Resolving the Hubble Tension Using Differential Age, Cosmic Chronometry, and Machine Learning Techniques

We present a machine learning based pipeline for the identification and age dating of cosmic chronometers in order to calculate the Hubble parameter 𝐻 (𝑧) and constrain the Hubble constant 𝐻0 using the differential age-redshift relation. This is with the goal of minimising the Hubble tension by using a method that is not dependent on the uncertainties associated with late Universe measurements of the distance ladder whilst avoiding the model uncertainties associated with early Universe methods. The pipeline predicts ages of galaxies in the Galaxy and Mass Assembly survey using a physically motivated artificial neural network (ANN). The ANN consists of four hidden layers with an input layer that takes 14 equivalent widths from GAMA as input features. It is trained using GAMA median mass-weighted ages generated from the spectral energy distribution fitting software MagPhys in order to make predictions of galaxy age. The ANN is able to produce ages with a mean squared error (MSE), mean absolute error (MAE) and 𝑅2 score of 𝑀𝑆𝐸 = 0.020, 𝑀 𝐴𝐸 = 0.108 and 𝑅2 = 0.530 respectively. Cosmic chronometers are identified with a combined convolutional autoencoder (CAE) and K-means clustering method. The CAE takes the photometric 𝑢−band images and produces loss values that the clustering algorithm uses in combination with 𝑢 − 𝑔 and 𝑔 − 𝑟 colours as the basis to classify galaxies as cosmic chronometers. Our K-means algorithm successfully classifies cosmic chronometers from normal galaxies with an accuracy, precision and recall of 0.819, 0.816, and 0.824 respectively. Finally, we evaluate the pipeline by calculating 𝐻 (𝑧) and 𝐻0 using the results of the previous methods. Our final value of 𝐻 (𝑧 = 0.19) = 71.65 ± 49.46kms−1Mpc−1 whereas a less strict sample of CCs yields 𝐻 (𝑧 = 0.18) = 84.66 ± 55.7kms−1Mpc−1 which are in agreement with both early and late measurements with the caverat that there are large uncertainties associated with the measurements which we thoroughly discuss and evaluate.