arXiv 1006.28762010-06-15hep-thgr-qc

Kähler模膨胀与WMAP7

Kähler moduli inflation and WMAP7

Sunggeun Lee, Soonkeon Nam

备注：: 22 pages, 6 figures
发表信息：: Int.J.Mod.Phys.A26:1073-1096,2011
DOI：: 10.1142/S0217751X1105155X

摘要：

通过通量紧化研究了IIB型弦论中特定模型的暴胀势。作为具体的模型，我们研究了几种情况下，内部空间是加权射影空间。我们考虑的模型有两个、三个或四个凯勒模量。的凯勒模起着暴胀子领域的作用，我们考虑的情况下，只有一个模的行为作为暴胀子领域。对于具有两个以上模的情况，我们选择对角基来表示卡-丘体积，它可以写成四圈的函数。通过多个模的组合，我们可以将多维问题表示为有效的一维问题。在大容量的情况下，这三个模型的潜力是相同的类型。通过取模量与体积之间关系的特定极限，势被简化为引起暴胀的更简单的势。作为一个玩具模型，我们首先考虑简单势。我们计算了每个暴胀势的慢滚参数$ε$、$η$和$ξ$。然后，通过与最近公布的7年WMAP数据的比较，我们检验了这些势是否给出了合理的谱指数$n_s$和它们的运行$α_s$。对于这两个模型，我们看到合理的频谱指数的e-折叠$47<N_e<61$的数量。相反，通过插入观察到的7年WMAP数据，我们看到玩具模型的势给出了必要的e折叠数，而Kähler模量的势给出了小得多的e折叠数。最后，我们看到，两个模型不产生合理的值的运行的光谱指数。

英文摘要：

Inflationary potentials are investigated for specific models in type IIB string theory via flux compactification. As concrete models, we investigate several cases where the internal spaces are weighted projective spaces. The models we consider have two, three, or four Kähler moduli. The Kähler moduli play a role of inflaton fields and we consider the cases where only one of the moduli behaves as the inflaton field. For the cases with more than two moduli, we choose the diagonal basis for the expression of the Calabi-Yau volume, which can be written down as a function of four-cycle. With the combination of multiple moduli, we can express the multi-dimensional problem as an effective one-dimensional problem. In the large volume scenario, the potentials of these three models turn out to be of the same type. By taking the specific limit of the relation between the moduli and the volume, the potentials are reduced to simpler ones which induce inflation. As a toy model we first consider the simple potential. We calculate the slow roll parameters $ε$, $η$ and $ξ$ for each inflationary potential. Then, we check whether the potentials give reasonable spectral indices $n_s$ and their running $α_s$'s by comparing with the recently released seven-year WMAP data. For both models, we see reasonable spectral indices for the number of e-folding $47<N_e<61$. Conversely, by inserting the observed seven-year WMAP data, we see that the potential of the toy model gives requisite number of e-folds while the potential of the Kähler moduli gives much smaller number of e-folding. Finally, we see that two models do not produce reasonable values of the running of the spectral index.

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