Constrain spatial curvature and dark energy with strong lenses and complementary probes: a forecast for next-generation surveys

ABSTRACT Inferring spatial curvature of the Universe with high fidelity is a longstanding interest in cosmology. However, the strong degeneracy between dark energy equation-of-state parameter $w$ and curvature density parameter $\Omega _{\rm K}$ has always been a hurdle for precision measurements of curvature from late-Universe probes. With the imminent commissioning of Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), we demonstrate for the first time, using simulations of stage-IV surveys, the crucial role of time-delay distances from strong gravitational lenses in breaking this degeneracy. Our findings suggest that in non-flat $ow$CDM model, while strong lensing data alone only yield a $\Omega _{\rm K}$ constraint at $\sim \mathcal {O}(10^{-1})$ level, the integration with type Ia supernova and baryon acoustic oscillation data breaks the $w$–$\Omega _{\rm K}$ degeneracy and refines the $\Omega _{\rm K}$ constraint to $\sim \mathcal {O}(10^{-2})$. This surpasses the constraints typically derived from type Ia supernova Hubble diagrams and baryon acoustic oscillation data and is comparable to the constraints obtained from Planck primary cosmic microwave background data. Additionally, we present a non-parametric approach using Gaussian process to avoid parameter-dependence of the expansion history $H(z)$ and achieve similar $\mathcal {O}(10^{-2})$ level constraint on $\Omega _{\rm K}$. This study demonstrates the significant potential of strong gravitational lenses and Stage-IV surveys like LSST to achieve high-fidelity, independent constraints on $\Omega _{\rm K}$, contributing to our understanding of the Universe’s geometry and the dynamics of dark energy.