Seeking new physics in cosmology with Bayesian neural networks: Dark energy and modified gravity

Abstract

We study the potential of Bayesian neural networks (BNNs) to detect new physics in the dark matter power spectrum, concentrating here on evolving dark energy and modifications to general relativity. After introducing a new technique to quantify classification uncertainty in BNNs, we train two BNNs on mock matter power spectra produced using the publicly available code react in the $k$ range $(0.01\ensuremath{-}2.5)\text{ }\text{ }h{\mathrm{Mpc}}^{\ensuremath{-}1}$ and redshift bins (0.1, 0.478, 0.783, 1.5) with Euclid-like noise. The first network classifies spectra into five labels including $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$, $f(R)$, $w\mathrm{CDM}$, Dvali-Gabadadze-Porrati gravity and a ``random'' class, whereas the second is trained to distinguish $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ from non-$\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. Both networks achieve a comparable training, validation and test accuracy of $\ensuremath{\sim}95%$. Each network is also capable of correctly classifying spectra with deviations from $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ that were not included in the training set, demonstrated with spectra generated using the growth index $\ensuremath{\gamma}$. To obtain an indication of the BNNs classification capability, we compute the smallest deviation from $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ such that the noise-averaged non-$\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ classification probability is at least 95% according to our estimated error quantification, finding these bounds to be ${f}_{R0}\ensuremath{\lesssim}{10}^{\ensuremath{-}7}$, ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{rc}}\ensuremath{\lesssim}{10}^{\ensuremath{-}2}$, $\ensuremath{-}1.05\ensuremath{\lesssim}{w}_{0}\ensuremath{\lesssim}0.95$, $\ensuremath{-}0.2\ensuremath{\lesssim}{w}_{a}\ensuremath{\lesssim}0.2$, and $0.52\ensuremath{\lesssim}\ensuremath{\gamma}\ensuremath{\lesssim}0.59$. The bounds on $f(R)$ can be improved by training a specialist network to distinguish solely between $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ and $f(R)$ power spectra which can detect a nonzero ${f}_{R0}$ at $\mathcal{O}({10}^{\ensuremath{-}8})$. We expect that further developments, such as the inclusion of smaller length scales or additional extensions to $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$, will only improve the potential of BNNs to indicate the presence of new physics in cosmological datasets, regardless of the underlying theory.