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 $\tt{ReACT}$ in the $k$range $\left(0.01  2.5\right) \, h \mathrm{Mpc}^{1} $ and redshift bins $\left(0.1,0.478,0.783,1.5\right)$ with Euclidlike noise. The first network classifies spectra into five labels including $\Lambda$CDM, $f(R)$, $w$CDM, DvaliGabadazePorrati (DGP) gravity and a "random" class whereas the second is trained to distinguish $\Lambda$CDM from non$\Lambda$CDM. Both networks achieve a comparable training, validation and test accuracy of $\sim 95\%$. Each network is also capable of detecting deviations from $\Lambda$CDM that were not included in the training set, demonstrated with spectra generated using the growthindex $\gamma$. We then quantify the constraining power of each network by computing the smallest deviation from $\Lambda$CDM such that the noiseaveraged non$\Lambda$CDM classification probability is at least $2\sigma$, finding these bounds to be $f_{R0} \lesssim 10^{7}$, $\Omega_{rc} \lesssim 10^{2} $, $1.05 \lesssim w_0 \lesssim 0.95 $, $0.2 \lesssim w_a \lesssim 0.2 $, $0.52 \lesssim \gamma \lesssim 0.59 $. The bounds on $f(R)$ can be improved by training a specialist network to distinguish solely between $\Lambda$CDM and $f(R)$ power spectra which can detect a nonzero $f_{R0}$ at $\mathcal{O}\left(10^{8}\right)$ with a confidence $>2\sigma$. We expect that further developments, such as the inclusion of smaller length scales or additional extensions to $\Lambda$CDM, will only improve the potential of BNNs to detect new physics using cosmological datasets.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.03992
 arXiv:
 arXiv:2012.03992
 Bibcode:
 2020arXiv201203992M
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 19+9 pages, 16 figures, code available at https://github.com/Mik3M4n/BaCoN, data available at https://doi.org/10.5281/zenodo.4309918. v2: matches version accepted for publication in PRD. v3: title matches published version