A comprehensive Bayesian analysis of Cosmic Microwave Background and baryon acoustic oscillation data (Martin, Ringeval and Vennin, JCAP 2024) left the inflationary model space constrained but not identified. Four linked issues remain open: (i) whether the sub-threshold BICEP/Keck BB-mode preference for primordial tensor modes (log⁡ε1>−3.9\log\varepsilon_1>-3.9 at 68% CL, ε1\varepsilon_1 the first Hubble-flow function) is a genuine primordial gravitational-wave signal or a fluctuation; (ii) whether the fourth Hubble-flow function ε4\varepsilon_4, whose posterior is currently flat over its prior, can ever be constrained by data, i.e. whether fourth-order slow-roll structure has detectable effects; (iii) whether the reheating history, now carrying about 1.3 bits of information but still model-dependent, can be further specified rather than marginalized over; and (iv) whether future CMB and large-scale-structure data can further discriminate among the ~20% of scenarios that survive in the favored region of the Bayesian evidence ranking, toward identifying the inflationary realization. The problem is to carry the observational program of inflation from this 'constrained but unidentified' snapshot toward identification, using next-generation CMB polarization and LSS data.

Background

Cosmic inflation is a hypothesized phase of quasi-exponential acceleration in the very early universe that explains the observed flatness, homogeneity, and scale-invariance of the Cosmic Microwave Background (CMB, the relic radiation field). In the single-field slow-roll paradigm, a scalar inflaton rolls gently down its potential; its dynamics is encoded in the Hubble-flow functions εn+1=dln⁡∣εn∣/dN\varepsilon_{n+1}=d\ln|\varepsilon_n|/dN (with NN the number of e-folds, ε1=−H˙/H2\varepsilon_1=-\dot H/H^2), which form a hierarchy generalizing the usual slow-roll parameters. Quantum fluctuations of the inflaton seed scalar (density) perturbations, and quantum gravitational waves generated during inflation seed tensor perturbations, observable as BB-mode (curl-type) CMB polarization; their relative amplitude is the tensor-to-scalar ratio r≃16ε1∗r\simeq16\varepsilon_{1*}, evaluated when observable scales exit the Hubble radius. To confront data order by order in the slow-roll hierarchy, the primordial scalar and tensor power spectra can be written as closed-form expansions in the Hubble-flow functions at a pivot scale; the third-order ('N3LO') expressions were derived exactly by Auclair and Ringeval (Phys. Rev. D 106 (2022) 063512). After inflation ends, the energy density locked in the inflaton must be converted into particles and thermalized ('reheating'); the kinematics of this era shifts the location of the observable window on the inflaton potential and is captured, for each model, by the rescaled reheating parameter ln⁡Rreh\ln R_{\mathrm{reh}}. Because different inflationary potentials predict different spectra and reheating histories, the field performs Bayesian model comparison: for each scenario one computes the Bayesian evidence (the likelihood integrated over all model parameters and priors) and ranks models on the Jeffreys' scale of evidence ratios. Martin, Ringeval and Vennin ('Cosmic Inflation at the Crossroads', JCAP 07 (2024) 087) performed the first Bayesian data analysis using third-order slow-roll spectra, combining Planck 2018, SPT-3G, BICEP/Keck 2018 (BK18) and baryon acoustic oscillation (BAO, a standard-ruler measurement of the distance-redshift relation from galaxy clustering) data over a landscape of 287 single-field slow-roll models. They found the third Hubble-flow function constrained to slow-roll-sized values, ε3∈[−0.44,0.55]\varepsilon_3\in[-0.44,0.55] at 95% CL, a flat (unconstrained) posterior for ε4\varepsilon_4, a weak and non-significant preference for nonzero tensors driven by a residual BB-mode excess in the BICEP/Keck data, a reheating information gain of 1.3±0.181.3\pm0.18 bits, and more than 40% of scenarios strongly disfavored with the best model (Exponential SUSY Inflation, ESIo_o) separated from its competitors by less than decisive evidence. The arbiters designed for the remaining questions are the LiteBIRD satellite (a JAXA-led CMB polarization mission targeting σ(r)∼10−3\sigma(r)\sim10^{-3}), the ground-based CMB-S4 and Simons Observatory programs, and large-scale-structure (LSS) surveys such as Euclid and the SKA radio telescope.

Problem Statement

Determine, from next-generation CMB polarization and large-scale-structure data analyzed within the third-order (and, where needed, higher-order) slow-roll framework, whether the inflationary realization underlying our Universe can be identified, by resolving the four linked questions left open by the 'Cosmic Inflation at the Crossroads' analysis: (1) Primordial tensors: forecast, from the projected next-generation BB-mode sensitivity σ(r)\sigma(r) (LiteBIRD, CMB-S4), whether the residual BICEP/Keck BB-mode preference (log⁡ε1>−3.9\log\varepsilon_1>-3.9 at 68% CL, i.e. rr of order 10−310^{-3} to a few 10−210^{-2}) would be confirmed as a genuine primordial gravitational-wave background or excluded as a statistical fluctuation and foreground residual at a stated significance. (2) Fourth-order slow roll: determine whether the fourth Hubble-flow function ε4\varepsilon_4, currently unconstrained (posterior flat over its prior), can be bounded by any foreseeable data, either by a detected departure from third-order predictions or by a non-flat ε4\varepsilon_4 posterior. (3) Reheating: determine whether next-generation data can further tighten the per-model reheating posteriors (ln⁡Rreh\ln R_{\mathrm{reh}} and the reheating equation of state) beyond the current average information gain of 1.3±0.181.3\pm0.18 bits, so that the reheating kinematics is specified rather than marginalized over; discriminating the underlying microscopic reheating mechanism (e.g. perturbative decay versus parametric resonance) is a further motivation but lies beyond this kinematic target. (4) Model identification: determine whether extending the Bayesian evidence comparison over the model landscape to next-generation CMB and LSS data further discriminates among the ~20% of scenarios that currently sit in the most probable Jeffreys region and are all 'as good as ESIo_o'. All four sub-questions are jointly required: a solution resolves each of them (positively or negatively), and the four together determine whether the underlying realization is identified or remains unidentified. These deliverables jointly serve one objective: carrying the current 'constrained but unidentified' status of inflation toward identification of the inflationary realization.

References

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