Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics
Scientific paper
2009-07-21
Phys.Rev.D80:123526,2009
Astronomy and Astrophysics
Astrophysics
Cosmology and Extragalactic Astrophysics
19 pages, no figures. v2: References and minor comments added. Published version in PRD
Scientific paper
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.
Arroja Frederico
Assadullahi Hooshyar
Koyama Kazuya
Wands David
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