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arXiv 1609.05069gr-qcastro-ph.COhep-th
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多场通货膨胀中的措施

Measures in Mutlifield Inflation

Richard Grumitt, David Sloan

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16 pages, 3 figures
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摘要：

我们研究了具有二次势的多场暴胀模型的经典动力学。这样的模型被证明在相空间中有膨胀吸引子，与膨胀过程中宇宙体积因子的相空间轨迹的拉伸一致。使用与哈密顿系统相关的辛结构，我们在相空间上形成了一个测度，正如Gibbons，Hawking和Stewart最初提出的那样。这是用来计算的观测协议的概率下限（即概率的模型给出的光谱指数在区域$n_{s}=0.968\pm{0.006}$）为相等的质量二和三场模型与二次电位，分别给出的值为0.982和0.997。我们推导出一般的$N$场模型的测量，并认为，随着场的数量接近无穷大，观测一致性的概率接近1。

英文摘要：

We examine the classical dynamics of multifield inflation models with quadratic potentials. Such models are shown to have inflationary attractors in phase space, consistent with the stretching of phase space trajectories along the volume factor of the universe during inflation. Using the symplectic structure associated with Hamiltonian systems we form a measure on the phase space, as initially proposed by Gibbons, Hawking and Stewart. This is used to calculate lower bounds on the probabilities of observational agreement (i.e. the probability the model gives a value for the spectral index within the region $n_{s}=0.968\pm{0.006}$) for equal mass two and three field models with quadratic potentials, giving values of 0.982 and 0.997 respectively. We derive the measure for a general $N$-field model and argue that as the number of fields approaches infinity, the probability of observational agreement approaches one.

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