Cosmological matching conditions for gravitational waves at second order
Cosmological matching conditions for gravitational waves at second order
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DOI：
10.1103/physrevd.80.123526
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发表时间：
2009-12-01
影响因子：
5
通讯作者：
Wands, David
中科院分区：
文献类型：
--
作者：
Arroja, Frederico;Assadullahi, Hooshyar;Wands, David
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，张量微扰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能是不连续的。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，我们解决了大尺度上的二阶张量扰动的演化方程为常数状态方程，我们使用的匹配条件，通过从暴胀时代到辐射时代的过渡演变的解决方案。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，我们得出结论，慢滚暴胀的二阶引力波被抑制。
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 nonadiabatic 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 nonadiabatic 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.