### Abstract

We generalize Starobinskiǐ's stochastic technique to the theory of a massless, minimally coupled scalar interacting with a massless fermion in a locally de Sitter geometry. The scalar is an "active" field that can engender infrared logarithms. The fermion is a passive field that cannot cause infrared logarithms but which can carry them, and which can also induce new interactions between the active fields. The procedure for dealing with passive fields is to integrate them out, then stochastically simplify the resulting effective action following Starobinskiǐ. Because Yukawa theory is quadratic in the fermion this can be done explicitly using the classic solution of Candelas and Raine. We check the resulting stochastic formulation against an explicit two loop computation. We also derive a nonperturbative, leading log result for the stress tensor. Because the scalar effective potential induced by fermions is unbounded below, backreaction from this model might dynamically cancel an arbitrarily large cosmological constant.

Original language | English |
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Article number | 044019 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 74 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2006 Aug 23 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*74*(4), [044019]. https://doi.org/10.1103/PhysRevD.74.044019

}

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 74, no. 4, 044019. https://doi.org/10.1103/PhysRevD.74.044019

**Leading log solution for inflationary Yukawa theory.** / Miao, Shun-Pei; Woodard, R. P.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Leading log solution for inflationary Yukawa theory

AU - Miao, Shun-Pei

AU - Woodard, R. P.

PY - 2006/8/23

Y1 - 2006/8/23

N2 - We generalize Starobinskiǐ's stochastic technique to the theory of a massless, minimally coupled scalar interacting with a massless fermion in a locally de Sitter geometry. The scalar is an "active" field that can engender infrared logarithms. The fermion is a passive field that cannot cause infrared logarithms but which can carry them, and which can also induce new interactions between the active fields. The procedure for dealing with passive fields is to integrate them out, then stochastically simplify the resulting effective action following Starobinskiǐ. Because Yukawa theory is quadratic in the fermion this can be done explicitly using the classic solution of Candelas and Raine. We check the resulting stochastic formulation against an explicit two loop computation. We also derive a nonperturbative, leading log result for the stress tensor. Because the scalar effective potential induced by fermions is unbounded below, backreaction from this model might dynamically cancel an arbitrarily large cosmological constant.

AB - We generalize Starobinskiǐ's stochastic technique to the theory of a massless, minimally coupled scalar interacting with a massless fermion in a locally de Sitter geometry. The scalar is an "active" field that can engender infrared logarithms. The fermion is a passive field that cannot cause infrared logarithms but which can carry them, and which can also induce new interactions between the active fields. The procedure for dealing with passive fields is to integrate them out, then stochastically simplify the resulting effective action following Starobinskiǐ. Because Yukawa theory is quadratic in the fermion this can be done explicitly using the classic solution of Candelas and Raine. We check the resulting stochastic formulation against an explicit two loop computation. We also derive a nonperturbative, leading log result for the stress tensor. Because the scalar effective potential induced by fermions is unbounded below, backreaction from this model might dynamically cancel an arbitrarily large cosmological constant.

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U2 - 10.1103/PhysRevD.74.044019

DO - 10.1103/PhysRevD.74.044019

M3 - Article

VL - 74

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 4

M1 - 044019

ER -