[论文解读] Cosmological Interpretations of Consistency Relation of Inflation Models with Current CMB Data

Cheng Cheng, Qing-Guo Huang+2 more|arXiv (Cornell University)|Jul 25, 2012

Cosmology and Gravitation Theories被引用 1

一句话总结

本研究利用七年WMAP、BICEP以及WMAP的$f_{\text{NL}}^{\text{equil.}}$、$f_{\text{NL}}^{\text{orth.}}$数据，检验了暴胀一致性关系$r = -8c_s n_t$，结果表明小声速$c_s$可显著收紧对张量标量比$r$的约束：当$c_s = 0.01$时，$r < 0.09$（95.4%置信水平），且在99.7%置信水平下排除了$c_s \lesssim 0.01$的区域；而单场慢滚暴胀模型（$c_s = 1$）在68.3%置信水平下略显不被支持。

ABSTRACT

We make a comprehensive investigation of the observational effect of the inflation consistency relation. We focus on the general single-field inflation model with the consistency relation $r=-8c_s n_t$, and investigate the observational constraints of sound speed $c_s$ by using the Seven-Year WMAP data, the BICEP tensor power spectrum data, and the constraints on $f_{ m NL}^{ m equil.}$ and $f_{ m NL}^{ m orth.}$ from the Five-Year WMAP observations. We find that the constraints on the tensor-to-scalar ratio $r$ is much tighter if $c_s$ is small, since a large tilt $n_t$ is strongly constrained by the observations. We obtain $r<0.37, 0.27$ and 0.09 ($dn_s/d\ln k=0$) for $c_s$=1, 0.1 and 0.01 models at 95.4% confidence level. When taking smaller values of $c_s$, the positive correlation between $r$ and $n_s$ also leads to slightly tighter constraint on the upper bound of $n_s$, while the running of scalar spectral index $dn_s/d\ln k$ is generally unaffected. For the sound speed $c_s$, it is not well constrained if only the CMB power spectrum data is used, while the constraints are obtainable by taking $f_{ m NL}^{ m equil.}$ and $f_{ m NL}^{ m orth.}$ priors into account. With the constraining data of $f_{ m NL}^{ m equil.}$ and $f_{ m NL}^{ m orth.}$, we find that, $c_s\lesssim 0.01$ region is excluded at 99.7% CL, and the $c_s=1$ case (the single-field slow-roll inflation) is slightly disfavored at 68.3% CL. In addition, the inclusion of $f_{ m NL}^{ m equil.}$ and $f_{ m NL}^{ m orth.}$ into the analysis can improve the constraints on $r$ and $n_s$. We further discuss the implications of our constraints on the test of inflation models.

研究动机与目标

• 评估单场暴胀模型中暴胀一致性关系$r = -8c_s n_t$的观测影响。
• 利用当前CMB数据（包括张量功率谱与非高斯性参数）约束声速$c_s$。
• 评估$f_{\text{NL}}^{\text{equil.}}$与$f_{\text{NL}}^{\text{orth.}}$先验对$r$、$n_s$与$c_s$约束的影响。
• 在当前观测限制下，评估单场暴胀模型的可行性，尤其关注$c_s$相关的约束。

提出的方法

• 分析七年WMAP的温度与极化功率谱，以约束$r$、$n_s$与$dn_s/d\ln k$。
• 引入BICEP对张量标量比$r$的测量数据，以收紧对$r$与$n_t$的约束。
• 将五年WMAP对等效型非高斯性（$f_{\text{NL}}^{\text{equil.}}$）与正交型非高斯性（$f_{\text{NL}}^{\text{orth.}}$）的约束作为先验，用于约束$c_s$。
• 应用一致性关系$r = -8c_s n_t$，将$r$、$n_t$与$c_s$关联，从而获得基于$c_s$的$r$的约束上限。
• 在68.3%、95.4%与99.7%置信水平下进行统计分析，推导出$r$、$n_s$与$c_s$的上限。
• 比较不同$c_s$值（1、0.1、0.01）下的约束结果，评估对声速的敏感性。

实验结果

研究问题

• RQ1 在一致性关系$r = -8c_s n_t$下，当前CMB数据如何约束张量标量比$r$，且该约束如何随声速$c_s$变化？
• RQ2 引入$f_{\text{NL}}^{\text{equil.}}$与$f_{\text{NL}}^{\text{orth.}}$先验后，对$c_s$、$r$与$n_s$的约束有何影响？
• RQ3 当声速$c_s$较小时，$r$与标量谱指数$n_s$的上限如何变化？
• RQ4 当前观测数据在多大程度上支持单场慢滚暴胀模型（$c_s = 1$）？
• RQ5 当结合CMB功率谱数据与非高斯性先验时，$c_s$的约束如何演变？

主要发现

• 当$c_s = 0.01$时，张量标量比的上限为$r < 0.09$（95.4%置信水平）。
• 随着$c_s$减小，$r$的约束显著收紧：在95.4%置信水平下，$c_s = 1$时$r < 0.37$，$c_s = 0.1$时$r < 0.27$，$c_s = 0.01$时$r < 0.09$。
• 当同时引入$f_{\text{NL}}^{\text{equil.}}$与$f_{\text{NL}}^{\text{orth.}}$先验时，$c_s \lesssim 0.01$的区域在99.7%置信水平下被排除。
• 在应用非高斯性先验后，单场慢滚暴胀模型（$c_s = 1$）在68.3%置信水平下略显不被支持。
• 引入$f_{\text{NL}}^{\text{equil.}}$与$f_{\text{NL}}^{\text{orth.}}$先验可显著改善对$r$与$n_s$的约束，尤其在小$c_s$时更为明显。
• 标量谱指数的运行$dn_s/d\ln k$基本不受$c_s$相关约束的影响，表明该参数具有较强的鲁棒性。