# Conservation of ζ with radiative corrections from heavy field

## Abstract

In this paper, we address a possible impact of radiative corrections from a heavy scalar field χ on the curvature perturbation ζ. Integrating out χ, we derive the effective action for ζ, which includes the loop corrections of the heavy field χ. When the mass of χ is much larger than the Hubble scale H, the loop corrections of χ only yield a local contribution to the effective action and hence the effective action simply gives an action for ζ in a single field model, where, as is widely known, ζ is conserved in time after the Hubble crossing time. Meanwhile, when the mass of χ is comparable to H, the loop corrections of χ can give a non-local contribution to the effective action. Because of the non-local contribution from χ, in general, ζ may not be conserved, even if the classical background trajectory is determined only by the evolution of the inflaton. In this paper, we derive the condition that ζ is conserved in time in the presence of the radiative corrections from χ. Namely, we show that when the dilatation invariance, which is a part of the diffeomorphism invariance, is preserved at the quantum level, the loop correctionsmore »

- Authors:

- Department of Physics, Kyoto University,Kyoto, 606-8502 (Japan)
- (Japan)
- Department of Physics and Astrophysics, Nagoya University,Nagoya 464-8602 (Japan)
- (United States)

- Publication Date:

- Sponsoring Org.:
- SCOAP3, CERN, Geneva (Switzerland)

- OSTI Identifier:
- 22572093

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2016; Journal Issue: 06; Other Information: PUBLISHER-ID: JCAP06(2016)020; OAI: oai:repo.scoap3.org:15917; cc-by Article funded by SCOAP3. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACTION INTEGRAL; CORRELATION FUNCTIONS; COSMOLOGICAL INFLATION; DISTURBANCES; INFLATIONARY UNIVERSE; MASS; MATHEMATICAL EVOLUTION; PERTURBATION THEORY; RADIATIVE CORRECTIONS; SCALAR FIELDS; WARD IDENTITY

### Citation Formats

```
Tanaka, Takahiro, Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto, 606-8502, Urakawa, Yuko, and School of Natural Sciences, Institute for Advanced Study,Olden Lane, Princeton, NJ 08540.
```*Conservation of ζ with radiative corrections from heavy field*. United States: N. p., 2016.
Web. doi:10.1088/1475-7516/2016/06/020.

```
Tanaka, Takahiro, Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto, 606-8502, Urakawa, Yuko, & School of Natural Sciences, Institute for Advanced Study,Olden Lane, Princeton, NJ 08540.
```*Conservation of ζ with radiative corrections from heavy field*. United States. doi:10.1088/1475-7516/2016/06/020.

```
Tanaka, Takahiro, Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto, 606-8502, Urakawa, Yuko, and School of Natural Sciences, Institute for Advanced Study,Olden Lane, Princeton, NJ 08540. Wed .
"Conservation of ζ with radiative corrections from heavy field". United States.
doi:10.1088/1475-7516/2016/06/020.
```

```
@article{osti_22572093,
```

title = {Conservation of ζ with radiative corrections from heavy field},

author = {Tanaka, Takahiro and Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto, 606-8502 and Urakawa, Yuko and School of Natural Sciences, Institute for Advanced Study,Olden Lane, Princeton, NJ 08540},

abstractNote = {In this paper, we address a possible impact of radiative corrections from a heavy scalar field χ on the curvature perturbation ζ. Integrating out χ, we derive the effective action for ζ, which includes the loop corrections of the heavy field χ. When the mass of χ is much larger than the Hubble scale H, the loop corrections of χ only yield a local contribution to the effective action and hence the effective action simply gives an action for ζ in a single field model, where, as is widely known, ζ is conserved in time after the Hubble crossing time. Meanwhile, when the mass of χ is comparable to H, the loop corrections of χ can give a non-local contribution to the effective action. Because of the non-local contribution from χ, in general, ζ may not be conserved, even if the classical background trajectory is determined only by the evolution of the inflaton. In this paper, we derive the condition that ζ is conserved in time in the presence of the radiative corrections from χ. Namely, we show that when the dilatation invariance, which is a part of the diffeomorphism invariance, is preserved at the quantum level, the loop corrections of the massive field χ do not disturb the constant evolution of ζ at super Hubble scales. In this discussion, we show the Ward-Takahashi identity for the dilatation invariance, which yields a consistency relation for the correlation functions of the massive field χ.},

doi = {10.1088/1475-7516/2016/06/020},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 06,

volume = 2016,

place = {United States},

year = {Wed Jun 08 00:00:00 EDT 2016},

month = {Wed Jun 08 00:00:00 EDT 2016}

}