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Unified framework for Early Dark Energy from $α$-attractors

Matteo Braglia, William T. Emond, Fabio Finelli, A. Emir Gumrukcuoglu, Kazuya Koyama

Abstract

One of the most appealing approaches to ease the Hubble tension is the inclusion of an early dark energy (EDE) component that adds energy to the Universe in a narrow redshift window around the time of recombination and dilutes faster than radiation afterwards. In this paper, we analyze EDE in the framework of $α$-attractor models. As well known, the success in alleviating the Hubble tension crucially depends on the shape of the energy injection. We show how different types of energy injections can be easily obtained, thanks to the freedom in choosing the functional form of the potential inspired by $α$-attractor models. To confirm our intuition we perform an MCMC analysis for three representative cases and find indeed that $H_0$ is significantly larger than in $Λ$CDM like in other EDE models. Unlike axion-driven EDE models with super Planckian decay constant, the curvature of EDE models required by the data is natural in the context of recent theoretical developments in $α$-attractors.

Unified framework for Early Dark Energy from $α$-attractors

Abstract

One of the most appealing approaches to ease the Hubble tension is the inclusion of an early dark energy (EDE) component that adds energy to the Universe in a narrow redshift window around the time of recombination and dilutes faster than radiation afterwards. In this paper, we analyze EDE in the framework of -attractor models. As well known, the success in alleviating the Hubble tension crucially depends on the shape of the energy injection. We show how different types of energy injections can be easily obtained, thanks to the freedom in choosing the functional form of the potential inspired by -attractor models. To confirm our intuition we perform an MCMC analysis for three representative cases and find indeed that is significantly larger than in CDM like in other EDE models. Unlike axion-driven EDE models with super Planckian decay constant, the curvature of EDE models required by the data is natural in the context of recent theoretical developments in -attractors.

Paper Structure

This paper contains 5 sections, 3 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background evolution and energy injection
  3. Cosmological constraints and implications for the $H_0$ tension
  4. Results
  5. Conclusions

Figures (4)

  • Figure 1: We plot the potential in Eq. \ref{['eq:potential2']} for $(p,\,n)=\{(2,\,0),\,(2,\,4),\,(4,\,2)\}$.
  • Figure 2: We plot the evolution of the normalized scalar field $\Theta$ [Left], equation of state parameter $w_{\rm EDE}$ [Center] and the energy injection $f_{\rm EDE}$ [Right] for the three models with $(p,\,n)=\{(2,\,0),\,(2,\,4),\,(4,\,2)\}$. For definiteness, we have chosen $f_{\rm EDE}=0.1$, $\log_{10} z_c=3.5$ and $\Theta_i=0.4$.
  • Figure 3: Constraints on main parameters and $H_0$ of the $\alpha$-attractor models A, B and C from Planck 2018 data (P18), BAO, Pantheon and SH0ES data. Parameters on the bottom axis are the standard cosmological parameters, and parameters on the left axis are the EDE parameters that we sample with flat priors, $r_s$ in [Mpc] and $H_0$ in [km s$^{-1}$Mpc$^{-1}$]. Constraints for the $\Lambda$CDM model obtained with the same dataset are also shown. Contours contain 68% and 95% of the probability.
  • Figure 4: One dimensional derived posterior distribution of the potential parameters $\log_{10}\, V_0/{\rm eV}^4$ and $\log_{10}\, \alpha$. The convention for the colors used is the same of Fig. \ref{['fig:MCMC']}.