Model-independent constraints on cosmic curvature: implication from the future gravitational wave observation DECIGO

Abstract

A model-independent test of the cosmic curvature parameter ${\Omega }_k$ is very important in cosmology. In order to estimate cosmic curvature from cosmological probes like standard candles, one has to be able to measure the luminosity distance $D_L(z)$, it's derivative with respect to redshift $D_L^{\prime }(z)$ and independently know the expansion rate $H(z)$ at the same redshift. In this paper, we study how such an idea could be implemented with the future generation of space-based DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO), in combination with cosmic chronometers providing cosmology-independent $H(z)$ data. Our results show that for the Hubble diagram of simulated DECIGO data acting as a new type of standard siren, it would be able to constrain cosmic curvature with the precision of $\Delta {\Omega }_k=0.09$ with the currently available sample of 31 measurements of Hubble parameters. In the framework of the third generation ground-based gravitational wave detectors, the spatial curvature is constrained to be $\Delta {\Omega }_k=0.13$ for Einstein Telescope (ET). More interestingly, compared to other approaches aiming for model-independent estimations of spatial curvature, our analysis also achieves the reconstruction of the evolution of ${\Omega }_k(z)$, in the framework of a model-independent method of Gaussian processes (GP) without assuming a specific form. Therefore, one can expect that the newly emerged gravitational wave astronomy can become useful in local measurements of cosmic curvature using distant sources.

arXiv comment7 pages, 8 figures, Accepted for publication in EPJC

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