论文标题
宇宙学扰动的单一悖论
Unitary paradox of cosmological perturbations
论文作者
论文摘要
如果我们将哈勃地平线的Bekenstein-Hawking熵解释为热力学熵，则将曲率扰动的超弯曲模式与subhorizon模式纠缠的超弯曲模式将超过Bekenstein-Hawking-Hawking在某个点结合；我们将其称为宇宙学扰动的统一悖论，该悖论与黑洞类似。为了避免微调问题，必须在通货膨胀时代发生悖论，$ t_c = \ ln（3 \sqrtπ/\ sqrt {2}ε_hh_{inf}）/2H_ {inf}慢速参数和$ h_ {inf} $是通货膨胀期间的哈勃速率。 If we instead accept the fine-tuned problem, then the paradox will occur during the dark energy era at the critical time $t_c'=\ln(3\sqrtπH_{inf}/\sqrt{2}fe^{2N}H_Λ^2)/2H_Λ$, where $H_Λ$ is the Hubble rate dominated by dark energy, $N$ is the total number of e-folds of通货膨胀和$ f $是纯化因子，范围为$ 0 <f <3 \sqrtπh_{inf}/\ sqrt {2} e^{2n}h_λ^2 $。
If we interpret the Bekenstein-Hawking entropy of the Hubble horizon as thermodynamic entropy, then the entanglement entropy of the superhorizon modes of curvature perturbation entangled with the subhorizon modes will exceed the Bekenstein-Hawking bound at some point; we call this the unitary paradox of cosmological perturbations by analogy with black hole. In order to avoid a fine-tuned problem, the paradox must occur during the inflationary era at the critical time $t_c=\ln(3\sqrtπ/\sqrt{2}ε_HH_{inf})/2H_{inf}$ (in Planck units), where $ε_H= -\dot{H}/H^2$ is the first Hubble slow-roll parameter and $H_{inf}$ is the Hubble rate during inflation. If we instead accept the fine-tuned problem, then the paradox will occur during the dark energy era at the critical time $t_c'=\ln(3\sqrtπH_{inf}/\sqrt{2}fe^{2N}H_Λ^2)/2H_Λ$, where $H_Λ$ is the Hubble rate dominated by dark energy, $N$ is the total number of e-folds of inflation, and $f$ is a purification factor that takes the range $0<f<3\sqrtπH_{inf}/\sqrt{2}e^{2N}H_Λ^2$.
