https://doi.org/10.1140/epjc/s10052-021-09020-z
Regular Article – Theoretical Physics
On the order reduction
Instituto de Física, Universidade de Brasília, Brasília, Brazil
Received:
6
August
2020
Accepted:
2
March
2021
Published online:
15
March
2021
In this work we present an extension of the technique of the order reduction to higher perturbative approximations in an iterative fashion. The intention is also to analyze more carefully the conditions for the validity of the order reduction technique. With this in mind, a few simple situations in which the iterative order reduction converges analytically to the exact solutions are presented as examples. It is discovered that the order reduction as a perturbative iterative technique does not converge in the weak coupling limit as most of the known perturbative schemes, at least when applied to these examples. Also, considering these specific examples, the convergence of the order reduction occurs in strong coupling regimes. As a more realistic case, the order reduction is applied to Starobinsky’s inflationary model is presented. It is verified that the method converges to the inflationary solution in the slow-roll regime.
© The Author(s) 2021
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