Inflation, the Hubble Tension and Early Dark Energy: an alternative overview

TL;DR

This paper explores how modifications in early universe physics, such as dark energy and relativistic species, influence inflationary parameters and the Hubble tension, suggesting that certain models can alter preferred inflation scenarios.

Contribution

It analyzes the impact of fixing extra cosmological parameters on inflation constraints and examines the role of Early Dark Energy in resolving the Hubble tension and its implications for inflation models.

Findings

Fixing dark energy and relativistic species parameters affects inflation constraints.

Models with certain N_eff values can reconcile H_0 estimates but are disfavored.

Early Dark Energy models can mildly reduce H_0 tension and influence inflation model preferences.

Abstract

I review and discuss the possible implications for inflation resulting from considering new physics in light of the Hubble tension. My study is motivated by a simple argument that the constraints on inflationary parameters, most typically the spectral index $n_s$, depend to some extent on the cosmological framework. To avoid broadening the uncertainties resulting from marginalizing over additional parameters (typical in many alternative models), I first adopt the same alternative viewpoint of previous studies and analyze what happens if a physical theory can fix extra parameters to non-standard values. Focusing on the dark energy equation of state $w$ and the effective number of relativistic species $N_{\rm{eff}}$, I confirm that physical theories able to fix $w \approx -1.2$ or $N_{\rm{eff}} \approx 3.9$ produce values of $H_0$ from CMB and BAO in line with the local distance ladder estimate. While in the former case I do not find any relevant implications for inflation, in the latter scenarios, I observe a shift towards $n_s \approx 1$. From a model-selection perspective, both cases are strongly disfavored compared to $\Lambda$CDM. However, models with $N_{\rm{eff}} \approx 3.3 - 3.4$ could bring the $H_0$ tension down to $\sim 3\sigma$ while being moderately disfavored. Yet, this is enough to change the constraints on inflation so that the most accredited models (e.g., Starobinsky inflation) would no longer be favored by data. I then focus on Early Dark Energy (EDE), arguing that an EDE fraction $f_{\rm{EDE}}\sim 0.04 - 0.06$ (only able to mildly reduce the $H_0$-tension down to $\sim 3\sigma$) could already require a similar change in perspective on inflation. In fact, performing a full joint analysis of EDE and Starobinsky inflation, I find that the two models can hardly coexist for $f_{\rm{EDE}}\gtrsim 0.06$.