Seeking New Physics in Cosmology with Bayesian Neural Networks: Dark
  Energy and Modified Gravity
  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 Euclid-like noise.
The first network classifies spectra into five labels including $\Lambda$CDM,
$f(R)$, $w$CDM, Dvali-Gabadaze-Porrati (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 growth-index $\gamma$. We then
quantify the constraining power of each network by computing the smallest
deviation from $\Lambda$CDM such that the noise-averaged 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 non-zero $f_{R0}$ 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.
