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Current and future large-scale structure surveys aim to constrain cosmological parameters with unprecedented precision by analyzing vast amounts of data. This imposes a pressing need to develop fast and accurate methods for computing the matter power spectrum $P(k)$, or equivalently, the matter transfer function $T(k)$. In previous works, we introduced precise fitting formulas for these quantities within the standard cosmological model, including extensions such as the presence of massive neutrinos and modifications of gravity. However, these formulations overlooked a key characteristic imprinted in $P(k)$: the baryon acoustic oscillation signal. Here, we leverage our understanding of the well-known physics behind this oscillatory pattern to impose constraints on our genetic algorithm, a machine learning technique. By employing this ``physics-informed'' approach, we introduce an expression that accurately describes the matter transfer function with sub-percent mean accuracy. The high interpretability of the output allows for straightforward extensions of this formulation to other scenarios involving massive neutrinos and modifications of gravity. We anticipate that this formula will serve as a competitive fitting function for $P(k)$, meeting the accuracy requirements essential for cosmological analyses., Comment: 15 pages, 6 figures. Comments are very welcome!

We propose a novel approach using neural networks (NNs) to differentiate between cosmological models, especially in the case where they are nested and the additional model parameters are close to zero, making it difficult to discriminate them with traditional approaches. Our method complements Bayesian analyses for cosmological model selection, which heavily depend on the chosen priors and average the unnormalized posterior over potentially large prior volumes. By analyzing simulated realistic data sets of the growth rate of the large scale structure (LSS) of the Universe, based on current galaxy-clustering survey specifications, for the cosmological constant and cold dark matter ($\Lambda$CDM) model and the Hu-Sawicki $f(R)$ model, we demonstrate the potential of NNs to enhance the extraction of meaningful information from cosmological LSS data. We find that the NN can successfully distinguish between $\Lambda$CDM and the $f(R)$ models, by predicting the correct model with approximately $97\%$ overall accuracy, thus demonstrating that NNs can maximise the potential of current and next generation surveys to probe for deviations from general relativity., Comment: 8 pages, 7 figures, comments are welcome