Equivalence Principle Experiments Research Articles

Constraining light scalar field with torsion-balance gravity experiments

The light scalar field with a coupling to standard model particles provide a possible source of the long-range Yukawa forces or violation of the weak equivalence principle, which can be potentially explored by precision gravity experiments. We describe the searches for such light scalar fields with the three types of gravity experiments, including the G-measurement experiments, Inverse-Square Law (ISL) experiments, and equivalence principle experiments. We investigate the potential influences of the scalar field as a function of its mass, and focus on the experimental constraints from torsion-balance gravity experiments. HUST-18 G-measurement torsion-balance experiments place bounds on the photon coupling and electron coupling at up to Λγ=7×1017 GeV and Λe=1×1017 GeV in the mass ranges 10−9–10−4eV. Results from the ISL experiments by the Universities of Washington, Stanford, IUPUI, HUST, Colorado, Irvine, Yale and others allow us to set limits on the photon coupling and electron coupling at up to Λγ=5×1017 GeV and Λe=3×1016 GeV for scalar field mass ranges between 10−5 and 10−1eV. Additionally, we also discuss the limits from equivalence principle experiments, and MICROSCOPE final result updates the constrains on the coupling parameters at up to Λγ=7×1022 GeV and Λe=4×1021 GeV for mass ranges ≲10−13eV. These results contribute experimental constraints to relatively unexplored mass regions of light scalar field parameter space and improve upon previous limits in some mass ranges. This work paves the way for long-range Yukawa forces mediated by light scalar fields in future high-precision gravity experiments.

Varying alpha generalized Dirac-Born-Infeld models

We study the cosmological consequences of a class of Dirac-Born-Infeld models, and assess their viability as a candidate for the recent acceleration of the Universe. The model includes both the rolling tachyon field and the generalized Chaplygin gas models as particular limits, and phenomenologically each of these provides a possible mechanism for a deviation of the value of the dark energy equation of state from its canonical (cosmological constant) value. The field-dependent potential that is characteristic of the rolling tachyon also leads to variations of the fine-structure constant $\alpha$, implying that the model can be constrained both by standard cosmological probes and by astrophysical measurements of $\alpha$. Our analysis, using the latest available low-redshfit data and local constraints from atomic clock and weak equivalence principle experiments, shows that the two possible deviations of the dark energy equation of state are constrained to be $\log_{10}{(1+w_0)_V}<-7.85$ and $\log_{10}{(1+w_0)_C}<-0.85$, respectively for the rolling tachyon and Chaplygin components, both being at the $95.4\%$ confidence level (although the latter depends on the choice of priors, in a way that we quantify). Alternatively, the $95.4\%$ confidence level bound on the dimensionless slope of the potential is $\log_{10}{\lambda}<-5.36$. This confirms previous analyses indicating that in these models the potential needs to be extremely flat.

Design and Fabrication of a Differential Electrostatic Accelerometer for Space-Station Testing of the Equivalence Principle.

The differential electrostatic space accelerometer is an equivalence principle (EP) experiment instrument proposed to operate onboard China’s space station in the 2020s. It is designed to compare the spin-spin interaction between two rotating extended bodies and the Earth to a precision of 10−12, which is five orders of magnitude better than terrestrial experiment results to date. To achieve the targeted test accuracy, the sensitive space accelerometer will use the very soft space environment provided by a quasi-drag-free floating capsule and long-time observation of the free-fall mass motion for integration of the measurements over 20 orbits. In this work, we describe the design and capability of the differential accelerometer to test weak space acceleration. Modeling and simulation results of the electrostatic suspension and electrostatic motor are presented based on attainable space microgravity condition. Noise evaluation shows that the electrostatic actuation and residual non-gravitational acceleration are two major noise sources. The evaluated differential acceleration noise is 1.01 × 10−9 m/s2/Hz1/2 at the NEP signal frequency of 0.182 mHz, by neglecting small acceleration disturbances. The preliminary work on development of the first instrument prototype is introduced for on-ground technological assessments. This development has already confirmed several crucial fabrication processes and measurement techniques and it will open the way to the construction of the final differential space accelerometer.

PATCH EFFECT IN CYLINDRICAL GEOMETRY: THE STEP ACCELEROMETER

The actual distribution of charges on a metal does not guarantee its surface to be equipotential because of the impurities and microcrystal structure of the material. This phenomenon, known as patch effect, is responsible for the mutual force and torque between two metallic surfaces at a finite distance. Patch effect is important for any precision measurement whose set-up includes conducting surfaces in a closed proximity to each other. This is particularly true for the Satellite Test of the Equivalence Principle experiment where the differential motion of cylindrical test masses will be used to test the universality of free fall to an unprecedented accuracy of about 1 part in 1018.

Nutational Oscillatory Effect of the Test Body in Space Equivalence Principle Experiments**The project supported by National Natural Science Foundation of China under Grant Nos. 10205005 and 10121503

The significance of quadrupole gravitational force is discussed for test mass in equivalence principle (EP), and the angular moment acting on a cylindrically symmetrical body due to quadrupole force is calculated, which will result in nutational oscillatory effect. The oscillations contain a perturbation with the same frequency of EP violation signal, which is mitigated by two different methods as in Galileo Galilei (GG) mission and μSCOPE. In GG the sensor for readout is sensitive to differential forces in the orbital plane perpendicular to spin axis of test cylinders. In order to mitigate the nutational oscillatory effect, test mass should be rapidly rotated with the spin axis. However, in μSCOPE, the readout sensitive axis is the symmetry axis in the orbital plane. This nutational oscillation will produce a second order effect in the rotation amplitude at twice the signal frequency, and could be subtracted easily, too.

Electrostatic charging of test masses in Equivalence Principle experiments in low-Earth, near-polar orbits

Experiments to test the Equivalence Principle in space are typically suggested for flight in low-Earth, circular, Sun-synchronous orbits at 400–600 km altitude. In these orbits the spacecraft routinely traverses the South Atlantic Anomaly (SAA), where the fluxes of trapped charged particles are enhanced. These particles, together with energetic solar flare protons and galactic cosmic rays, will penetrate the spacecraft structure and develop into a shower of lower energy particles which deposit electrical charge, energy (heat), and momentum on the test masses. Of these, charge leads to the most serious disturbances. Estimates of the charging rates have been computed using the GEANT radiation transport code, in conjunction with realistic proton flux models.

Selection of test mass materials for Equivalence Principle experiments

The aim of STEP is to improve by some five orders of magnitude the test of the validity of the Equivalence Principle (EP) of General Relativity or to detect new interactions possibly violating it. Such do occur in some attempts of unification of gravitation with quantum field theories. The procedures developed for M3 STEP (a possible ESA mission) for optimising the sensitivity by selecting materials as ‘different’ as possible are presented. Parameters like N + Z, N − Z as well as nuclear electrostatic energy density have been used. The experimental requirements for the highly sensitive differential accelerometers are also taken into account.

Principle of the STEP accelerometer design

The superconducting differential accelerometers both for the Equivalence Principle experiment and geodesy within the European STEP mission have common design principles. The test masses are suspended by stable superconducting magnetic levitation. The suspension design makes all the degrees of freedom of the masses stiff, except for the axial differential mode which is made compliant in order to obtain a high intrinsic sensitivity of the differential accelerometer, ⪅ 10 −14 m s −2 Hz −1 2 . Trimming of persistent currents circulating in the levitation system allows to achieve rejection ratios for the unwanted common and radial accelerations ⪆ 10 6. Two separate superconducting circuits couple the axial displacements of the test masses to two SQUIDs. Persistent currents are stored in the two circuits such that one SQUID is only coupled to the differential displacement while the other only senses the common one. By differencing the signal before its detection, one highly reduces the dynamic range needs of the SQUIDs, of the following amplifiers and of the final A/D converters.

Effect of Earth's Rotation on Trajectories of Free-Fall Bodies in Equivalence Principle Experiment**The project supported in part by National Natural Science Foundation of China under Grant Nos. 19835040, 10175070, and 10047004 as well as by NKBRSF (G19990754)

Owing to Earth's rotation a free-fall body would move in an elliptical orbit rather than along a straight line forward to the center of the Earth. In this paper on the basis of the theory for spin-spin coupling between macroscopic rotating bodies we study violation of the equivalence principle from long-distance free-fall experiments by means of a rotating ball and a non-rotating shell. For the free-fall time of 40 s, the difference between the orbits of the two free-fall bodies is of the order of 10−9 cm which could be detected by an SQUID magnetometer because such a magnetometer can be used to measure displacements as small as 10−13 cm.

Gravitational quadrupolar coupling to equivalence principle test masses: the general case

This paper discusses the significance of the quadrupolar gravitational force in the context of test masses destined for use in equivalence principle (EP) experiments, such as STEP and MICROSCOPE. The relationship between quadrupolar gravity and rotational inertia for an arbitrary body is analysed, and the special, gravitational, role of a body's principal axes of inertia is revealed. From these considerations the gravitational quadrupolar force acting on a cylindrically symmetrical body, due to a point-like attracting source mass, is derived in terms of the body's mass quadrupole tensor. The result is shown to be in agreement with that obtained from MacCullagh's formula (as the starting point). The theory is then extended to cover the case of a completely arbitrary solid body, and a compact formulation for the quadrupolar force on such a body is derived. A numerical example of a dumb-bell's attraction to a local point-like gravitational source is analysed using this theory. Close agreement is found between the resulting quadrupolar force on the body and the difference between the net and the monopolar forces acting on it, underscoring the utility of the approach. A dynamical technique for experimentally obtaining the mass quadrupole tensors of EP test masses is discussed, and a means of validating the results is noted.

Dynamical measurements of thegravitational quadrupole coupling to experimental test masses

This paper reports and discusses the first experimental results obtainedusing a novel dynamical method for measuring the inertial imbalanceΔI/I of three reference test masses. Good agreement betweenexperiment and theory is found, and a measurement precision for ΔI/I of better than one part in 104 is demonstrated. The measuredvalues of ΔI/I can be converted with high sensitivity intogravitational quadrupolar coupling, e.g. for assessing masses intended foruse in equivalence principle experiments. Some future developments forquantifying systematic error are discussed, in order to convert thecurrent level of precision into measurement accuracy.

New Limits on the Couplings of Light Pseudoscalars from Equivalence Principle Experiments

The exchange of light pseudoscalar quanta between fermions leads to long-range spin-dependent forces in order g^2, where g is the pseudoscalar-fermion coupling constant. We demonstrate that laboratory bounds on the Yukawa couplings of pseudoscalars to nucleons can be significantly improved using results from recent equivalence principle experiments, which are sensitive to the spin-independent long-range forces that arise in order g^4 from two-pseudoscalar exchange.

Aspherical gravitational monopoles

We show how to construct non-spherically symmetric extended bodies of uniform density behaving exactly as pointlike masses. These “gravitational monopoles” have the following equivalent properties: (i) they generate, outside them, a spherically symmetric gravitational potential M/b x − x ob ; (ii) their interaction energy with an external gravitational potential U( x) is −MU( x o) ; and (iii) all their multipole moments (of order ℓ ⩾ 1) with respect to their centre of mass O vanish identically. The method applies for any number of space dimensions. The free parameters entering the construction are: (1) an arbitrary surface Σ bounding a connected open subset Ω of R 3; (2) the arbitrary choice of the centre of mass O within Ω; and (3) the total volume of the body. An extension of the method allows one to construct homogeneous bodies which are gravitationally equivalent (in the sense of having exactly the same multipole moments) to any given body. Though our method generally assumes that the domain Ω is bounded (which leads to bounded monopoles with closed internal cavities), it can also generate unbounded monopoles, with exponentially decreasing thicknesses at infinity, and cylindriclike internal cavities reachable from infinity. This may be useful for optimizing the shape of test masses in high-precision Equivalence Principle experiments, such as the planned Satellite Test of the Equivalence Principle (STEP). By suppressing the couplings to gravity gradients, one can design, with great flexibility in the choice of shapes, differential accelerometers made of nested bodies, which are (exactly or exponentially) insensitive to all external gravitational disturbances. Alternatively, one can construct nested bodies of arbitrary densities having identical (or proportional) sequences of multipole moments, thereby also suppressing any differential acceleration caused by external gravity gradients.

Equivalence principle and anomalous magnetic moment experiments

We investigate the possibility of testing of the Einstein Equivalence Principle (EEP) using measurements of anomalous magnetic moments of elementary particles. We compute the one loop correction for the $g-2$ anomaly within the class of non metric theories of gravity described by the \tmu formalism. We find several novel mechanisms for breaking the EEP whose origin is due purely to radiative corrections. We discuss the possibilities of setting new empirical constraints on these effects.

Mini-STEP: a minimal satellite test of the equivalence principle experiment

The Mini-STEP concept was conceived from a desire by NASA to reduce the cost of the satellite test of the equivalence principle (STEP) experiment below that of the already downsized Quick STEP concept. The goal was for the total cost, including payload, spacecraft, launch vehicle, reserves and operations, to be in the $50 million range. Stanford University and the Jet Propulsion Laboratory studied this simplified STEP concept between March and June 1995. A similar concept was developed in parallel by the European Space Agency (ESA) as an alternative to the M3 STEP mission.

Principles of STEP accelerometer design

The superconducting differential accelerometers for the equivalence principle and geodesy experiments on the European STEP mission have been designed under common guiding principles. Both accelerometers rely on stable superconducting magnetic levitation. The suspension is stiff against all unwanted degrees of freedom while the axial differential mode is kept compliant to obtain a high intrinsic sensitivity of the differential accelerometer, . The sensitive axis of each component accelerometer is aligned to by adjusting persistent currents in the alignment coils and a restoring force is provided by persistent currents to prevent unwanted rotation about the sensitive axis. The dynamic alignment of the sensitive axes improves the common-mode rejection ratio to . The axial displacements of the two test masses in each differential accelerometer are coupled through two separate superconducting circuits to two DC SQUIDs. Persistent currents are stored in the two circuits such that the acceleration signals are differenced in one circuit and summed in the other before detection by the respective SQUIDs. The signal differencing before detection reduces the dynamic range requirement of the following amplifiers and analogue-to-digital (A/D) converters by orders of magnitude.

The gravitational coupling between longitudinal segments of a hollow cylinder and an arbitrary gravitational source: relevance to the STEP experiment

The gravitational interaction is derived between a solid longitudinal segment cut from a cylinder of uniform density, and an external point mass. The derivation is expressed in terms of the associated Legendre functions , and the parametric form of the coupling coefficients is presented. This theory is applied to the gravitational interaction between a point mass and a finite hollow cylinder, where the cylinder bears a number of `flats' cut into its outer surface. The `flats' are imagined to be regularly spaced in azimuth around the cylinder, each flat being treated as the removal of a solid segment from the full cylinder. Such forms of test mass have been proposed for the satellite test of the equivalence principle (STEP) experiment, since the masses may then be prevented from rotating in azimuth - a factor which is considered to be essential for this experiment. The gravitational theory developed here is applied to such STEP test masses, and two `low gravitational susceptibility' designs for test-mass pairs are considered, having four and six `flats', respectively. An expression for the axial force on such masses is derived which is more than times faster to compute than a Monte Carlo integration of similar accuracy, by virtue of which it is shown that a design with six or more `flats' is to be preferred. This theory is shown to have much wider applicability to gravitational problems involving general segmented cylindrical bodies, including square- and hexagonal-section prisms of finite length (hollow or solid).

Spherical harmonic representation of the gravitational coupling between a truncated sector of a hollow cylinder and an arbitrary gravitational source: Relevance to the STEP experiment

The gravitational interaction between grooves machined in a hollow cylindrical mass of uniform density, and an external point mass, is derived in terms of the Associated Legendre functions, and the parametric form of the coupling coefficients is presented. The cross-sections of the grooves, which are regularly spaced in azimuth, are in the form of truncated sectors of the cylinder's end-faces. This theory is applied to the test-masses for the Satellite Test of the Equivalence Principle (STEP) experiment, for which four grooves have been assumed, and an expression for the axialforce is derived which is more than 104 times faster to compute than a Monte-Carlo integration of similar accuracy. Following this analysis it is suggested that the STEP test-masses should carry at least 6 grooves. This theory has wider application to gravitational problems involving general sectored cylindrical bodies.

Differential gravitational coupling between cylindrically-symmetric, concentric test masses and an arbitrary gravitational source: relevance to the STEP experiment

The gravitational interaction between a point mass and a finite, hollow, thick-walled cylinder is calculated, the axial force is derived, and the parametric form of the coupling coefficients k2p is presented. This theory is applied to the test-masses for the Satellite Test of the Equivalence Principle (STEP) experiment, and an equation is derived for the differential gravitational coupling to these masses which is more than 105 times faster to compute than a Monte-Carlo integration of similar accuracy.

Scientific significance of STEP

The equivalence principle is fundamental to any theory of gravitation. In its weakest and thus most general form, called the weak equivalence principle, the principle states that in a gravitational field all test bodies fall at the same speed, i.e. the ratios of their inertial and passive gravitational masses are the same, regardless of the composition of the bodies. This very fundamental principle is the premise of the two more precise forms of the equivalence principle, namely the Einsteinian and the strong; the latter leading almost directly to Einstein's general relativity theory. The Satellite Test of the Equivalence Principle (STEP) experiment is being proposed to test the weak equivalence principle in the Earth's orbit at the 10 −17 level. Several co-experiments deepen and enrich the project: the Short-Range Equivalence Principle, the Constant of Gravity G, the Geodesy and the Aeronomy Co-Experiment.