Natural Inflation, Planck Scale Physics and Oscillating Primordial Spectrum

TL;DR

The paper investigates Planck-scale physics imprinting on natural inflation by adding a non-derivative Planck-suppressed term to the PNGB potential: $V(\phi)=\Lambda^4[1+\cos(\phi/f)]+\delta\Lambda^4\cos(N\phi/f+\theta)$. It computes the resulting scalar and tensor spectra, $P_S(k)$ and $P_T(k)$, via numerical integration of the mode equations, revealing oscillatory, scale-dependent modulations in $P_S(k)$ and $n_s(k)$ with amplitudes up to about 10% for $\delta N^2<1$, while the Stewart-Lyth approximation remains accurate in that regime. By projecting these spectra onto CMB and LSS observables, the study shows that some parameter regions are disfavored by current data, but others with high oscillation frequencies could yield detectable features such as peak splitting or wiggles in the CMB and matter power spectra. Overall, the work demonstrates that Planck-scale corrections can broaden natural inflation’s viable parameter space and offer testable signatures for future high-precision measurements like Planck.

Abstract

In the ``natural inflation'' model, the inflaton potential is periodic. We show that Planck scale physics may induce corrections to the inflaton potential, which is also periodic with a greater frequency. Such high frequency corrections produce oscillating features in the primordial fluctuation power spectrum, which are not entirely excluded by the current observations and may be detectable in high precision data of cosmic microwave background (CMB) anisotropy and large scale structure (LSS) observations.

Figures (11)

• Figure 1: Plot of the power spectrum with numerical results and Stewart-Lyth approximation. In the calculation, we take $f=0.95 M_{pl}$, $\delta N^2 \approx 11$ ($\delta=-3\times 10^{-5}, N=599$). $k_c$ is taken to be $k_c = 7.0a_0H_0$.
• Figure 2: Modulation of the power spectrum and index, with $f=0.7M_{Pl}$, $\Lambda^4=2.0\times 10^{-13} M_{Pl}^4$. From left top to bottom, the lines stand for $\delta N^2 =0.8, 0.42, 0, -0.42, -0.8$ respectively.
• Figure 3: The same as Fig.\ref{['fig:f7ns']}, however with different model parameters, $f=0.4 M_{Pl}$, $\Lambda^4=5.0\times 10^{-17} M_{Pl}^4$. From above, the lines represent $\delta N^2$=$-0.7$, $-0.2$, $-0.07$, $0$, $0.07$, $0.2$, $0.7$ respectively.
• Figure 4: The CMB anisotropy and matter power spectrum for the parameters shown in Fig. \ref{['fig:f7ns']}, with $\delta N^2=0.8, 0.42, 0, -0.42, -0.8$ from above. The observational LSS data is from the PSCZ catalogueHT.
• Figure 5: $\tilde{C_l}$ (left) and matter power spectrum (right) for a fixed $f=0.4 M_{Pl}$ but different values of other model parameters. For the solid line, $\Lambda^4=1.3\times 10^{-16} M_{Pl}^4$, $\delta N^2=0$; The dotted line stands for $\Lambda^4=3.6\times 10^{-16} M_{Pl}^4$, $\delta N^2=-0.34$; For the dashed line, $\Lambda^4=5.2\times 10^{-16} M_{Pl}^4$, $\delta N^2=-0.78$.