# Consistency relations and conservation of ζ in holographic inflation

## Abstract

It is well known that, in single clock inflation, the curvature perturbation ζ is constant in time on superhorizon scales. In the standard bulk description this follows quite simply from the local conservation of the energy momentum tensor in the bulk. On the other hand, in a holographic description, the constancy of the curvature perturbation must be related to the properties of the RG flow in the boundary theory. Here, we show that, in single clock holographic inflation, the time independence of correlators of ζ follows from the absence of the anomolous dimension of the energy momentum tensor in the boundary theory, and from the so-called consistency relations for vertex functions with a soft leg.

- Authors:

- Departament de Física Fonamental i Institut de Ciències del Cosmos,Universitat de Barcelona,Martí i Franquès 1, 08028 Barcelona (Spain)
- (United States)
- Department of Physics and Astrophysics, Nagoya University,Chikusa, Nagoya 464-8602 (Japan)

- Publication Date:

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

- OSTI Identifier:
- 22572167

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2016; Journal Issue: 10; Other Information: PUBLISHER-ID: JCAP10(2016)030; OAI: oai:repo.scoap3.org:17560; 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; COSMOLOGICAL INFLATION; DISTURBANCES; ENERGY-MOMENTUM TENSOR; HOLOGRAPHIC PRINCIPLE; INFLATIONARY UNIVERSE; PERTURBATION THEORY; QUANTUM COSMOLOGY; RENORMALIZATION; VERTEX FUNCTIONS

### Citation Formats

```
Garriga, Jaume, Institute of Cosmology, Department of Physics and Astronomy, Tufts University,Medford, MA 02155, and Urakawa, Yuko.
```*Consistency relations and conservation of ζ in holographic inflation*. United States: N. p., 2016.
Web. doi:10.1088/1475-7516/2016/10/030.

```
Garriga, Jaume, Institute of Cosmology, Department of Physics and Astronomy, Tufts University,Medford, MA 02155, & Urakawa, Yuko.
```*Consistency relations and conservation of ζ in holographic inflation*. United States. doi:10.1088/1475-7516/2016/10/030.

```
Garriga, Jaume, Institute of Cosmology, Department of Physics and Astronomy, Tufts University,Medford, MA 02155, and Urakawa, Yuko. Tue .
"Consistency relations and conservation of ζ in holographic inflation". United States.
doi:10.1088/1475-7516/2016/10/030.
```

```
@article{osti_22572167,
```

title = {Consistency relations and conservation of ζ in holographic inflation},

author = {Garriga, Jaume and Institute of Cosmology, Department of Physics and Astronomy, Tufts University,Medford, MA 02155 and Urakawa, Yuko},

abstractNote = {It is well known that, in single clock inflation, the curvature perturbation ζ is constant in time on superhorizon scales. In the standard bulk description this follows quite simply from the local conservation of the energy momentum tensor in the bulk. On the other hand, in a holographic description, the constancy of the curvature perturbation must be related to the properties of the RG flow in the boundary theory. Here, we show that, in single clock holographic inflation, the time independence of correlators of ζ follows from the absence of the anomolous dimension of the energy momentum tensor in the boundary theory, and from the so-called consistency relations for vertex functions with a soft leg.},

doi = {10.1088/1475-7516/2016/10/030},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 10,

volume = 2016,

place = {United States},

year = {Tue Oct 18 00:00:00 EDT 2016},

month = {Tue Oct 18 00:00:00 EDT 2016}

}

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