Punctuated inflation and the low CMB multipoles

TL;DR

The authors propose punctuated inflation, a single-field scenario where a brief fast-roll phase sits between two slow-roll periods, driven by an inflection-point potential motivated by MSSM-like constructions. This background yields a step-like suppression of the scalar power spectrum at large scales, aligning with the observed low CMB quadrupole without requiring a pre-inflationary regime. Using CAMB and COSMOMC with WMAP5 data, the n=3 realization provides a significantly better fit than a featureless power-law spectrum, improving the effective chi-squared by about 6.6 with only one extra parameter, while predicting an exceptionally small tensor contribution ($r\lesssim10^{-4}$). The model remains testable via future CMB measurements of large-scale polarization and could be realized in beyond-standard-model frameworks such as string theory or extended MSSM scenarios.

Abstract

We investigate inflationary scenarios driven by a class of potentials which are similar in form to those that arise in certain minimal supersymmetric extensions of the standard model. We find that these potentials allow a brief period of departure from inflation sandwiched between two stages of slow roll inflation. We show that such a background behavior leads to a step like feature in the scalar power spectrum. We set the scales such that the drop in the power spectrum occurs at a length scale that corresponds to the Hubble radius today--a feature that seems necessary to explain the lower power observed in the quadrupole moment of the Cosmic Microwave Background (CMB) anisotropies. We perform a Markov Chain Monte Carlo analysis to determine the values of the model parameters that provide the best fit to the recent WMAP 5-year data for the CMB angular power spectrum. We find that an inflationary spectrum with a suppression of power at large scales that we obtain leads to a much better fit (with just one extra parameter, $χ_{\rm eff}^{2}$ improves by 6.62) of the observed data when compared to the best fit reference $Λ$CDM model with a featureless, power law, primordial spectrum.

Figures (8)

• Figure 1: Illustration of the inflaton potential (\ref{['eq:mssm-p']}) for $n=3$. The solid line corresponds to the following values for the potential parameters: $m=1.5368\times 10^{-7}$ and $\lambda=6.1517\times10^{-15}$ (corresponding to $\phi_{0}=1.9594$), values which turn out to provide the best fit to the WMAP $5$-year data (cf. Tab. \ref{['tab:bfv']}). The dashed lines correspond to values that are $1$-$\sigma$ away from the best fit ones. The black dots denote the points of inflection.
• Figure 2: The phase portrait of the scalar field described by the potential (\ref{['eq:mssm-p']}) in the case of $n=3$ and for the values of the parameters $m$ and $\lambda$ mentioned in the last figure. The arrow points to the attractor. Note that, as discussed in the text, all the trajectories quickly approach the attractor. We should mention that, though we have plotted the phase portrait for just the $n=3$ case, we find that such a behavior is exhibited by higher values of $n$ (such as, for example, $n=4,6$) as well.
• Figure 3: The background quantity $(z'/z\, {\cal H})$ has been plotted as a function of the number of $e$-folds, say, $N$, for the cases of $n=3$ and $n=4$ in potential (\ref{['eq:mssm-p']}). The solid line represents the $n=3$ case with the same values for the potential parameters as in the previous two figures. The dashed line corresponds to the $n=4$ case with $m =1.1406\times 10^{-7}$ and $\lambda =1.448\times 10^{-16}$ (corresponding to $\phi_{0}=2.7818$) and, as in the $n=3$ case, we have chosen these values as they provide the best fit to the WMAP $5$-year data. Also, note that we have imposed the following initial conditions for the background field in both the cases: $\phi_{\rm ini}=10$ and ${\dot \phi}_{\rm ini}=0$. Evidently, the $n=3$ case departs from slow roll when $7\lesssim N \lesssim 15$, while the departure occurs during $4\lesssim N \lesssim 12$ in the case of $n=4$.
• Figure 4: The evolution of the scalar field has been plotted (as the solid black line) in the plane of the first two Hubble slow roll parameters $\epsilon$ and $\delta$ in the case of $n=3$ and for the best fit values of the parameters $m$ and $\lambda$ we have used earlier in Figs. \ref{['fig:mssm-p']} and \ref{['fig:pp']}. The black dots have been marked at intervals of one $e$-fold, while the dashed line corresponds to $\epsilon=-\delta$. Note that $\epsilon >1$ during $8<N<9$. In other words, during fast roll, inflation is actually interrupted for about a $e$-fold.
• Figure 5: The scalar power spectrum ${\cal P}_{_{\rm S}}(k)$ (the solid black line) have been plotted as a function of the wavenumber $k$ for the cases of $n=3$ (on top) and $n=4$ (at the bottom). We have chosen the same values for the potential parameters as in the earlier figures. Moreover, we should emphasize that we have arrived at these spectra by imposing the standard, Bunch-Davies, initial condition on all the modes. The red line in these plots is the spectrum (\ref{['eq:ps-ecm']}) with the exponential cut off. It corresponds to $A_{_{\rm S}} = 2\times 10^{-9}$, $n_{_{\rm S}}\simeq 0.945$, $\alpha=3.35$ and $k_{\ast}= 2.4\times 10^{-4}\; {\rm Mpc}^{-1}$ in the $n=3$ case, while $A_{_{\rm S}} = 2\times 10^{-9}$, $n_{_{\rm S}}\simeq 0.95$, $\alpha=3.6$ and $k_{\ast} = 9.0\times 10^{-4}\; {\rm Mpc}^{-1}$ in the case of $n=4$. Note that the vertical blue line denotes $k_{\ast}$. The inset in the top panel illustrates the difference between our model and the standard power law case (i.e. when ${\cal P}_{_{\rm S}}(k)=A_{_{\rm S}}\; k^{n_{_{\rm S}}-1}$, with the best fit values $A_{_{\rm S}}=2.1\times 10^{-9}$ and $n_{_{\rm S}}\simeq 0.955$) at smaller scales. This disparity leads to a difference in the CMB angular power spectrum at the higher multipoles, which we have highlighted in the inset in Fig. \ref{['fig:cl']}.