Measurement on the cosmic curvature using the Gaussian process method

Abstract

Inflation predicts that the Universe is spatially flat. The Planck 2018 measurements of the cosmic microwave background anisotropy favour a spatially closed universe at more than 2σ confidence level. We use model independent methods to study the issue of cosmic curvature. The method reconstructs the Hubble parameter H(z) from cosmic chronometers data with the Gaussian process method. The distance modulus is then calculated with the reconstructed function H(z) and fitted by type Ia supernovae data. Combining the cosmic chronometers and type Ia supernovae data, we obtain Ωk0h2 = 0.102 ± 0.066 which is consistent with a spatially flat universe at the 2σ confidence level. By adding the redshift space distortions data to the type Ia supernovae data with a proposed novel model independent method, we obtain $\Omega _{k0}h^2=0.117^{+0.058}_{-0.045}$ and no deviation from ΛCDM model is found.

Constraining the curvature density parameter in cosmology

“…Our work is similar to the recent works by Yang & Gong [33] and Dhawan, Alsing & Vagonzzi [34], but there are quite a few differences to list. Yang and Gong [33], Dhawan, Alsing and Vagnozzi [34] have used the Pantheon compilation by Scolnic et al [31] in their analysis.…”

“…Our work is similar to the recent works by Yang & Gong [33] and Dhawan, Alsing & Vagonzzi [34], but there are quite a few differences to list. Yang and Gong [33], Dhawan, Alsing and Vagnozzi [34] have used the Pantheon compilation by Scolnic et al [31] in their analysis. However, in this work we have utilized the very recent redshift corrected version of Pantheon compilation by Steinhardt, Sneppen and Sen [68].…”

“…Wang, Ma and Xia [32] employed a machine learning algorithm called Artificial Neural Network (ANN) to constrain Ω k0 using data from CC, SN-Ia and GWs. Recently, Yang and Gong [33] constrained the Ω k0 h 2 using CC-H(z), Pantheon SN-Ia and RSD data where h = H0 100 km Mpc −1 s −1 is the dimensionless Hubble parameter at the present epoch. Non-parametric spatial curvature inference using CC and Pantheon data was performed by Dhawan, Alsing and Vagnozzi [34].…”

“…We use observational data more recent than most of these investigations, but the major difference is that we include a wider variety of data in combination, measuring different features of the evolution. We also include a section where the RSD dataset which has mostly eluded the attention so far, except the work of Yang and Gong [33] in the reconstruction of Ω k0 h 2 despite its utmost relevance in this connection, as the growth of perturbations has to be consistent with the spatial curvature.…”

Model-independent constraints on $Ω_m$ and $H(z)$ from the link between geometry and growth

“…The literature already hosts a number of examples of the possible uses of Gaussian processes to test certain aspects of the present cosmological paradigm in model-agnostic ways. For example, one can find tests for the model dependence of the 𝐻 0 (Gómez-Valent & Amendola 2018; Cai et al 2020;Liao et al 2020;Bonilla et al 2021) and 𝑆 8 (Benisty 2021) tensions, for the non-zero curvature of space-time (Vagnozzi et al 2021;Yang & Gong 2021), as well as tests for the density and the equation of state of dark energy (Gerardi et al 2019;Zhang & Li 2018). More closely related to the topic of this work, in Perenon et al (2021) Gaussian processes were used to study the statistical correlations between the expansion history, cosmological distances, and the linear growth rate without appealing to the physical relationships between the three functions.…”