论文标题
一环星系功率谱的Fisher矩阵：测量膨胀和增长率而不假设宇宙学模型
Fisher matrix for the one-loop galaxy power spectrum: measuring expansion and growth rates without assuming a cosmological model
论文作者
论文摘要
我们引入了一种方法，将Fisher基质预测扩展到轻度非线性尺度，而无需选择宇宙学模型。我们利用标准的非线性扰动理论来对反对者进行补充，并假设可以用标准蜡烛准确地测量宇宙距离。我们没有选择特定模型，而是将线性功率谱和增长率参数为几个$ k $和$ z $ bin。我们表明，除了偏见功能之外，我们还可以获得扩展率$ e（z）= h（z）/h_0 $的模型无关约束和增长率$ f（k，z）$。我们将该技术应用于$ 0.6 \ le z \ le 1.8 $的欧几里得和DESI公共规格，并表明从$ k _ {\ rm max} = 0.1 $ to $ k _ {\ rm max} = 0.1 $至$ 0.2 \，h $/mpc时的收益大约为二倍至三ford到ninefold左右，而将$ __到达$ ___________________________________ 0.3 \，h $/mpc。绝对用$ k _ {\ rm max} = 0.2 \，h/$ mpc，每个$ z $ -shell：$Δz= 0.1 $，5-6％的Euclid for Euclid for $ΔZ= 0.2-0-0.3 $。如果将增长率$ f $视为$ k $独立的，这将提高到1-2％。增长率本身通常具有弱化的约束，除非认为是$ k $独立的，在这种情况下，收益与$ e（z）$的收益相似，并且在每个$ z $ bin上可以达到5-15％的不确定性。我们还讨论了忽略非线性校正如何对限制产生很大的影响，即使对于$ k _ {\ rm max} = 0.1 \，h/$ mpc，除非有人对非线性参数具有独立的强有力的先验信息。
We introduce a methodology to extend the Fisher matrix forecasts to mildly non-linear scales without the need of selecting a cosmological model. We make use of standard non-linear perturbation theory for biased tracers complemented by counterterms, and assume that the cosmological distances can be measured accurately with standard candles. Instead of choosing a specific model, we parametrize the linear power spectrum and the growth rate in several $k$ and $z$ bins. We show that one can then obtain model-independent constraints of the expansion rate $E(z)=H(z)/H_0$ and the growth rate $f(k,z)$, besides the bias functions. We apply the technique to both Euclid and DESI public specifications in the range $0.6\le z \le 1.8$ and show that the gain in precision when going from $k_{\rm max} = 0.1$ to $0.2\,h$/Mpc is around two- to threefold, while it reaches four- to ninefold when extending to $k_{\rm max} = 0.3\,h$/Mpc. In absolute terms, with $k_{\rm max}=0.2\,h/$Mpc, one can reach high precision on $E(z)$ at each $z$-shell: 8-10% for DESI with $Δz=0.1$, 5-6% for Euclid with $Δz=0.2-0.3$. This improves to 1-2% if the growth rate $f$ is taken to be $k$-independent. The growth rate itself has in general much weaker constraints, unless assumed to be $k$-independent, in which case the gain is similar to the one for $E(z)$ and uncertainties around 5-15% can be reached at each $z$-bin. We also discuss how neglecting the non-linear corrections can have a large effect on the constraints even for $k_{\rm max}=0.1\,h/$Mpc, unless one has independent strong prior information on the non-linear parameters.
