# Sub-Planckian two-field inflation consistent with the Lyth bound

## Abstract

The BICEP2 observation of a large tensor-to-scalar ratio, r = 0.20{sup +0.07}{sub -0.05}, implies that the inflaton φ in single-field inflation models must satisfy φ ∼ 10M{sub Pl} in order to produce sufficient inflation. This is a problem if interaction terms suppressed by the Planck scale impose a bound φ ∼< M{sub Pl}. Here we consider whether it is possible to have successful sub-Planckian inflation in the case of two-field inflation. The trajectory in field space cannot be radial if the effective single-field inflaton is to satisfy the Lyth bound. By considering a complex field Φ, we show that a near circular but aperiodic modulation of a |Φ|{sup 4} potential can reproduce the results of φ{sup 2} chaotic inflation for n{sub s} and r while satisfying |Φ| ∼< 0.01 M{sub Pl} throughout. More generally, for models based on a |Φ|{sup 4} potential, the simplest sub-Planckian models are equivalent to φ{sup 2} and φ{sup 4/3} chaotic inflation.

- Authors:

- Department of Physics, University of Lancaster, Lancaster LA1 4YB (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 22375880

- 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; CHAOS THEORY; COSMOLOGICAL INFLATION; INTERACTIONS; MODULATION; POTENTIALS; SCALARS; SPACE; TENSORS; TRAJECTORIES

### Citation Formats

```
McDonald, John, E-mail: j.mcdonald@lancaster.ac.uk.
```*Sub-Planckian two-field inflation consistent with the Lyth bound*. United States: N. p., 2014.
Web. doi:10.1088/1475-7516/2014/09/027.

```
McDonald, John, E-mail: j.mcdonald@lancaster.ac.uk.
```*Sub-Planckian two-field inflation consistent with the Lyth bound*. United States. doi:10.1088/1475-7516/2014/09/027.

```
McDonald, John, E-mail: j.mcdonald@lancaster.ac.uk. Mon .
"Sub-Planckian two-field inflation consistent with the Lyth bound". United States.
doi:10.1088/1475-7516/2014/09/027.
```

```
@article{osti_22375880,
```

title = {Sub-Planckian two-field inflation consistent with the Lyth bound},

author = {McDonald, John, E-mail: j.mcdonald@lancaster.ac.uk},

abstractNote = {The BICEP2 observation of a large tensor-to-scalar ratio, r = 0.20{sup +0.07}{sub -0.05}, implies that the inflaton φ in single-field inflation models must satisfy φ ∼ 10M{sub Pl} in order to produce sufficient inflation. This is a problem if interaction terms suppressed by the Planck scale impose a bound φ ∼< M{sub Pl}. Here we consider whether it is possible to have successful sub-Planckian inflation in the case of two-field inflation. The trajectory in field space cannot be radial if the effective single-field inflaton is to satisfy the Lyth bound. By considering a complex field Φ, we show that a near circular but aperiodic modulation of a |Φ|{sup 4} potential can reproduce the results of φ{sup 2} chaotic inflation for n{sub s} and r while satisfying |Φ| ∼< 0.01 M{sub Pl} throughout. More generally, for models based on a |Φ|{sup 4} potential, the simplest sub-Planckian models are equivalent to φ{sup 2} and φ{sup 4/3} chaotic inflation.},

doi = {10.1088/1475-7516/2014/09/027},

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}

}