New Constraints on Oscillations in the Primordial Spectrum of Inflationary Perturbations

TL;DR

The study investigates whether brief violations of slow-roll during inflation, modeled as a step in the inflaton potential, imprint localized oscillations in the primordial power spectrum. It develops a model-agnostic, phenomenological description of these oscillations and confronts three inflationary scenarios with updated CMB and LSS data, including BAO from SDSS LRG. Through MCMC analyses, it finds that degeneracies with standard cosmological parameters are minimal and that newer data tighten constraints, with no compelling evidence for oscillatory features beyond modest amplitudes. The results emphasize that current cosmological data can robustly constrain extensions to simple inflationary models, while BAO data emerge as particularly sensitive to oscillatory spectra. Future polarization and bispectrum analyses could provide additional discriminants for slow-roll interruptions during inflation.

Abstract

We revisit the problem of constraining steps in the inflationary potential with cosmological data. We argue that a step in the inflationary potential produces qualitatively similar oscillations in the primordial power spectrum, independently of the details of the inflationary model. We propose a phenomenological description of these oscillations and constrain these features using a selection of cosmological data including the baryonic peak data from the correlation function of luminous red galaxies in the Sloan Digital Sky Survey. Our results show that degeneracies of the oscillation with standard cosmological parameters are virtually non-existent. The inclusion of new data severely tightens the constraints on the parameter space of oscillation parameters with respect to older work. This confirms that extensions to the simplest inflationary models can be successfully constrained using cosmological data.

Figures (8)

• Figure 1: Top: $z"/z$ divided by $a^2 H^2$ for $b=14$, $c=10^{-3}$ and $d=2\times10^{-2}$ versus the number of $e$-foldings. $N$ is set to zero for $\phi = b$. It takes the inflaton field roughly half an $e$-folding to roll over the step. Bottom: Hubble slow roll parameters at the step, $\epsilon_\text{H}$ (dotted green line) remains negligible throughout, while $\eta_\text{H}$ (solid red line) and $\xi^2_\text{H}$ (dashed blue line) violate the slow roll conditions.
• Figure 2: These figures show the evolution of $u_k$ in the complex plane, where $u_k$ has been normalised to one in the oscillating limit. The choice of initial conditions (\ref{['ukic']},\ref{['dotukic']}) ensures that the motion will be initially circular. The top left plot shows a mode that is not affected by the feature, so that the circular oscillation goes straight into a growing motion. In the other two plots the circle gets deformed by an intermittent phase of growth triggered by the peak of $\tfrac{z"}{z}$, to be followed by another phase of elliptic oscillations (caused by the dip of $\tfrac{z"}{z}$) until finally the modes leave the horizon and start growing. Whether a mode is suppressed or enhanced by this mechanism depends on the phase of the oscillation when the growth sets in. Growth along the semi-major axis will lead to an enhancement (top right), whereas growth along the semi-minor axis entails a suppression (bottom) with respect to the modes of the corresponding featureless model.
• Figure 3: Primordial power spectrum for a model with $m = 7.5 \times 10^{-6}$, $b=14$, $c=10^{-3}$ and $d=2\times10^{-2}$ (solid black line) with wavenumber $k$ given in units of $a H |_{\phi=b}$. The dotted red line depicts the spectrum of the same model with $c$ set to zero.
• Figure 4: Primordial power spectra of a hybrid inflation type step model \ref{['hybridpot']} with $V_0= 3.7 \times 10^{-14}$, $m=3.2 \times 10^{-8}$, $b = 0.0125$, $c = 10^{-3}$ and $d=5 \times 10^{-5}$ (dashed blue line), and of potential \ref{['phi4pot']} with parameters $\lambda = 6 \times 10^{-14}$, $b=21$, $c=5 \times 10^{-4}$ and $d=0.02$ (dotted green line). The hybrid inflation background model has $n_\text{S} > 1$, suppressing large scale fluctuations, while the $\lambda \phi^4$ model has $n_\text{S} < 1$ with more power on large scales.
• Figure 5: Marginalised likelihoods for model A (solid red line), model B (dot-dashed line) and model C (solid black line). The differences between the results for A and C are marginal. For some parameters, the results for model B differ slightly. This should be attributed to the degeneracies of the spectral index with these parameters and the fact that the tilt of the spectrum is fixed in this model, it is not due to the presence of a feature.