# Non-relativistic Matrix Inflation

## TL;DR

This paper explores a string theory inflation model involving multiple D3-branes, showing its connection to wrapped D5-branes, analyzing non-relativistic limits, and deriving observational constraints on flux parameters.

## Contribution

It demonstrates the large n limit of the multiple D3-brane action converges to a D5-brane action, providing a consistency check and new insights into non-Abelian effects in inflation.

## Key findings

- Large n limit converges to D5-brane action
- Non-Abelian inflaton modifies slow-roll parameters
- Bounds on background fluxes from observational data

## Abstract

We reconsider a string theoretic inflationary model, where inflation is driven by $n$ multiple coincident $D3$-branes in the finite $n$ limit. We show that the finite $n$ action can be continued to the limit of large $n$, where it converges to the action for a wrapped $D5$-brane with $n$ units of U(1) flux. This provides an important consistency check of the scenario and allows for more control over certain back-reaction effects. We determine the most general form of the action for a specific sub-class of models and examine the non-relativistic limits of the theory where the branes move at speeds much less than the speed of light. The non-Abelian nature of the world-volume theory implies that the inflaton field is matrix valued and this results in modifications to the slow-roll parameters and Hubble-flow equations. A specific small field model of inflation is investigated where the branes move out of an AdS throat, and observational constraints are employed to place bounds on the background fluxes.