Models of the Primordial Standard Clock

TL;DR

The paper investigates primordial Standard Clock signals as a direct probe of the early-universe expansion history and develops a full inflationary model that realizes these clocks. It combines data analysis of Planck 2013 with theoretical construction, showing a marginal yet intriguing clock-signal candidate and providing detailed predictions for the clock and sharp-feature components in the power spectrum and non-Gaussianities. Through MCMC studies of both clock-alone and full clock-plus-sharp-feature signals, it demonstrates how future CMB polarization and LSS data could sharpen tests of the Standard Clock scenario. The work also clarifies model-building requirements, derives perturbation theory results for small- and large-field cases, and discusses the implications for higher-point correlations and polarization observables. Overall, it establishes a concrete framework to use oscillating heavy fields as clocks to distinguish inflation from alternatives and highlights pathways for more stringent empirical tests.

Abstract

Oscillating massive fields in the primordial universe can be used as Standard Clocks. The ticks of these oscillations induce features in the density perturbations, which directly record the time evolution of the scale factor of the primordial universe, thus if detected, provide a direct evidence for the inflation scenario or the alternatives. In this paper, we construct a full inflationary model of primordial Standard Clock and study its predictions on the density perturbations. This model provides a full realization of several key features proposed previously. We compare the theoretical predictions from inflation and alternative scenarios with the Planck 2013 temperature data on Cosmic Microwave Background (CMB), and identify a statistically marginal but interesting candidate. We discuss how future CMB temperature and polarization data, non-Gaussianity analysis and Large Scale Structure data may be used to further test or constrain the Standard Clock signals.

Figures (10)

• Figure 4: The distribution of $\chi^2$ in the MCMC chains. Inflation has lower $\chi^2$ on average compared with alternatives, with $\Delta\chi^2= 2.89$. (We have also compared the distribution of inflation with three different types of alternative scenarios separately and observed very similar results as the figure in the left panel.) Clock signal has lower $\chi^2$ on average compared with pure sharp feature signal, with $\Delta\chi^2= 1.91$.
• Figure 5: The triangle plot for model \ref{['clock_template']}. Here the value of $p \in [-15,15]$ spans over inflation and alternatives.
• Figure 6: The triangle plot for model \ref{['clock_template']}. Here the value of $p \in [50,150]$ is chosen for inflation.
• Figure 7: An illustration of the model (\ref{['model_Lagrangian']}). The model starts as a two-field inflation model. The inflaton rolls on a plateau for a few efolds before falling into a potential valley. The massive field is excited and oscillating. Eventually the model settles down to the 2nd stage of inflation as an effective single-field slow-roll model.
• Figure 8: An example of background evolution of the clock field $\sigma_0$ and the slow-roll parameter $\epsilon$. In this example, the attractor value of $\epsilon$ is $10^{-6}$. The model parameters in this example are $V_{\rm inf}=5.33\times 10^{-13}$, $V_{\sigma 0}=2.66\times 10^{-14}$, $\sigma_f = 1.64\times 10^{-2}$, ${\tilde{R}}=2.05$, $\beta=1.55\times 10^{-15}$. Initially we put the inflaton at the potential plateau $\theta_{\rm initial} =0$, $\sigma_{\rm initial}=8.33\times 10^{-2}$ so that the clock starts oscillating at $N \approx 6$ efolds. In this paper, we set $M_{\rm P}=1$.