Inflationary perturbations with Lifshitz scaling
Inflationary perturbations with Lifshitz scaling
复制标题
Lifshitz 尺度的通货膨胀扰动
DOI：
10.1088/1475-7516/2019/03/034
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发表时间：
2019
影响因子：
6.4
通讯作者：
Urakawa Yuko
中科院分区：
文献类型：
--
作者：
Arai Shun;Sibiryakov Sergey;Urakawa Yuko
引力自由度在高能量下可能服从利弗希茨标度，而不是洛伦兹不变性，就像霍洛维茨娃的量子引力方案中所发生的那样。我们研究的后果，这一建议的原始扰动在通货膨胀产生的频谱。打破四维同胚（Diff）不变性下降到叶理保持Diff在Hoelava-Lifshitz（HL）重力导致出现的标量自由度的重力部门，khronon，它描述了动态的时间叶理。人们可以天真地认为，暴胀子和khronon之间的混合将危及超级哈勃尺度下绝热扰动的守恒。这确实发生在理论的可投射版本中。相比之下，我们发现，在HL引力的不可投射版本，khronon获得的有效质量远大于哈勃尺度之前的哈勃穿越时间和绝热曲率扰动源的暴胀子波动的两倍。结果表明，在超哈勃尺度下，绝热微扰的行为与有效的单场系统相同，其谱在时间上是守恒的。通过对暴胀子色散关系的修正，将Lifshitz标度印刻在暴胀子的功率谱中。指出了张量标量比与原初引力波谱倾斜之间的相容关系的破坏，并认为它可以提供暴胀时代洛伦兹破坏的信号。
Instead of Lorentz invariance, gravitational degrees of freedom may obey Lifshitz scaling at high energies, as it happens in Hořava's proposal for quantum gravity. We study consequences of this proposal for the spectra of primordial perturbations generated at inflation. Breaking of 4D diffeomorphism (Diff) invariance down to the foliation-preserving Diff in Hořava-Lifshitz (HL) gravity leads to appearance of a scalar degree of freedom in the gravity sector, khronon, which describes dynamics of the time foliation. One can naively expect that mixing between inflaton and khronon will jeopardize conservation of adiabatic perturbations at super Hubble scales. This indeed happens in the projectable version of the theory. By contrast, we find that in the non-projectable version of HL gravity, khronon acquires an effective mass which is much larger than the Hubble scale well before the Hubble crossing time and decouples from the adiabatic curvature perturbation ζ sourced by the inflaton fluctuations. As a result, at super Hubble scales the adiabatic perturbation ζ behaves as in an effectively single field system and its spectrum is conserved in time. Lifshitz scaling is imprinted in the power spectrum of ζ through the modified dispersion relation of the inflaton. We point out violation of the consistency relation between the tensor-to-scalar ratio and the spectral tilt of primordial gravitational waves and suggest that it can provide a signal of Lorentz violation in inflationary era.