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最小修正引力理论中的暴胀模型

Inflationary model in minimally modified gravity theories

Jakkrit Sangtawee, Khamphee Karwan

备注：
19 pages, 7 figures, references added, accepted for publication in Physical Review D, clarifications of the definition for the curvature perturbation, corrected typos
发表信息：
Phys. Rev. D 104, 023511 (2021)
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摘要：

研究了由最小修正引力理论构造的暴胀模型。研究了$f({\bf H}) \propto {\bf H}^{1+p}$引力形式的MMG理论，其中${\bf H}$是爱因斯坦引力中的哈密顿约束，$p$是常数。在这个引力理论中，如果不引入一个起暴胀子作用的附加标量场，暴胀是很难实现的。我们发现具有指数势的暴胀子可以驱动与爱因斯坦引力不同的优美存在的暴胀。指数势和幂律势的慢滚参数与e折叠数成反比，类似于爱因斯坦引力的情况。我们还发现，对于标量微扰，在超哈勃半径尺度上的共动规范中的曲率微扰在暴胀期间迅速增长，除非$p =0$。对于张量模，扰动的振幅在大尺度上是恒定的，并且扰动的声速可以偏离单位，并且可以随时间变化，这取决于$f({\bf H})$的形式。

英文摘要：

We have investigated inflationary model constructed from minimally modified gravity (MMG) theories. The MMG theory in the form of $f({\bf H}) \propto {\bf H}^{1+p}$ gravity where, ${\bf H}$ is the Hamiltonian constraint in the Einstein gravity and $p$ is constant, has been studied. An inflation is difficult to be achieved in this theory of gravity unless an additional scalar field playing a role of inflaton is introduced in the model. We have found that the inflaton with exponential potential can drive inflation with graceful exist different from the case of Einstein gravity. The slow-roll parameter for both the exponential and the power-law potentials is inversely proportional to number of e-folding similar to the case of the Einstein gravity. We also have found for the scalar perturbation that the curvature perturbation in the comoving gauge on super Hubble radius scales grows rapidly during inflation unless $p =0$. For the tensor modes, the amplitude of the perturbations is constant on large scales, and sound speed of the perturbations can diviate from unity and can vary with time depending on the form of $f({\bf H})$.

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