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arXiv 1112.0502astro-ph.COgr-qc
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具有指数势的典型(暴胀)宇宙学模型的精确解

On exact solutions for quintessential (inflationary) cosmological models with exponential potentials

Ester Piedipalumbo, Paolo Scudellaro, Giampiero Esposito, Claudio Rubano

摘要:

我们首先研究具有最小耦合标量场和指数势的暗能量模型,承认宇宙学方程的精确解:实际上,事实证明,对于这类势,爱因斯坦场方程表现出替代拉格朗日,并且是完全可积和可分的(即,至少通过求积可以对系统进行解析积分)。我们分析这样的解决方案,特别是讨论当他们是兼容的宇宙的后期时间典型的膨胀。作为进一步的问题,我们讨论了这种典型的标量场如何与暴胀相联系,为这类势建立了一个典型的暴胀情景:事实上,从暴胀到后期指数典型尾部的过渡存在一个kination周期,这是这类理论模型不可或缺的组成部分。所有这些考虑也都通过将辐射纳入模型来完成。

英文摘要:

We first study dark energy models with a minimally-coupled scalar field and exponential potentials, admitting exact solutions for the cosmological equations: actually, it turns out that for this class of potentials the Einstein field equations exhibit alternative Lagrangians, and are completely integrable and separable (i.e. it is possible to integrate the system analytically, at least by quadratures). We analyze such solutions, especially discussing when they are compatible with a late time quintessential expansion of the universe. As a further issue, we discuss how such quintessential scalar fields can be connected to the inflationary phase, building up, for this class of potentials, a quintessential inflationary scenario: actually, it turns out that the transition from inflation toward late-time exponential quintessential tail admits a kination period, which is an indispensable ingredient of this kind of theoretical models. All such considerations have also been done by including radiation into the model.

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