[Paper Review] Is the CMB revealing signs of pre-inflationary physics?

Suddhasattwa Brahma, Jaime Calderón-Figueroa|ArXiv.org|Apr 3, 2025

Geomagnetism and Paleomagnetism Studies6 citations

TL;DR

The paper argues that non–Bunch-Davies initial states for primordial perturbations can reconcile popular inflation models (like Starobinsky and Higgs inflation) with current CMB constraints, without altering the underlying EFT framework.

ABSTRACT

Given the latest observational constraints coming from the joint analyses of the Atacama Cosmology Telescope, the Planck Satellite and other missions, we point out the possibility of reconciling fundamental particle-physics models of inflation with data by considering non-Bunch-Davies initial conditions for primordial density perturbations.

Motivation & Objective

• Motivate why standard single-field inflation is increasingly constrained by Planck/ACT/BK18 data.
• Propose non–Bunch-Davies initial states as a principled alternative to fine-tuned potentials.
• Show how small excited-state initial conditions can adjust the scalar power spectrum and spectral tilt to fit observations.
• Discuss backreaction and non-Gaussianity constraints to maintain EFT control while modifying initial conditions.

Proposed method

• Express non–Bunch-Davies initial modes as v_k(η) = α_k u_k^{BD}(η) + β_k u_k^{BD}_{k}(η).
• Use the constraint |α_k|^2 − |β_k|^2 = 1 to derive a corrected power spectrum P_ζ = P_ζ^{BD} γ_k with γ_k = 1 + 2N_k + 2√{N_k(N_k+1)} cos Θ_k.
• Relate the tilt to the BD case via n_s − 1 = (n_s − 1)^{BD} + d ln γ_k / d ln k and similarly for running.
• Parametrize the excited-state spectrum with N_k or a sigmoid-like γ_k to control scale dependence and satisfy Hadamard and backreaction constraints.
• Illustrate with Starobinsky inflation to show how modest N_k can bring predictions into agreement with data.
• Discuss implications for tensor-to-scalar ratio r and potential future constraints from r measurements.

Experimental results

Research questions

• RQ1 Can non–Bunch-Davies initial conditions bring inflationary models like Starobinsky and Higgs inflation into alignment with current CMB constraints without abandoning EFT control?
• RQ2 What forms of N_k(k) or γ_k(k) maximize compatibility with observed n_s and α_s while respecting backreaction and non-Gaussianity limits?
• RQ3 To what extent can pre-inflationary physics leave observable imprints that survive inflation, given current and future data on r and γ_k?
• RQ4 How do different parameterizations of the initial-state modifications affect predictions for r and the running of the spectral index?

Key findings

• A small non–Bunch-Davies component can adjust the spectral tilt sufficiently to render Starobinsky-like models compatible with current data.
• With a simple choice (θ = π) and N_k^0 ≈ 5.89×10^−3 for N=60, γ_{k*} ≈ 0.86, yielding r ≈ 0.0034, while for N=50 a larger N_k^0 ≈ 2.4×10^−2 yields γ_{k*} ≈ 0.74 and r ≈ 0.0057.
• A sigmoid-like γ_k(k) = c1 + (1 − c1)/(1 + (e k*/k)^{c2}) can better fit α_s while keeping γ_k → 1 at large k and γ_k ≈ c1 at small k, improving consistency with observations.
• For N=60, the sigmoid fit yields γ_{k*} ≈ 0.978 with parameters (c1, c2) = (0.974, 1.651); for N=50, γ_{k*} ≈ 0.96 with (c1, c2) = (0.945, 1.137).
• The approach can be extended to other inflationary models beyond Starobinsky, potentially including non-minimal Higgs inflation, while remaining within EFT consistency.
• The authors note that while this avoids fine-tuning of potentials, it introduces pre-inflationary assumptions that could be constrained by future observations of r and α_s.