Gamma measures spatial curvature per unit mass
The target of the test is the parameterized post-Newtonian (PPN) parameter gamma, which quantifies how much spatial curvature gravity produces per unit rest mass. In General Relativity gamma equals 1. The paper writes the weak-field metric with a Newtonian potential Phi, which drives gravitational time dilation, and a curvature potential Psi, with Psi = gamma times Phi. A deviation of gamma from 1 would therefore signal a departure from GR in how mass bends space.
The regime matters because it is largely untested. The paper notes that GR is well constrained on solar-system and galaxy scales, but poorly constrained where the dimensionless Newtonian potential is around 1e-8. That is the scale the authors compute for a microlensing event whose impact parameter is of order the Einstein radius, roughly GM/(c^2 theta_E D_L). Screening-mechanism theories and MOND-like modifications are cited as reasons this diffuse regime could hide deviations that strong-field tests cannot see.
Two mass estimates separate Phi from Psi
The method rests on a comparison of two masses for the same lens. The first is the lensing mass M_lens^GR, inferred from the microlensing light curve under the assumption of GR; the paper expresses it as (c^2 AU / 4G) times theta_E / pi_E, where theta_E is the Einstein angular radius and pi_E the microlensing parallax. The second is the dynamical mass M_dyn, obtained from Keplerian orbital motion of the binary components, which depends only on the Newtonian potential Phi.
In modified gravity the lensing mass is interpreted as ((1+gamma)/2) times M_dyn. Because M_dyn responds only to Phi while M_lens^GR responds to Phi plus Psi, dividing one by the other isolates gamma. This is why the test needs a binary lens rather than a single lens: only a resolved pair supplies the orbital motion that fixes M_dyn independently.
The authors also check that the microlensing fit itself does not smuggle gamma into the answer. For static and linear-motion binary lens models, the lens equation is dimensionless and gamma does not appear, so the modeling is independent of kinematic equations. Full-orbit models are different: their orbital energy and angular momentum are governed by M_lens^GR, so those events would require gamma as a new free parameter in the fitting code. The paper excludes such events here.
GRAVITY+ makes milliarcsecond orbits trackable
Binary lenses are hard to track because they are faint and their components sit only a few milliarcseconds apart, beyond single-aperture telescopes. Long-baseline optical interferometry supplies that angular resolution, and the paper points to the VLTI, which combines four 8-meter Unit Telescopes or four 1.8-meter Auxiliary Telescopes. The GRAVITY+ upgrade is what the authors say pushes sensitivity and astrometric precision far enough for this measurement.
The demonstration case is ASASSN-22av, the first binary microlensing event with multiple resolved images and a precisely determined M_lens^GR. Its two M-dwarfs are separated by about 3 mas with a total K-band magnitude near 18.5. The authors simulate GRAVITY+ observations using ASPRO2 to estimate uncertainties in squared visibility amplitudes and closure phases, fit a binary model to extract separations, and then use Octofitter to recover orbital parameters. Data are sampled every three years from 2070 to 2097, a cadence chosen to match the long orbital period.
The simulated constraint reaches about 23%
Combining the astrometric orbit with the microlensing mass gives gamma = 1.017 (+0.244/-0.224), a relative precision of about 23%. The central value sits close to the GR prediction of 1, but the uncertainty is the real result: this is a forecast from simulated data, not a measurement from an actual observing campaign.
The error budget explains where the precision comes from and where it is lost. The semi-major axis is tightly constrained, with sigma_a/a about 0.4%. The lens parallax term dominates, with sigma_pi_L/pi_L about 4.4%, because M_dyn depends on pi_L^-3 while M_lens^GR scales as theta_E/pi_E. The authors therefore expect better pi_L measurements to improve gamma directly.
The astrometric residuals also carry a geometric signature. Along right ascension the root-mean-square residual is 22.6 microarcseconds with mean formal uncertainty 89 microarcseconds; along declination it is 98 microarcseconds with mean uncertainty 178 microarcseconds. The larger declination error follows from the Unit Telescope array geometry at the scheduled April observation dates, where the effective baseline along the v-axis is shorter and spatial frequency sampling is sparser.
A larger golden-event sample could reach 3%
The 23% figure is a single-event forecast. The paper projects that a sample of about 68 suitable events would bring the test to roughly 3%, since precision scales inversely with the square root of the number of systems. That projection is built from stated assumptions: the Roman Space Telescope is expected to detect 27,000 microlensing events with impact parameter |u_0| < 1, about 5% of which are binary lens events with distinct caustic crossings, and the authors further assume 5% of that subsample meets the observational requirements.
Those requirements are demanding. A precise M_lens^GR needs high-precision light curves, which set the extraction precision of pi_E and the finite-source parameter rho. A precise M_dyn needs both good astrometry and an accurate source parallax pi_S, which is geometrically coupled to pi_E and pi_L. In practice the lens must not be too faint and the binary components must be well separated.
The authors also flag an alternative route. If gamma were treated as a free parameter in full-orbit fits to high-precision light curves, some events might constrain it without any astrometric data; Gaia16aye and Gaia20fnr are named as candidate targets. Asteroseismic lens masses are mentioned as a further possibility, but the paper notes lenses are mostly solar-like stars or M-dwarfs with radial oscillation amplitudes of order cm/s, which is a severe instrumental demand.
An independent probe of diffuse gravity
The value of this approach is not that it beats solar-system tests of gamma on precision today; at 23% it does not. Its value is that it reaches a potential regime around 1e-8 that those tests do not cover, and it does so without the complex galactic mass models that strong gravitational lensing relies on. Because microlenses are distributed widely across the Galaxy, the method also samples diverse interstellar environments rather than a single line of sight.
The comparison the paper draws is between probes in potential-curvature space: the Sun as constrained by Cassini Shapiro delay, Jupiter via Gaia lensing, strong-lensing galaxies, and the M-dwarf binary ASASSN-22av. Placing the microlensing event on that diagram is the paper's argument for why the regime is distinct rather than merely another point on an existing curve.
The honest boundary is that the headline number is a simulation of one event, with an assumed eccentricity and inclination and an assumed apastron geometry during the event, and with the well-known (omega, Omega) mirror degeneracy left in the astrometric fit because no radial velocity data are available. The 3% projection depends on the stated event-yield assumptions. What the paper establishes is a workable measurement chain and a realistic error budget, not a completed test of GR.
Sources used in this answer
Testing General Relativity with Binary Lens Microlensing Events
Simulated GRAVITY+ astrometry of the binary microlensing event ASASSN-22av, combined with its microlensing lens mass, yields the PPN parameter gamma = 1.017 (+0.244/-0.224), about 23% precision, with ~3% projected from a larger sample of suitable events.