Null test of the cosmic curvature usingH(z)and supernovae data

Abstract

We introduce a model-independent approach to the null test of the cosmic curvature which is geometrically related to the Hubble parameter H(z) and luminosity distance dL(z). Combining the independent observations of H(z) and dL(z), we use the model-independent smoothing technique, Gaussian processes, to reconstruct them and determine the cosmic curvature Ω (0) K in the null test relation. The null test is totally geometrical and does not assume any cosmological model. We show that the cosmic curvature Ω (0) K = 0 is consistent with current observational data sets, falling within the 1σ limit. To demonstrate the effect on the precision of the null test, we produce a series of simulated data of the models with different Ω 98.80.Es, 98.80Jk

New Model-Independent Method to Test the Curvature of The universe

“…Therefore, with GP method, we don't need any prior cosmological model. There is a good python package for GP method called Gapp developed by Seikel et al (2012a) which was used in many works (Seikel et al 2012b;Bilicki & Seikel 2012;Cai et al 2016). It can reconstruct the function as long as observed data was input.…”

“…However, the large uncertainty in gravitational lens system restricts its efficiency on constraining the curvature (Räsänen et al 2015). Another important model-independent method was proposed in Clarkson, Cortês, & Bassett (2007), by comparing the Hubble parameter H(z) and the derivative function of transverse comoving distance d M gained from d A , which has been used in many works (Clarkson et al 2008;Yahya et al 2014;Li et al 2014;Cai et al 2016) (hereafter, C07 method). The basis of this method is that one can determine the curvature by combining measurements of the Hubble parameter H(z) and the…”

Revisiting Studies of the Statistical Property of a Strong Gravitational Lens System and Model-Independent Constraint on the Curvature of the Universe

“…However, these constrains on Ω k are obtained by using a model-dependent method. Therefore, constraints on curvature using the model-independent method is still very attractive in the literature (Bernstein 2006;Clarkson et al 2007;Oguri et al 2012;Li et al 2014;Räsänen et al 2015;Cai et al 2016;Yu & Wang 2016). For instance, in Bernstein (2006), based on the basic distance sum rule, they used the weak lensing to test the curvature in a model-independent way.…”

Measuring the cosmic proper distance from fast radio bursts

“…As we described above, we used the open-source Python package Gapp to apply the GP. This code is widely used (Cai, Guo, & Yang 2016;Yu & Wang 2016). The kernel function in this code is…”