Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2002-09-05
Phys.Rev. D68 (2003) 025004
Physics
High Energy Physics
High Energy Physics - Phenomenology
17 pages, 9 figures, revised version with extra section 4.2 including second order calculation
Scientific paper
10.1103/PhysRevD.68.025004
We show how the linear delta expansion, as applied to the slow-roll transition in quantum mechanics, can be recast in the closed time-path formalism. This results in simpler, explicit expressions than were obtained in the Schr\"odinger formulation and allows for a straightforward generalization to higher dimensions. Motivated by the success of the method in the quantum-mechanical problem, where it has been shown to give more accurate results for longer than existing alternatives, we apply the linear delta expansion to four-dimensional field theory. At small times all methods agree. At later times, the first-order linear delta expansion is consistently higher that Hartree-Fock, but does not show any sign of a turnover. A turnover emerges in second-order of the method, but the value of $<\hat{\Phi}^2(t)>$ at the turnover is larger that that given by the Hartree-Fock approximation. Based on this calculation, and our experience in the corresponding quantum-mechanical problem, we believe that the Hartree-Fock approximation does indeed underestimate the value of $<\hat{\Phi}^2(t)>$ at the turnover. In subsequent applications of the method we hope to implement the calculation in the context of an expanding universe, following the line of earlier calculations by Boyanovsky {\sl et al.}, who used the Hartree-Fock and large-N methods. It seems clear, however, that the method will become unreliable as the system enters the reheating stage.
Bedingham Daniel J.
Jones Hugh F.
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