论文标题
通过贝叶斯神经网络寻求宇宙学的新物理学：黑暗能量和改良的重力
Seeking New Physics in Cosmology with Bayesian Neural Networks: Dark Energy and Modified Gravity
论文作者
论文摘要
我们研究了贝叶斯神经网络（BNN）在暗物质功率谱中检测新物理学的潜力，在这里集中于不断发展的暗能量和对一般相对论的修改。在引入了一种新技术来量化BNN中的分类不确定性之后，我们在$ k $ -range $ \ weft（0.01-2.5 \ right）中使用公开代码$ \ tt {react} $生成的模拟物质功率谱训练了两个BNN， $ \ left（0.1,0.478,0.783,1.5 \ right）$，带有类似欧几里德的噪声。第一个网络将光谱分类为五个标签，包括$λ$ cdm，$ f（r）$，$ w $ cdm，dvali-gabadaze-porrati（DGP）重力和“随机”类，而第二个则经过培训可以区分$λ$ cdm与non-un-$λ$ CDM。两个网络都获得了$ \ sim 95 \％$的可比培训，验证和测试准确性。每个网络还能够检测到与$λ$ CDM的偏差，这些差异未包含在训练集中，这是使用使用增长索引$γ$生成的光谱证明的。然后，我们通过计算从$λ$ CDM的最小偏差来量化每个网络的约束功率，以使噪声平均的非$ $ $ cdm CDM分类概率至少为$2σ$，发现这些界限为$ f_ {r0} \ lyssim 10^{-7} $，$ω____________________{$ω \ Lessim W_0 \ Lessim 0.95 $，$ -0.2 \ Lesssim W_A \ Lessim 0.2 $，$ 0.52 \sillsimγ\ Lessim 0.59 $。 $ f（r）$的界限可以通过训练专业网络来改进，以仅区分$λ$ cdm和$ f（r）$ power Spectra，该频谱可以检测到$ f_ {r0} $ at $ \ mathcal {o} {o} \ left（10^{ - 8} \ right）$ fusited $>2σ$ $>2σ$。我们希望进一步的发展，例如包含较小的长度尺度或额外扩展到$λ$ CDM，只会提高BNN使用宇宙学数据集检测新物理学的潜力。
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 $Λ$CDM, $f(R)$, $w$CDM, Dvali-Gabadaze-Porrati (DGP) gravity and a "random" class whereas the second is trained to distinguish $Λ$CDM from non-$Λ$CDM. Both networks achieve a comparable training, validation and test accuracy of $\sim 95\%$. Each network is also capable of detecting deviations from $Λ$CDM that were not included in the training set, demonstrated with spectra generated using the growth-index $γ$. We then quantify the constraining power of each network by computing the smallest deviation from $Λ$CDM such that the noise-averaged non-$Λ$CDM classification probability is at least $2σ$, finding these bounds to be $f_{R0} \lesssim 10^{-7}$, $Ω_{rc} \lesssim 10^{-2} $, $-1.05 \lesssim w_0 \lesssim 0.95 $, $-0.2 \lesssim w_a \lesssim 0.2 $, $0.52 \lesssim γ\lesssim 0.59 $. The bounds on $f(R)$ can be improved by training a specialist network to distinguish solely between $Λ$CDM and $f(R)$ power spectra which can detect a non-zero $f_{R0}$ at $\mathcal{O}\left(10^{-8}\right)$ with a confidence $>2σ$. We expect that further developments, such as the inclusion of smaller length scales or additional extensions to $Λ$CDM, will only improve the potential of BNNs to detect new physics using cosmological datasets.
