Searching for oscillations in the primordial power spectrum with CMB and LSS data

Different inflationary models predict oscillatory features in the primordial power spectrum. These can leave an imprint on both the cosmic microwave background (CMB) and the large-scale structure (LSS) of our Universe that can be searched for with current data. Inspired by the axion-monodromy model of inflation, we search for primordial oscillations that are logarithmic in wave number, using both CMB data from the Planck satellite and LSS data from the WiggleZ galaxy survey. We find that, within our search range for the new oscillation parameters (amplitude, frequency and phase), both CMB-only and $\mathrm{CMB}+\mathrm{LSS}$ data yield the same best-fit oscillation frequency of ${\log }_{10}\omega =1.5$, improving the fit over $\mathrm{\Lambda }\mathrm{CDM}$ by $\mathrm{\Delta }{\chi }^2=-9$ and $\mathrm{\Delta }{\chi }^2=-13$ (roughly corresponding to $2\sigma$ and $2.8\sigma$ significance), respectively. Bayesian evidence for the log-oscillation model versus $\mathrm{\Lambda }\mathrm{CDM}$ indicates a very slight preference for the latter. Future CMB and LSS data will further probe this scenario.

Figure 1

The frequency modes constrained by “unbinned” Planck 2015 $\mathrm{TT}+\mathrm{lowTEB}$, WiggleZ [31], and their combination using MultiNest. Each dot gives the $\mathrm{\Delta }{\chi }^2$ value at each peak in the parameter space of log frequency. We simultaneously constrain all nine parameters while fixing the foregrounds for each data set. Further validation is carried out by setting a flat instead of a log-spaced prior on the frequency with range $\omega =[0,125.89]$ (darker squares) so as to potentially remove any nested-sampling dependence on the prior. With the complementary LSS data (blue dots), ${\log }_{10}\omega \approx 1.5$, the frequency suggested by the Planck paper [18], remains the most significant.

Figure 2

1D posteriors for oscillation amplitude $\epsilon$ and phase ${\varphi }_k$ with different data sets. We simultaneously constrain all nine parameters while fixing the foregrounds for each data set.

Figure 3

The temperature power spectrum residuals of Planck 2015 [36] and the log-oscillation model (last row of Table 2), each with respect to the $\mathrm{\Lambda }\mathrm{CDM}$ best fits (Table 2, third row).

Figure 4

Comparison of the six parameters in $\mathrm{\Lambda }\mathrm{CDM}$ (blue and green) and log-oscillation (black and red) posteriors with broad prior range of $\omega$. Legends on the top show the different model–data set combinations. The foreground parameters are fixed to the best-fits in the Monte Python results, and we vary the nine parameters simultaneously.

Figure 5

2D posteriors for the $\mathrm{\Lambda }\mathrm{CDM}$ parameters under the oscillation-based model, jointly constrained by CMB and LSS data using MultiNest. We vary the nine parameters simultaneously.