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严格Brans-Dicke引力理论与最新观测的约束

Constraining An Exact Brans-Dicke gravity theory with Recent Observations

Hassan Amirhashchi, Anil Kumar Yadav

备注：
10 pages, 8 Figures, Unlike the previous version, this one uses Observational Hubble data, the baryon acoustic oscillation distance ratio data as well as cosmic microwave background data from Planck to constrain parameters of the obtained Brans-Dicke model
发表信息：
Physics of the Dark Universe 30 (2020) 100711
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摘要：

本文首先研究带宇宙常数的Brans-Dicke方程在空间平坦Robertson-Walker度规中的精确解。然后利用哈勃观测数据、重子声振荡距离比数据以及普朗克宇宙微波背景数据对所得到的Brans-Dicke模型参数进行约束。为了比较我们的结果，找出偏离广义相对论的量，我们还用同样的数据约束了和谐宇宙学模型。在我们的理论模型中，Brans-Dicke耦合常数被一个新的参数代替，即\textgravedbl标量场密度$Ω_ϕ$ \textacutedbl。因此，作为等价于$ω\to \infty$的$Ω_ϕ\to 0$，恢复了广义相对论。总的来说，我们没有发现与广义相对论的重大偏离。我们的估计显示$Ω_ϕ=0.010^{+0.021}_{-0.012}$在$95\%$置信水平下等同于$ω>1560$。我们还得到了引力常数$\dot{G}/G$的变化率的约束条件，即目前为$1.150\times 10^{-13}yr^{-1}<\dot{G}/G<1.198\times 10^{-13}yr^{-1}$（在$1σ$误差下）。在$68\%$置信水平下，自重组时期以来引力常数的总变化也被约束为$-0.0084<δG/G<-0.0082$。

英文摘要：

In this paper first we study Brans-Dicke equations with the cosmological constant to find an exact solution in the spatially flat Robertson-Walker metric. Then we use Observational Hubble data, the baryon acoustic oscillation distance ratio data as well as cosmic microwave background data from Planck to constrain parameters of the obtained Brans-Dicke model. To compare our results and find out the amount of deviation from general relativity, we also constrain concordance cosmological model using the same data. In our theoretical model the Brans-Dicke coupling constant is replaced by a , say new, parameter namely \textgravedbl scalar field density $Ω_ϕ$\textacutedbl. Therefore, as $Ω_ϕ\to 0$ which is equivalent to $ω\to \infty$ general relativity is recovered. In general, we found no significant deviation from general relativity. Our estimations show $Ω_ϕ=0.010^{+0.021}_{-0.012}$ which is equivalent to $ω>1560$ at $95\%$ confidence level. We also obtained constraint the rate of change of gravitational constant, $\dot{G}/G$, at present time as $1.150\times 10^{-13}yr^{-1}<\dot{G}/G<1.198\times 10^{-13}yr^{-1}$ (at $1σ$ error). The total variation of gravitational constant, since the epoch of recombination, is also constrained as $-0.0084<δG/G<-0.0082$ at $68\%$ confidence level.

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