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arXiv 2004.08544gr-qc
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由标量场的物理势重建引力的广义标量张量理论

Generalized scalar-tensor theory of gravity reconstruction from physical potentials of a scalar field

I. V. Fomin, S. V. Chervon, A. V. Tsyganov

摘要:

我们描述了如何重建广义标量张量引力(GSTG)理论,它承认的物理类型的潜力的精确解。我们考虑的宇宙暴胀模型的基础上GSTG与非最小耦合的(非正则)标量场的Ricci标量。这些模型的分析方法的基础是哈勃参数$H$和非最小耦合$F=1+δF$的函数$H\propto\sqrt{F}$之间的先验指定关系。对爱因斯坦引力$δF$的偏离导致相应的势$δV$偏离常值,并修正了来自纯de Sitter指数展开的动力学。我们分析了模型的指数幂律演化的标度因子,我们找到的影响方程的非最小耦合,选择它的特殊形式,对潜在的和动能。这样的考虑使我们能够将物理势代入得到的方程,然后计算非最小耦合函数和动力学项,定义GSTG参数。利用这种方法,我们重建了多项式势、指数势、Higgs势、Higgs-Starobinsky势和Coleman-Weinberg势的GSTG。特别注意我们支付的宇宙学扰动的参数,并证明对应获得的解决方案,从普朗克观测数据。

英文摘要:

We describe how to reconstruct generalized scalar-tensor gravity (GSTG) theory, which admits exact solutions for physical type of the potentials. Our consideration deals with cosmological inflationary models based on GSTG with non-minimal coupling of a (non-canonical) scalar field to the Ricci scalar. The basis of proposed approach to the analysis of these models is a priori specified relation between the Hubble parameter $H$ and a function of non-minimal coupling $F=1+δF$ as $H\propto\sqrt{F}$. Deviations from Einstein gravity $δF$ induce a corresponding deviations of the potential $δV$ from a constant value and modify the dynamics from pure de Sitter exponential expansion. We analyze the models with exponential power-law evolution of the scale factor and we find the equations of influence of non-minimal coupling, choosing it in the special form, on the potential and kinetic energies. Such consideration allows us to substitute the physical potential into obtained equations and then to calculate the non-minimal coupling function and kinetic term that are define GSTG parameters. With this method, we reconstruct GSTG for polynomial, exponential, Higgs, Higgs-Starobinsky and Coleman-Weinberg potentials. Special attention we pay to parameters of cosmological perturbations and prove correspondence obtained solutions to observational data from Planck.

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