The Observational Status of Cosmic Inflation after Planck

TL;DR

This paper synthesizes Planck-era observations to assess the observational status of cosmic inflation, arguing that data strongly favor simple single-field slow-roll inflation with plateau-like potentials and negligible non-Gaussianities or isocurvature perturbations. It details how CMB measurements constrain the inflaton potential, slow-roll parameters, and the reheating epoch, and explains the implications for curvature and the energy scale of inflation. Bayesian model comparison shows plateau models are preferred, while many more complex scenarios are disfavored due to wasted parameter space. The work also outlines the prospects and experimental goals for future B-mode polarization measurements to directly probe primordial gravitational waves and the inflationary energy scale.

Abstract

The observational status of inflation after the Planck 2013 and 2015 results and the BICEP2/Keck Array and Planck joint analysis is discussed. These pedagogical lecture notes are intended to serve as a technical guide filling the gap between the theoretical articles on inflation and the experimental works on astrophysical and cosmological data. After a short discussion of the central tenets at the basis of inflation (negative self-gravitating pressure) and its experimental verifications, it reviews how the most recent Cosmic Microwave Background (CMB) anisotropy measurements constrain cosmic inflation. The fact that vanilla inflationary models are, so far, preferred by the observations is discussed and the reason why plateau-like potential versions of inflation are favored within this subclass of scenarios is explained. Finally, how well the future measurements, in particular of $B$-Mode CMB polarization or primordial gravity waves, will help to improve our knowledge about inflation is also investigated.

Figures (22)

• Figure 1: Mass-radius relations of neutron stars for different equations of state ("standard" in the left panel, more "exotic" in the right panel). Black curves correspond to the standard GR calculation while red curves represent the case where self-gravity of pressure is absent. Figure taken from Ref. Schwab:2008ce.
• Figure 2: Mass radius relations for different equations of state and associated theoretical uncertainties. In black are represented the mass radius relations obtained when $\chi=1$ (standard GR calculation) while, in red, are represented the mass radius relations obtained without self-gravity pressure (namely $\chi=0$). The hatched regions show the theoretical uncertainty associated with the fact that the equation of state is in fact unknown. It is clear from the plot that this completely dominates the differences between the $\chi=1$ and $\chi=0$ situations. Figure taken from Ref. Schwab:2008ce.
• Figure 3: Light elements abundances calculated when the Friedmann equation is modified according to Eq. (\ref{['eq:friedmodified']}). Greens contours are for deuterium abundance, blue ones for helium-$4$ and purple ones for lithium-$7$. The two gray ellipses indicate the region in parameter space allowed by observations. Figure taken from Ref. Rappaport:2007ct.
• Figure 4: Temperature anisotropy multipole moments obtained from the Planck $2013$ data versus the angular scale $\ell$ (notice that, for $\ell \leq 49$, the scale is logarithmic). The gray points denote the value of the multipole $C_{\ell}$ for each $\ell$ while the blue points represent the value of $C_{\ell}$ averaged in bands of width $\Delta \ell \simeq 31$. The red solid line shows the prediction of the best fit six-parameters $\Lambda$CDM model. The error bars correspond to $\pm 1\sigma$ uncertainties. The lower panel shows the residual signal once the best fit model has been subtracted. Figure taken from Ref. Ade:2013zuv.
• Figure 5: Same as Fig. \ref{['fig:TTplanck13']} but with the Planck $2015$ data. Notice that the quantity ${\cal D}_{\ell}$ is defined by ${\cal D}_{\ell}=\ell(\ell+1)C_{\ell}/(2\pi)$. This plot should be compared to Fig. \ref{['fig:TTplanck13']}. Figure taken from Ref. Planck:2015xua.