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arXiv 1809.07034gr-qcastro-ph.COhep-phhep-th
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在$Λ$ CDM背景中修正重力与递减的$G_{\rm eff}(z)$的一致性

Consistency of Modified Gravity with a decreasing $G_{\rm eff}(z)$ in a $Λ$CDM background

Radouane Gannouji, Lavrentios Kazantzidis, Leandros Perivolaropoulos, David Polarski

备注：
10 pages, 3 figures
发表信息：
Phys. Rev. D 98, 104044 (2018)
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摘要：

最近的分析\cite{Nesseris:2017vor,Kazantzidis:2018rnb}表明，随着红移而减小的有效牛顿常数$G_{\rm eff}(z)$可以缓解观测到的普朗克15最佳拟合$Λ$ CDM宇宙学背景（{ \it i.e.} Planck 15/ $Λ$ CDM）和相应的$Λ$ CDM背景有利于生长$fσ_8$和弱透镜数据。我们调查的一致性，这种减少$G_{\rm eff}(z)$与一些可行的标量张量模型和$f(R)$理论。我们强调，$f(R)$理论一般不能导致任何宇宙学背景的减少$G_{\rm eff}(z)$。对于标量张量模型，我们推断，在$Λ$ CDM宇宙学背景的上下文中，一个减少的$G_{\rm eff}(z)$是不符合一个大的Brans-Dicke参数$ω_{BD,0}$今天。这种不一致性仍然存在，并放大了幻影暗能量状态方程参数（$w < -1$）的存在。但是，对于$w >-1$可以避免。我们还发现，任何修改后的重力模型与所需的减少$G_{\rm eff}(z)$和$G_{{\rm eff},0}=G$，将有一个特征的签名，在其增长指数$γ$与$0.61\lesssim γ_0\lesssim 0.69$和大斜率$γ_0'$，$0.16\lesssim γ_0'\lesssim 0.4$，这是一个特征的签名减少（与$z$）$G_{\rm eff}(z)<G$小红移。这是一个实质性的偏离今天的准静态行为在$Λ$ CDM与$(γ_0,γ_0')\approx (0.55,-0.02)$。

英文摘要：

Recent analyses \cite{Nesseris:2017vor,Kazantzidis:2018rnb} have indicated that an effective Newton's constant $G_{\rm eff}(z)$ decreasing with redshift may relieve the observed tension between the Planck15 best fit $Λ$CDM cosmological background ({\it i.e.} Planck15/$Λ$CDM) and the corresponding $Λ$CDM background favored by growth $fσ_8$ and weak lensing data. We investigate the consistency of such a decreasing $G_{\rm eff}(z)$ with some viable scalar-tensor models and $f(R)$ theories. We stress that $f(R)$ theories generically can not lead to a decreasing $G_{\rm eff}(z)$ for any cosmological background. For scalar-tensor models we deduce that in the context of a $Λ$CDM cosmological background, a decreasing $G_{\rm eff}(z)$ is not consistent with a large Brans-Dicke parameter $ω_{BD,0}$ today. This inconsistency remains and amplifies in the presence of a phantom dark energy equation of state parameter ($w < -1$). However it can be avoided for $w >-1$. We also find that any modified gravity model with the required decreasing $G_{\rm eff}(z)$ and $G_{{\rm eff},0}=G$, would have a characteristic signature in its growth index $γ$ with $0.61\lesssim γ_0\lesssim 0.69$ and large slopes $γ_0'$, $0.16\lesssim γ_0'\lesssim 0.4$, which is a characteristic signature of a decreasing (with $z$) $G_{\rm eff}(z)<G$ on small redshifts. This is a substantial departure today from the quasi-static behaviour in $Λ$CDM with $(γ_0,γ_0')\approx (0.55,-0.02)$.

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