# Orbital Inflation: inflating along an angular isometry of field space

## TL;DR

Orbital Inflation explores a multi-field inflation model with an angular isometry in field space, providing analytical solutions that mimic single-field predictions while allowing controlled deviations and rich phenomenology.

## Contribution

It introduces a new method to construct two-field inflation models with an angular symmetry, enabling exact solutions and detailed phenomenological analysis of quasi-single field inflation.

## Key findings

- Predictions are similar to single-field inflation but with violations of consistency relations.
- The entropy mass influences the ($n_s$, $r$) predictions, allowing diverse inflationary scenarios.
- Non-Gaussianity can vary from slow-roll suppressed to a few, depending on isocurvature self-interactions.

## Abstract

The simplicity of the CMB data, so well described by single-field inflation, raises the question whether there might be an equally simple multi-field realization consistent with the observations. We explore the idea that an approximate 'angular' shift symmetry in field space (an isometry) protects the dynamics of coupled inflationary perturbations. This idea relates to the recent observation that multi-field inflation mimics the predictions of single-field inflation, if the inflaton is efficiently and constantly coupled to a second massless degree of freedom (the isocurvature perturbation). In multi-field inflation, the inflationary trajectory is in general not aligned with the gradient of the potential. As a corollary the potential does not reflect the symmetries of perturbations. We propose a new method to reconstruct simultaneously a two-field action and an inflationary trajectory which proceeds along an `angular' direction of field space, with a constant radius of curvature, and that has a controlled mass of `radial' isocurvature perturbations (entropy mass). We dub this `Orbital Inflation'. In this set-up the Hubble parameter determines the behavior of both the background and the perturbations. First, Orbital Inflation provides a playground for quasi-single field inflation. Second, the exquisite analytical control of these models allows us to exactly solve the phenomenology of Orbital Inflation with a small entropy mass and a small radius of curvature, a regime not previously explored. The predictions are single-field-like, although the consistency relations are violated. Moreover, the value of the entropy mass dictates how the inflationary predictions fan out in the ($n_s$, $r$) plane. Depending on the size of the self interactions of the isocurvature perturbations, the non-Gaussianity parameter $f_{NL}$ can range from slow-roll suppressed to $\mathcal{O}(\text{a few})$.

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Source: https://tomesphere.com/paper/1907.02020