ParamANN: A Neural Network to Estimate Cosmological Parameters for $\Lambda$CDM Universe Using Hubble Measurements

In this article, we employ a machine learning (ML) approach for the estimations of four fundamental parameters, namely, the Hubble constant ($H_0$), matter ($\Omega_{0m}$), curvature ($\Omega_{0k}$) and vacuum ($\Omega_{0\Lambda}$) densities of non-flat $\Lambda$CDM model. We use $31$ Hubble parameter values measured by differential ages (DA) technique in the redshift interval $0.07 \leq z \leq 1.965$. We create an artificial neural network (ParamANN) and train it with simulated values of $H(z)$ using various sets of $H_0$, $\Omega_{0m}$, $\Omega_{0k}$, $\Omega_{0\Lambda}$ parameters chosen from different and sufficiently wide prior intervals. We use a correlated noise model in the analysis. We demonstrate accurate validation and prediction using ParamANN. ParamANN provides an excellent cross-check for the validity of the $\Lambda$CDM model. We obtain $H_0 = 68.14 \pm 3.96$ $\rm{kmMpc^{-1}s^{-1}}$, $\Omega_{0m} = 0.3029 \pm 0.1118$, $\Omega_{0k} = 0.0708 \pm 0.2527$ and $\Omega_{0\Lambda} = 0.6258 \pm 0.1689$ by using the trained network. These parameter values agree very well with the results of global CMB observations of the Planck collaboration. We compare the cosmological parameter values predicted by ParamANN with those obtained by the MCMC method. Both the results agree well with each other. This demonstrates that ParamANN is an alternative and complementary approach to the well-known Metropolis-Hastings algorithm for estimating the cosmological parameters by using Hubble measurements.