Abstract
We re-examine the predictiveness of single-field inflationary models and discuss how an unknown UV completion can complicate determining inflationary model parameters from observations, even from precision measurements. Besides the usual naturalness issues associated with having a shallow inflationary potential, we describe another issue for inflation, namely, unknown UV physics modifies the running of Standard Model (SM) parameters and thereby introduces uncertainty into the potential inflationary predictions. We illustrate this point using the minimal Higgs Inflationary scenario, which is arguably the most predictive single-field model on the market, because its predictions for $A_s$, $r$ and $n_s$ are made using only one new free parameter beyond those measured in particle physics experiments, and run up to the inflationary regime. We find that this issue can already have observable effects. At the same time, this UV-parameter dependence in the Renormalization Group allows Higgs Inflation to occur (in principle) for a slightly larger range of Higgs masses. We comment on the origin of the various UV scales that arise at large field values for the SM Higgs, clarifying cut off scale arguments by further developing the formalism of a non-linear realization of $\rm SU_L(2) \times U(1)$ in curved space. We discuss the interesting fact that, outside of Higgs Inflation, the effect of a non-minimal coupling to gravity, even in the SM, results in a non-linear EFT for the Higgs sector. Finally, we briefly comment on post BICEP2 attempts to modify the Higgs Inflation scenario.
Highlights
Very benign, and arguably simple modification of known physics, since the new term is proportional to a dimensionless coupling (ξ) that is allowed by the symmetries given the Standard Model (SM) field content
Besides the usual naturalness issues associated with having a shallow inflationary potential, we describe another issue for inflation, namely, unknown UV physics modifies the running of Standard Model (SM) parameters and thereby introduces uncertainty into the potential inflationary predictions
We revisit the issue of the sensitivity of inflationary predictions to unknown UV physics, with the effects of this physics systematized within an Effective Field Theory (EFT) framework [20, 21] for gravity
Summary
We here briefly describe in more detail, and contrast, the various kinds of UV sensitivity that can arise, in order to set the context for the quantitative calculation of their effects in the minimal HI model. For the HI model, one measures the couplings within the scalar potential in particle physics experiments at comparatively low energy, and inflationary predictions are made in terms of these parameters. Λ = Λ(H†H) is Higgs-field dependent [31], and arises because the coupling to gravity is not renormalizable, and so the size of quantum effects can only be quantified within an EFT framework Within this framework (as we review be√low) Λ ∼ Mp/ξ for the small fields,√H Mp/ξ, relevant to particle physics; while Λ ∼ Mp/ ξ for th√e larger fields, H Mp/ ξ, relevant to inflation.
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