### Abstract

We study primordial perturbations generated from quantum fluctuations of an inflaton based on the formalism of stochastic gravity. Integrating out the degree of freedom of the inflaton field, we analyze the time evolution of the correlation function of the curvature perturbation at tree level and compare it with the prediction made by the gauge-invariant linear perturbation theory. We find that our result coincides with that of the gauge-invariant perturbation theory if the e-folding from the horizon-crossing time is smaller than some critical value (∼| slow-roll parameter |-1), which is the case for the scales of the observed cosmological structures. However, in the limit of the superhorizon scale, we find a discrepancy in the curvature perturbation, which suggests that we should include the longitudinal part of the gravitational field in the quantization of a scalar field even in stochastic gravity.

Original language | English |
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Article number | 024013 |

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

Volume | 77 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2008 Jan 9 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematical Physics

### Cite this

**Cosmological density fluctuations in stochastic gravity : Formalism and linear analysis.** / Urakawa, Yuko; Maeda, Keiichi.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Cosmological density fluctuations in stochastic gravity

T2 - Formalism and linear analysis

AU - Urakawa, Yuko

AU - Maeda, Keiichi

PY - 2008/1/9

Y1 - 2008/1/9

N2 - We study primordial perturbations generated from quantum fluctuations of an inflaton based on the formalism of stochastic gravity. Integrating out the degree of freedom of the inflaton field, we analyze the time evolution of the correlation function of the curvature perturbation at tree level and compare it with the prediction made by the gauge-invariant linear perturbation theory. We find that our result coincides with that of the gauge-invariant perturbation theory if the e-folding from the horizon-crossing time is smaller than some critical value (∼| slow-roll parameter |-1), which is the case for the scales of the observed cosmological structures. However, in the limit of the superhorizon scale, we find a discrepancy in the curvature perturbation, which suggests that we should include the longitudinal part of the gravitational field in the quantization of a scalar field even in stochastic gravity.

AB - We study primordial perturbations generated from quantum fluctuations of an inflaton based on the formalism of stochastic gravity. Integrating out the degree of freedom of the inflaton field, we analyze the time evolution of the correlation function of the curvature perturbation at tree level and compare it with the prediction made by the gauge-invariant linear perturbation theory. We find that our result coincides with that of the gauge-invariant perturbation theory if the e-folding from the horizon-crossing time is smaller than some critical value (∼| slow-roll parameter |-1), which is the case for the scales of the observed cosmological structures. However, in the limit of the superhorizon scale, we find a discrepancy in the curvature perturbation, which suggests that we should include the longitudinal part of the gravitational field in the quantization of a scalar field even in stochastic gravity.

UR - http://www.scopus.com/inward/record.url?scp=38049128891&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38049128891&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.77.024013

DO - 10.1103/PhysRevD.77.024013

M3 - Article

AN - SCOPUS:38049128891

VL - 77

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 0556-2821

IS - 2

M1 - 024013

ER -