# Effective action for the Abelian Higgs model in FLRW

## Abstract

We compute the divergent contributions to the one-loop action of the U(1) Abelian Higgs model. The calculation allows for a Friedmann-Lemaitre-Robertson-Walker space-time and a time-dependent expectation value for the scalar field. Treating the time-dependent masses as two-point interactions, we use the in-in formalism to compute the first, second and third order graphs that contribute quadratic and logarithmic divergences to the effective scalar action. Working in R{sub ξ} gauge we show that the result is gauge invariant upon using the equations of motion.

- Authors:

- Nikhef, Science Park 105, 1098 XG Amsterdam (Netherlands)

- Publication Date:

- OSTI Identifier:
- 22279828

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2012; Journal Issue: 11; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACTION INTEGRAL; COSMOLOGICAL MODELS; COSMOLOGY; EQUATIONS OF MOTION; EXPECTATION VALUE; GAUGE INVARIANCE; GRAPH THEORY; HIGGS MODEL; MASS; SCALAR FIELDS; SCALARS; SPACE-TIME; TIME DEPENDENCE; U-1 GROUPS

### Citation Formats

```
George, Damien P., Mooij, Sander, and Postma, Marieke, E-mail: dpgeorge@nikhef.nl, E-mail: smooij@nikhef.nl, E-mail: mpostma@nikhef.nl.
```*Effective action for the Abelian Higgs model in FLRW*. United States: N. p., 2012.
Web. doi:10.1088/1475-7516/2012/11/043.

```
George, Damien P., Mooij, Sander, & Postma, Marieke, E-mail: dpgeorge@nikhef.nl, E-mail: smooij@nikhef.nl, E-mail: mpostma@nikhef.nl.
```*Effective action for the Abelian Higgs model in FLRW*. United States. doi:10.1088/1475-7516/2012/11/043.

```
George, Damien P., Mooij, Sander, and Postma, Marieke, E-mail: dpgeorge@nikhef.nl, E-mail: smooij@nikhef.nl, E-mail: mpostma@nikhef.nl. Thu .
"Effective action for the Abelian Higgs model in FLRW". United States. doi:10.1088/1475-7516/2012/11/043.
```

```
@article{osti_22279828,
```

title = {Effective action for the Abelian Higgs model in FLRW},

author = {George, Damien P. and Mooij, Sander and Postma, Marieke, E-mail: dpgeorge@nikhef.nl, E-mail: smooij@nikhef.nl, E-mail: mpostma@nikhef.nl},

abstractNote = {We compute the divergent contributions to the one-loop action of the U(1) Abelian Higgs model. The calculation allows for a Friedmann-Lemaitre-Robertson-Walker space-time and a time-dependent expectation value for the scalar field. Treating the time-dependent masses as two-point interactions, we use the in-in formalism to compute the first, second and third order graphs that contribute quadratic and logarithmic divergences to the effective scalar action. Working in R{sub ξ} gauge we show that the result is gauge invariant upon using the equations of motion.},

doi = {10.1088/1475-7516/2012/11/043},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 11,

volume = 2012,

place = {United States},

year = {2012},

month = {11}

}

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