SENSITIVITY OF THE PARAMETRIZED POST NEWTONIAN PARAMETER γPPN TO COSMOLOGICAL MODELS IN STRONG GRAVITATIONAL LENSING

Yasmin Mufidanisa (Master Program of Physics, Department of Physics, Faculty of Science, Institut Teknologi Sumatera, Jl. Terusan Ryacudu, Jati Agung, Lampung Selatan 35365, Indonesia)
Agustina Widiyani (Master Program of Physics, Department of Physics, Faculty of Science, Institut Teknologi Sumatera, Jl. Terusan Ryacudu, Jati Agung, Lampung Selatan 35365, Indonesia)
Azrul Sulaiman Karim Pohan (Master Program of Physics, Department of Physics, Faculty of Science, Institut Teknologi Sumatera, Jl. Terusan Ryacudu, Jati Agung, Lampung Selatan 35365, Indonesia)
Ikah Ning Prasetiowati Permanasari (Master Program of Physics, Department of Physics, Faculty of Science, Institut Teknologi Sumatera, Jl. Terusan Ryacudu, Jati Agung, Lampung Selatan 35365, Indonesia)
Annisa Novia Indra Putri (Atmospheric and Planetary Science Department, Faculty of Science, Institut Teknologi Sumatera, Jl. Terusan Ryacudu, Jati Agung, Lampung Selatan 35365, Indonesia)

Indonesian Physical Review
Vol. 9 No. 2 (2026)

The parametrized post-Newtonian (PPN) parameter γ measures spacetime curvature per unit gravitational potential, with general relativity (GR) predicting γ = 1 exactly. Strong gravitational lensing at galactic scales offers a cosmological-scale avenue for estimating γ beyond solar system experiments; however, such estimates depend sensitively on angular diameter distances, which in turn depend on the assumed cosmological model. We perform a controlled sensitivity analysis using 40 Sloan Lens ACS (SLACS) strong lensing systems with catalogue SIE Einstein masses MEin fixed under a fiducial ΛCDM cosmology, while varying the background model across ΛCDM, wCDM, Dynamical Dark Energy (DDE), and Early Dark Energy (EDE), all adopting Planck 2018 parameters. Angular diameter distances are computed by numerically integrating the model-specific expansion function E(z), so that any variation in recovered γPPN reflects cosmological distance geometry rather than a gravitational signal. ΛCDM, wCDM, and DDE yield effectively degenerate estimates: mean γ ≈ 1.08 ± 0.020, with inter-model spread of only ~0.5–0.7%. EDE yields a systematically lower mean γ = 0.903 ± 0.019, approximately 16.3% below ΛCDM and below the GR prediction of unity. This shift arises because EDE elevates H(z) near matter-radiation equality (z ~ 3000), compressing angular diameter distances by ~10% relative to ΛCDM; since the γ estimator scales as DL × DS / DLS, this compression propagates into a downward shift in recovered γ. The total inter-model range of ~17% substantially exceeds statistical uncertainties in targeted lensing studies, establishing cosmological model selection as a leading systematic in lensing-based γ measurements. EDE in particular introduces a distinctive geometric signature not captured by late-time dark energy parameterizations. Because MEin is fixed under ΛCDM, these findings should not be interpreted as evidence for or against GR, but as a geometric sensitivity analysis within a specific set of modeling assumptions.