Gradient corrections to the oneloop effective action
Abstract
We derive the oneloop effective action to second order in gradients. This expansion of the effective action is useful to study problems in cosmological settings where spatial or time gradients are important, such as bubble nucleation in strong firstorder phase transitions. Assuming spacetime dependent background fields, we work in Wigner space and perform a midpoint gradient expansion, which is consistent with the equation of motion satisfied by the propagator. In particular, we consider the fact that the propagator is nontrivially constrained by an additional equation of motion, obtained from symmetry requirements. We show the calculations for the case of a single scalar field and then generalise the result to the multifield case. While we find a vanishing result in the single field case, the oneloop secondorder gradient corrections can be significant when considering multiple fields. Finally, we apply our result to a simple toy model of two scalar fields with canonical kinetic terms and mass mixing at treelevel.
 Publication:

arXiv eprints
 Pub Date:
 August 2022
 DOI:
 10.48550/arXiv.2208.12142
 arXiv:
 arXiv:2208.12142
 Bibcode:
 2022arXiv220812142C
 Keywords:

 High Energy Physics  Theory;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Phenomenology
 EPrint:
 24 pages, references added in v2