# On the initial state and consistency relations

## Abstract

We study the effect of the initial state on the consistency conditions for adiabatic perturbations. In order to be consistent with the constraints of General Relativity, the initial state must be diffeomorphism invariant. As a result, we show that initial wavefunctional/density matrix has to satisfy a Slavnov-Taylor identity similar to that of the action. We then investigate the precise ways in which modified initial states can lead to violations of the consistency relations. We find two independent sources of violations: i) the state can include initial non-Gaussianities; ii) even if the initial state is Gaussian, such as a Bogoliubov state, the modified 2-point function can modify the q-vector → 0 analyticity properties of the vertex functional and result in violations of the consistency relations.

- Authors:

- Center for Particle Cosmology, Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104 (United States)

- Publication Date:

- OSTI Identifier:
- 22375890

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2014; Journal Issue: 09; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; DENSITY MATRIX; FUNCTIONS; GENERAL RELATIVITY THEORY; VECTORS

### Citation Formats

```
Berezhiani, Lasha, and Khoury, Justin, E-mail: lashaber@sas.upenn.edu, E-mail: jkhoury@sas.upenn.edu.
```*On the initial state and consistency relations*. United States: N. p., 2014.
Web. doi:10.1088/1475-7516/2014/09/018.

```
Berezhiani, Lasha, & Khoury, Justin, E-mail: lashaber@sas.upenn.edu, E-mail: jkhoury@sas.upenn.edu.
```*On the initial state and consistency relations*. United States. doi:10.1088/1475-7516/2014/09/018.

```
Berezhiani, Lasha, and Khoury, Justin, E-mail: lashaber@sas.upenn.edu, E-mail: jkhoury@sas.upenn.edu. Mon .
"On the initial state and consistency relations". United States.
doi:10.1088/1475-7516/2014/09/018.
```

```
@article{osti_22375890,
```

title = {On the initial state and consistency relations},

author = {Berezhiani, Lasha and Khoury, Justin, E-mail: lashaber@sas.upenn.edu, E-mail: jkhoury@sas.upenn.edu},

abstractNote = {We study the effect of the initial state on the consistency conditions for adiabatic perturbations. In order to be consistent with the constraints of General Relativity, the initial state must be diffeomorphism invariant. As a result, we show that initial wavefunctional/density matrix has to satisfy a Slavnov-Taylor identity similar to that of the action. We then investigate the precise ways in which modified initial states can lead to violations of the consistency relations. We find two independent sources of violations: i) the state can include initial non-Gaussianities; ii) even if the initial state is Gaussian, such as a Bogoliubov state, the modified 2-point function can modify the q-vector → 0 analyticity properties of the vertex functional and result in violations of the consistency relations.},

doi = {10.1088/1475-7516/2014/09/018},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 09,

volume = 2014,

place = {United States},

year = {Mon Sep 01 00:00:00 EDT 2014},

month = {Mon Sep 01 00:00:00 EDT 2014}

}