Inflation, the Hubble tension, and early dark energy: an alternative overview

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 ns, 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 nonstandard values. Focusing on the dark energy equation of state w and the effective number of relativistic species Neff, I confirm that physical theories able to fix w ≈−1.2 or Neff ≈3.9 produce values of H0 from Cosmic Microwave Background and Baryon Acoustic Oscillations 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 toward ns ≈ 1. From a modelselection perspective, both cases are strongly disfavored compared to Λ cold dark matter. However, models with Neff ≈ 3.3–3.4 could bring the H0 tension down to ∼3σ 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 fEDE ∼ 0.04–0.06 (only able to mildly reduce the H0 tension down to ∼3σ) 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 fEDE ≳ 0.06.