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arXiv 0907.3618astro-ph.COgr-qc
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二阶引力波的宇宙学匹配条件

Cosmological matching conditions for gravitational waves at second order

Frederico Arroja, Hooshyar Assadullahi, Kazuya Koyama, David Wands

摘要:

我们计算了状态方程突变时张量度规扰动的二阶匹配条件。对于大尺度的绝热扰动,匹配超曲面与均匀密度超曲面重合。我们证明了在均匀密度规范中,张量扰动及其时间导数在这种情况下都是连续的。对于非绝热扰动,匹配超曲面不需要与均匀密度超曲面重合,并且均匀密度规范中的张量扰动可以是不连续的。然而,我们表明,在泊松规范的张量扰动和它的时间导数是连续的绝热或非绝热扰动。作为应用,我们求解了大尺度下二阶张量扰动的演化方程,并利用匹配条件将解从暴胀时代演化到辐射时代。我们表明,在辐射时代所产生的自由部分的大规模张量扰动(恒定模式)是慢滚抑制均匀密度和泊松规范。因此,我们的结论是,二阶引力波从慢卷暴胀被抑制。

英文摘要:

We compute the second-order matching conditions for tensor metric perturbations at an abrupt change in the equation of state. For adiabatic perturbations on large scales the matching hypersurface coincides with a uniform-density hypersurface. We show that in the uniform-density gauge both the tensor perturbation and its time-derivative are continuous in this case. For non-adiabatic perturbations, the matching hypersurface need not coincide with a uniform-density hypersurface and the tensor perturbation in the uniform-density gauge may be discontinuous. However, we show that in the Poisson gauge both the tensor perturbation and its time-derivative are continuous for adiabatic or non-adiabatic perturbations. As an application we solve the evolution equation for second-order tensor perturbations on large scales for a constant equation of state and we use the matching conditions to evolve the solutions through the transition from an inflationary era to a radiation era. We show that in the radiation era the resulting free part of the large-scale tensor perturbation (constant mode) is slow-roll suppressed in both the uniform-density and Poisson gauges. Thus, we conclude that second-order gravitational waves from slow-roll inflation are suppressed.

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