Distinguishing Coupled Dark Energy Models with Neural Networks

We investigate whether neural networks (NNs) can accurately differentiate between growth-rate data of the large-scale structure (LSS) of the Universe simulated via two models: a cosmological constant and $\mathrm{\Lambda }$ cold dark matter (CDM) model and a tomographic coupled dark energy (CDE) model. We built an NN classifier and tested its accuracy in distinguishing between cosmological models. For our dataset, we generated $f{\sigma }_8(z)$ growth-rate observables that simulate a realistic Stage IV galaxy survey-like setup for both $\mathrm{\Lambda }$CDM and a tomographic CDE model for various values of the model parameters. We then optimised and trained our NN with $\mathtt{\text{Optuna}}$, aiming to avoid overfitting and to maximise the accuracy of the trained model. We conducted our analysis for both a binary classification, comparing between $\mathrm{\Lambda }$CDM and a CDE model where only one tomographic coupling bin is activated, and a multi-class classification scenario where all the models are combined. For the case of binary classification, we find that our NN can confidently (with $>86\mathrm{\%}$ accuracy) detect non-zero values of the tomographic coupling regardless of the redshift range at which coupling is activated and, at a $100\mathrm{\%}$ confidence level, detect the $\mathrm{\Lambda }$CDM model. For the multi-class classification task, we find that the NN performs adequately well at distinguishing $\mathrm{\Lambda }$CDM, a CDE model with low-redshift coupling, and a model with high-redshift coupling, with 99%, 79%, and 84% accuracy, respectively. By leveraging the power of machine learning, our pipeline can be a useful tool for analysing growth-rate data and maximising the potential of current surveys to probe for deviations from general relativity.