying on cryogenic conditions will have to be operated in sequence, and as a result the overall lifetime needs to be the sum of the anticipated operating time for these experiments. As a first approach, it has been assumed that the outer diameter of a STEPlike dewar can be increased to 1.5 m and still remain shadowed by the solar array at all times. No attempt has been made to assess secondary effects, such as additional residual atmospheric drag or mechanical strengthening or stiffening of the dewar. With a 1.5 m diameter the LHe capacity increases to approximately 500 l. Assuming a heat load of 25 mW (as for STEP) this provides a lifetime compatible with the science requirements, including margin, of approximately 20 months.
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