Cosmography with the Double-source-plane Strong Gravitational Lens <tt>AGEL</tt>150745+052256

Abstract Strong gravitational lenses with two background sources at widely separated redshifts are a promising independent probe of cosmological parameters. We can use these systems, known as double-source-plane lenses (DSPLs), to measure the ratio ( β ) of angular-diameter distances of the sources, which is sensitive to the matter density (Ω m ) and the equation-of-state parameter for dark-energy ( w ). However, DSPLs are rare and require high-resolution imaging and spectroscopy for detection, lens modeling, and measuring β . Here, we report only the second DSPL ever used to measure cosmological parameters. We model the DSPL AGEL 150745+052256 from the ASTRO 3D Galaxy Evolution with Lenses ( AGEL ) survey using Hubble Space Telescope/Wide-Field Camera 3 imaging and Keck Cosmic Web Imager spectroscopy. The spectroscopic redshifts for the deflector and two sources in AGEL 1507 are z defl = 0.594, z S1 = 2.163, and z S2 = 2.591. We measure a stellar velocity dispersion of σ obs = 109 ± 27 km s −1 for the nearer source (S1). Using σ obs for the main deflector (from literature) and S1, we test the robustness of our DSPL model. We measure <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>β</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.95</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.010</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.008</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> for AGEL 1507 and infer Ω m <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>=</mml:mo> <mml:mspace width="0.25em"/> <mml:mn>0.3</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.23</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.38</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> for ΛCDM cosmology. Combining AGEL 1507 with the published model of the Jackpot lens improves the precision on Ω m (ΛCDM) and w ( w CDM) by ∼10%. The inclusion of DSPLs significantly improves the constraints when combined with Planck’s cosmic microwave background observations, enhancing the precision on w by 30%. This paper demonstrates the potential constraining power of DSPLs and their complementarity to other standard cosmological probes. Tighter future constraints from larger DSPL samples discovered from ongoing and forthcoming large-area sky surveys would provide insights into the nature of dark energy.