arXiv 0806.06032008-06-17hep-thastro-phgr-qc

具有大非高斯性的约束修正引力

Constraining Modified Gravity with Large non-Gaussianities

Samuel E. Vazquez

备注：: 17 pages, 7 figures, RevTeX format
发表信息：: Phys.Rev.D79:043520,2009
DOI：: 10.1103/PhysRevD.79.043520

摘要：

在写单场暴胀的协变有效作用量时，允许加入高斯-博内耦合和轴子型曲率耦合。这些耦合代表重力的修正，并且是导致四维中的二阶运动方程的独特的高曲率项。在本文中，我们研究的观测后果，这种耦合模型与大的非高斯性。我们的重点是Gauss-Bonnet项。特别是，我们研究了一个有效的作用量的标量拉格朗日是一个一般的函数的暴胀子和它的一阶导数。我们表明，对于大的非高斯性，可以写$f_{NL}$方面只有三个参数。我们还研究了$f_{NL}$的形状，发现它与k-暴胀的形状非常相似。我们表明，高斯-邦纳项增强生产的引力波，并允许一个较小的声速的标量扰动。这反过来又会导致更大的非高斯性，这可能会受到观测的约束。使用当前WMAP对$f_{NL}$和张量/标量比的限制，我们对所有参数施加约束。作为一个例子，我们表明，对于DBI膨胀，高斯-邦纳耦合导致一个有趣的观测窗口，既有大的$f_{NL}$和大振幅的引力波。最后，我们表明，高斯-博内耦合承认一个deSitter阶段与相对论色散关系的标量微扰。

英文摘要：

In writing a covariant effective action for single field inflation, one is allowed to add a Gauss-Bonnet and axion-type curvature couplings. These couplings represent modifications of gravity, and are the unique higher-curvature terms that lead to second order equations of motion in four dimensions. In this paper we study the observational consequences of such couplings for models with large non-gaussianities. Our focus is on the Gauss-Bonnet term. In particular, we study an effective action where the scalar Lagrangian is a general function of the inflaton and its first derivative. We show that, for large non-gaussianities, one can write $f_{NL}$ in terms of only three parameters. The shape of $f_{NL}$ is also studied, and we find that it is very similar to that of k-inflation. We show that the Gauss-Bonnet term enhances the production of gravitational waves, and allows a smaller speed of sound for scalar perturbations. This, in turn, can lead to larger non-gaussianities which can be constrained by observations. Using current WMAP limits on $f_{NL}$ and the tensor/scalar ratio, we put constraints on all parameters. As an example, we show that for DBI inflation, the Gauss-Bonnet coupling leads to an interesting observational window with both large $f_{NL}$ and a large amplitude of gravitational waves. Finally, we show that the Gauss-Bonnet coupling admits a de-Sitter phase with a relativistic dispersion relation for scalar perturbations.

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