Unique Fingerprints of Alternatives to Inflation in the Primordial Power Spectrum

Massive fields in the primordial Universe function as standard clocks and imprint clock signals in the density perturbations that directly record the scale factor of the primordial Universe as a function of time, $a(t)$. A measurement of such signals would identify the specific scenario of the primordial Universe in a model-independent fashion. In this Letter, we introduce a new mechanism through which quantum fluctuations of massive fields function as standard clocks. The clock signals appear as scale-dependent oscillatory signals in the power spectrum of alternative scenarios to inflation.

Figure 1

Corrections to scalar power spectrum from a massive field for two contraction scenarios. In each panel, two numerical results (described by blue and magenta solid lines) with different initial conditions are plotted against the analytical clock signals in Eq. (11) (dashed). In numerical calculations, the EOM approach [17] is applied and we use the examples ${\lambda }_2=0.05a(\tau )$ ($p=1/2$) and ${\lambda }_2=0.02a(\tau )$ ($p=2/3$) for faster convergence. The mismatch in low $\tilde{k}$ is because the condition $\tilde{k}\gg 1$ is needed for Eq. (4) to be a good approximation.

Figure 2

Illustration of clock signals for two types of alternative scenarios—expansion and contraction scenarios. Two different masses are plotted in each case.