New constraint on Early Dark Energy from Planck and BOSS data using the profile likelihood

TL;DR

This paper investigates constraints on early dark energy using Planck and BOSS data, employing profile likelihood analysis to address biases from volume effects and provide more robust limits on EDE's role in resolving the Hubble tension.

Contribution

It introduces a profile likelihood method to better constrain early dark energy, reducing biases from volume effects compared to traditional MCMC analyses.

Findings

Profile likelihood yields a robust EDE fraction of 0.072±0.036 at 68% CL.

Volume effects influence previous constraints, leading to potential biases.

The method clarifies EDE's viability as a solution to the Hubble tension.

Abstract

A dark energy-like component in the early universe, known as early dark energy (EDE), is a proposed solution to the Hubble tension. Currently, there is no consensus in the literature as to whether EDE can simultaneously solve the Hubble tension and provide an adequate fit to the data from the cosmic microwave background (CMB) and large-scale structure of the universe. In this work, we deconstruct the current constraints from the Planck CMB and the full-shape clustering data of the Baryon Oscillation Spectroscopic Survey (BOSS) to understand the origin of different conclusions in the literature. We use two different analyses, a grid sampling and a profile likelihood, to investigate whether the current constraints suffer from volume effects upon marginalization and are biased towards some values of the EDE fraction, $f_\mathrm{EDE}$. We find that $f_\mathrm{EDE}$ allowed by the data strongly depends on the particular choice of the other parameters of the model and that several choices of these parameters prefer larger values of $f_\mathrm{EDE}$ than in the Markov Chain Monte Carlo analysis. This suggests that volume effects are the reason behind the disagreement in the literature. Motivated by this, we use a profile likelihood to analyze the EDE model and compute a confidence interval for $f_\mathrm{EDE}$, finding $f_\mathrm{EDE} = 0.072\pm 0.036$ ($68\%$ C.L.). This confidence interval is not subject to volume effects; thus, our approach yields more robust constraints on EDE and provides a powerful tool to understand whether EDE is a possible solution to the Hubble tension.