Null test for cosmic curvature using Gaussian process

Abstract

The cosmic curvature , which determines the spatial geometry of the universe, is an important parameter in modern cosmology. Any deviation from would have a profound impact on the primordial inflation paradigm and fundamental physics. In this work, we adopt a cosmological model-independent method to test whether deviates from zero. We use the Gaussian process to reconstruct the reduced Hubble parameter and the derivative of the distance from observational data and then determine with a null test relation. The cosmic chronometer (CC) Hubble data, baryon acoustic oscillation (BAO) Hubble data, and supernovae Pantheon sample are considered. Our result is consistent with a spatially flat universe within the domain of reconstruction , at the confidence level. In the redshift interval , the result favors a flat universe, while at , it tends to favor a closed universe. In this sense, there is still a possibility for a closed universe. We also carry out the null test of the cosmic curvature at using the simulated gravitational wave standard sirens, CC+BAO, and redshift drift Hubble data. The result indicates that in the future, with the synergy of multiple high-quality observations, we can tightly constrain the spatial geometry or exclude the flat universe.