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arXiv 1402.6900hep-thastro-ph.COhep-ph
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暴胀期间和暴胀之前产生的真空涨落的演化

Evolution of vacuum fluctuations generated during and before inflation

Hajime Aoki, Satoshi Iso, Yasuhiro Sekino

备注：
54 pages, 12 figures; v2: references added; v3:version publised in PRD
发表信息：
Phys. Rev. D 89, 103536 (2014)
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摘要：

我们计算的期望值的能量动量张量的时间演化的最小耦合无质量标量场在宇宙时空中，与暗能量的应用。我们首先研究了从暴胀到现在的演化，固定Bunch-Davies初始条件。量子场的能量密度在物质主导（MD）周期中演化为$ρ\sim 3(H_I H)^2 /32 π^2 $，其中$H_I$和$H$是暴胀期间和每个时刻的哈勃参数。其状态方程$w=ρ/p$在辐射占优期由负值变为$w=1/3$，在MD期由$1/3$变为$w=0$。然后，我们考虑可能的影响普朗克宇宙，这可能已经存在的通货膨胀之前，假设有另一个通货膨胀与哈勃参数$H_P (> H_I)$。在这种情况下，波长大于当前视界半径的模式主要被放大，并且量子场的能量密度在MD周期中随着时间增长为$ρ\sim (a/a_0)(H_P H)^2/32$，其中$a$和$a_0$是每个时间和当前的标度因子。因此，如果$H_P$是普朗克尺度$M_P$的量级，那么$ρ$就变得与目前的临界密度$3(M_P H)^2$相当。在自由场近似下，普通暴胀前产生的长波涨落对$ρ$的贡献为$w=-1/3$。我们提到了一种可能性，即相互作用进一步放大了能量密度并改变了状态方程。

英文摘要：

We calculate the time evolution of the expectation value of the energy-momentum tensor for a minimally-coupled massless scalar field in cosmological spacetimes, with an application to dark energy in mind. We first study the evolution from inflation until the present, fixing the Bunch-Davies initial condition. The energy density of a quantum field evolves as $ρ\sim 3(H_I H)^2 /32 π^2 $ in the matter-dominated (MD) period, where $H_I$ and $H$ are the Hubble parameters during inflation and at each moment. Its equation of state, $w=ρ/p$, changes from a negative value to $w=1/3$ in the radiation-dominated period, and from $1/3$ to $w=0$ in the MD period. We then consider possible effects of a Planckian universe, which may have existed before inflation, by assuming there was another inflation with the Hubble parameter $H_P (> H_I)$. In this case, modes with wavelengths longer than the current horizon radius are mainly amplified, and the energy density of a quantum field grows with time as $ρ\sim (a/a_0)(H_P H)^2/32$ in the MD period, where $a$ and $a_0$ are the scale factors at each time and at present. Hence, if $H_P$ is of the order of the Planck scale $M_P$, $ρ$ becomes comparable to the critical density $3(M_P H)^2$ at the present time. The contribution to $ρ$ from the long wavelength fluctuations generated before the ordinary inflation has $w=-1/3$ in the free field approximation. We mention a possibility that interactions further amplify the energy density and change the equation of state.

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