# Asymptotic symmetries in de Sitter and inflationary spacetimes

## Abstract

Soft gravitons produced by the expansion of de Sitter can be viewed as the Nambu-Goldstone bosons of spontaneously broken asymptotic symmetries of the de Sitter spacetime. We explicitly construct the associated charges, and show that acting with the charges on the vacuum creates a new state equivalent to a change in the local coordinates induced by the soft graviton. While the effect remains unobservable within the domain of a single observer where the symmetry is unbroken, this change is physical when comparing different asymptotic observers, or between a transformed and un-transformed initial state, consistent with the scale-dependent statistical anisotropies previously derived using semiclassical relations. We then compute the overlap, (0| 0'), between the unperturbed de Sitter vacuum |0), and the state | 0') obtained by acting N times with the charge. We show that when N→ M {sub p} {sup 2}/ H {sup 2} this overlap receives order one corrections and 0(0| 0')→ , which corresponds to an infrared perturbative breakdown after a time t {sub dS} ∼ M {sub p} {sup 2}/ H {sup 3} has elapsed, consistent with earlier arguments in the literature arguing for a perturbative breakdown on this timescale. We also discuss the generalization to inflation,more »

- Authors:

- CP3-Origins, Center for Cosmology and Particle Physics Phenomenology, University of Southern Denmark, Campusvej 55, 5230 Odense M (Denmark)

- Publication Date:

- OSTI Identifier:
- 22679909

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 04; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANISOTROPY; ASYMPTOTIC SOLUTIONS; BREAKDOWN; COMPARATIVE EVALUATIONS; D S MESONS; DE SITTER SPACE; EXPANSION; GOLDSTONE BOSONS; GRAVITONS; INFLATIONARY UNIVERSE; SEMICLASSICAL APPROXIMATION; SPACE-TIME; SYMMETRY BREAKING

### Citation Formats

```
Ferreira, Ricardo Z., Sandora, McCullen, and Sloth, Martin S., E-mail: ferreira@cp3.sdu.dk, E-mail: sandora@cp3.sdu.dk, E-mail: sloth@cp3.sdu.dk.
```*Asymptotic symmetries in de Sitter and inflationary spacetimes*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/04/033.

```
Ferreira, Ricardo Z., Sandora, McCullen, & Sloth, Martin S., E-mail: ferreira@cp3.sdu.dk, E-mail: sandora@cp3.sdu.dk, E-mail: sloth@cp3.sdu.dk.
```*Asymptotic symmetries in de Sitter and inflationary spacetimes*. United States. doi:10.1088/1475-7516/2017/04/033.

```
Ferreira, Ricardo Z., Sandora, McCullen, and Sloth, Martin S., E-mail: ferreira@cp3.sdu.dk, E-mail: sandora@cp3.sdu.dk, E-mail: sloth@cp3.sdu.dk. Sat .
"Asymptotic symmetries in de Sitter and inflationary spacetimes". United States.
doi:10.1088/1475-7516/2017/04/033.
```

```
@article{osti_22679909,
```

title = {Asymptotic symmetries in de Sitter and inflationary spacetimes},

author = {Ferreira, Ricardo Z. and Sandora, McCullen and Sloth, Martin S., E-mail: ferreira@cp3.sdu.dk, E-mail: sandora@cp3.sdu.dk, E-mail: sloth@cp3.sdu.dk},

abstractNote = {Soft gravitons produced by the expansion of de Sitter can be viewed as the Nambu-Goldstone bosons of spontaneously broken asymptotic symmetries of the de Sitter spacetime. We explicitly construct the associated charges, and show that acting with the charges on the vacuum creates a new state equivalent to a change in the local coordinates induced by the soft graviton. While the effect remains unobservable within the domain of a single observer where the symmetry is unbroken, this change is physical when comparing different asymptotic observers, or between a transformed and un-transformed initial state, consistent with the scale-dependent statistical anisotropies previously derived using semiclassical relations. We then compute the overlap, (0| 0'), between the unperturbed de Sitter vacuum |0), and the state | 0') obtained by acting N times with the charge. We show that when N→ M {sub p} {sup 2}/ H {sup 2} this overlap receives order one corrections and 0(0| 0')→ , which corresponds to an infrared perturbative breakdown after a time t {sub dS} ∼ M {sub p} {sup 2}/ H {sup 3} has elapsed, consistent with earlier arguments in the literature arguing for a perturbative breakdown on this timescale. We also discuss the generalization to inflation, and rederive the 3-point and one-loop consistency relations.},

doi = {10.1088/1475-7516/2017/04/033},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 04,

volume = 2017,

place = {United States},

year = {Sat Apr 01 00:00:00 EDT 2017},

month = {Sat Apr 01 00:00:00 EDT 2017}

}