Can Planck-scale physics be seen in the cosmic microwave background ?

TL;DR

This work investigates whether trans-Planckian physics during inflation could leave detectable oscillatory imprints on the primordial power spectrum and thus on the CMB and large-scale structure. It adopts a parametric modulation $P(k;ε,ξ)=P_0(k)[1-ξ(k/k_n)^{-ε} sin((2/ξ)(k/k_n)^{ε})]$ and performs full likelihood analyses using current data and simulated future datasets from Planck and SDSS. The results show no significant evidence for oscillations in present data and only narrow excluded regions in the $ε$–$ξ$ plane; simulated Planck/SDSS data reveal that even with perfect measurements, the likelihood is highly multimodal and highly sensitive to parameter choices, making robust detection of small-amplitude trans-Planckian signatures extremely difficult. The study emphasizes the need for robust statistical methods, as naive Δχ^2 approaches can bias conclusions, and suggests that practical detection of Planck-scale modulations in cosmological data remains unlikely under plausible scenarios.

Abstract

We investigate the potential of observations of anisotropies in the cosmic microwave background (CMB) and large-scale structure in the Universe to detect possible modifications of standard inflationary models by physics beyond the Planck scale. A generic model of primordial density fluctuations is investigated, and we derive constraints on its parameters from current data. We conclude that the currently available data do not put very stringent constraints on this model. Furthermore, we use simulated power spectra from the Sloan Digital Sky Survey (SDSS) and the Planck satellite to show that it is unlikely that a trans-Planckian signature of this type can be detected in CMB and large-scale structure data.

Figures (10)

• Figure 1: 68% and 95% confidence exclusion plot of the parameters $\epsilon$ and $\xi$ for WMAP data only. The straight lines are isocontours for the parameter $\gamma$.
• Figure 2: 68% and 95% confidence exclusion plot of the parameters $\epsilon$ and $\xi$ for the WMAP data set combined with the pre-WMAP data compilation from Wang et al. The straight lines are isocontours for the parameter $\gamma$.
• Figure 3: 68% and 95% confidence exclusion plot of the parameters $\epsilon$ and $\xi$ with the previous CMB data plus additional data from the 2dF galaxy survey. The straight lines are isocontours for the parameter $\gamma$.
• Figure 4: Ratio of modulated to umodulated power spectrum, before (solid line) and after (dashed line) convolution with the mock SDSS window function.
• Figure 5: Ratio of modulated to umodulated power spectrum, both the exact result (solid line) and the approximation Eq. (16) (dashed line).