# An Emulator for the Lyman-alpha Forest

## TL;DR

This paper develops a Gaussian process emulator for the Lyman-alpha forest flux power spectrum, enabling fast, accurate interpolation between simulations to improve cosmological parameter estimation.

## Contribution

It introduces a Gaussian process-based emulator for the Lyman-alpha forest flux power spectrum that outperforms previous methods in accuracy and error estimation.

## Key findings

- Emulator achieves 1.5% typical accuracy, 4% worst-case.
- Emulator provides unbiased posterior constraints.
- Outperforms quadratic polynomial interpolation in accuracy.

## Abstract

We present methods for interpolating between the 1-D flux power spectrum of the Lyman-$\alpha$ forest, as output by cosmological hydrodynamic simulations. Interpolation is necessary for cosmological parameter estimation due to the limited number of simulations possible. We construct an emulator for the Lyman-$\alpha$ forest flux power spectrum from $21$ small simulations using Latin hypercube sampling and Gaussian process interpolation. We show that this emulator has a typical accuracy of 1.5% and a worst-case accuracy of 4%, which compares well to the current statistical error of 3 - 5% at $z < 3$ from BOSS DR9. We compare to the previous state of the art, quadratic polynomial interpolation. The Latin hypercube samples the entire volume of parameter space, while quadratic polynomial emulation samples only lower-dimensional subspaces. The Gaussian process provides an estimate of the emulation error and we show using test simulations that this estimate is reasonable. We construct a likelihood function and use it to show that the posterior constraints generated using the emulator are unbiased. We show that our Gaussian process emulator has lower emulation error than quadratic polynomial interpolation and thus produces tighter posterior confidence intervals, which will be essential for future Lyman-$\alpha$ surveys such as DESI.