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arXiv 2005.12747gr-qcastro-ph.COhep-th
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原初宇宙学扰动在广义非形式变换下的变换

Transformation of Primordial Cosmological Perturbations Under the General Extended Disformal Transformation

Allan L. Alinea, Takahiro Kubota

摘要:

原始的宇宙学扰动是暴胀和随后的动力学过程所培育的种子,最终导致了现在的宇宙。本文研究了规范不变标量和张量扰动在广义非形式变换$g_{μν} \rightarrow A(X,Y,Z)g_{μν} + Φ_μΦ_ν$下的行为,其中$X \equiv -\tfrac{1}{2}ϕ^{;μ}ϕ_{;μ}, Y \equiv ϕ^{;μ}X_{;μ}, Z \equiv X^{;μ}X_{;μ} $和$Φ_μ\equiv Cϕ_{;μ} + DX_{;μ}$,$C$和$D$是$(ϕ,X,Y,Z)$的一般泛函.我们发现在这种变换下,张量扰动是不变的。另一方面,标量曲率扰动只接受了保形项的修正;它至少在线性阶以下与非形式项无关。在完整的Horndeski理论的框架内,校正项变成线性依赖于规范不变的同动密度扰动及其一阶时间导数。在超视界极限,所有这些修正项消失,只剩下原来的标量曲率扰动。换句话说,在完全Horndeski理论的背景下,它在超视界极限的一般扩展非形式变换下是不变的。我们的工作包括一系列关于原始宇宙学扰动的变换或不变性的研究,在我们的一般扩展非形式变换下推广了他们的结果。

英文摘要:

Primordial cosmological perturbations are the seeds that were cultivated by inflation and the succeeding dynamical processes, eventually leading to the current Universe. In this work, we investigate the behavior of the gauge-invariant scalar and tensor perturbations under the general extended disformal transformation, namely, $g_{μν} \rightarrow A(X,Y,Z)g_{μν} + Φ_μΦ_ν$, where $X \equiv -\tfrac{1}{2}ϕ^{;μ}ϕ_{;μ}, Y \equiv ϕ^{;μ}X_{;μ}, Z \equiv X^{;μ}X_{;μ} $ and $Φ_μ\equiv Cϕ_{;μ} + DX_{;μ}$, with $C$ and $D$ being a general functional of $(ϕ,X,Y,Z)$. We find that the tensor perturbation is invariant under this transformation. On the other hand, the scalar curvature perturbation receives a correction due the conformal term only; it is independent of the disformal term at least up to linear order. Within the framework of the full Horndeski theory, the correction terms turn out to depend linearly on the gauge-invariant comoving density perturbation and the first time-derivative thereof. In the superhorizon limit, all these correction terms vanish, leaving only the original scalar curvature perturbation. In other words, it is invariant under the general extended disformal transformation in the superhorizon limit, in the context of full Horndeski theory. Our work encompasses a chain of research studies on the transformation or invariance of the primordial cosmological perturbations, generalizing their results under our general extended disformal transformation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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