Constraining Cut-off Physics in the Cosmic Microwave Background

TL;DR

This study assesses the observability of oscillatory features in the primordial power spectrum arising from a high-energy cutoff in inflationary physics. It introduces a four-parameter oscillation model (λ, ω, α, ε) tied to vacuum ambiguity and derives the associated spectrum Δ^2_ζ(k) with a log-periodic modulation, then constrains it using a full likelihood analysis on current CMB data and a cosmic-variance-limited forecast. The results show only weak current constraints (e.g., λ<0.77 at 2σ) due to degeneracies, while a future cosmic-variance-limited experiment could bound the oscillation amplitude to λ<0.005 (2σ), implying Λ>200 H_infl for |X|≈1. These findings highlight both the potential and the challenges of probing cutoff-physics in the CMB, with strong dependence on advanced sampling to navigate a multi-modal likelihood landscape.

Abstract

We investigate the ability to constrain oscillatory features in the primordial power spectrum using current and future cosmic microwave background observations. In particular, we study the observability of an oscillation arising from imprints of physics at the cut-off energy scale. We perform a likelihood analysis on the WMAP data set, and find that the current data set constrains the amplitude of the oscillations to be less than 0.77 at 2-sigma, consistent with a power spectrum without oscillations. In addition, we investigate the fundamental limitations in the measurement of oscillation parameters by studying the constraints from a cosmic variance limited experiment. We find that such an experiment is capable of constraining the amplitude of such oscillations to be below 0.005, implying that reasonable models with cut-off energy scales Lambda>200 H_infl are unobservable through the microwave background.

Figures (7)

• Figure 1: Fractional deviation of CAMB computation from the true power spectrum, for (a) $\lambda=0.01$, $\epsilon = 0.2$, $\omega=20$, $\alpha=0$, and (b) $\lambda=0.01$, $\epsilon = 0.2$, $\omega=30$, $\alpha=0$. At $\omega=20$, the deviations are at around $0.2\%$, while at $\omega=30$, the deviations approach $0.4\%$.
• Figure 2: WMAP likelihood contours for parameters describing the primordial power spectrum. The diagonals show the marginalized likelihoods as functions of the individual parameters. The off-diagonals show the two-dimensional likelihoods after marginalizing over the other parameters. Solid lines denote the 1$\sigma$ contours, and the gray lines the 2$\sigma$ contours.
• Figure 3: Marginalized likelihood plot for the parameters $\lambda$ and $\omega$, with the solid curve denoting the 1$\sigma$ contour and the gray curve the 2$\sigma$ contour. The contours curve around the $\lambda=0$ and $\omega=0$ lines and exhibit the degeneracy between $\lambda=0$ and $\omega=0$ models.
• Figure 4: Likelihood contours for $\epsilon$ vs. $\Omega_{\text{CDM}}h^2$. There are no measurable correlations between $\epsilon$ and $\Omega_{\text{CDM}}h^2$.
• Figure 5: 1$\sigma$ and 2$\sigma$ likelihood contours from a cosmic variance limited experiment, with a simulated data set containing no oscillations. The gray curved denote 2$\sigma$ contours. The diagonals show the marginalized likelihoods as functions of the individual parameters.