Inflation and Precision Cosmology

TL;DR

The paper surveys inflation as a generic mechanism for solving early-un universe problems and generating structure, focusing on the single-field slow-roll realization and how to compute predictions from a given model using gauge-invariant perturbation theory. It derives the scalar and tensor power spectra, showing that a nearly scale-invariant scalar spectrum with spectral index n_S−1 ≈ −2ε_1−ε_2 and a tensor-to-scalar ratio r ≈ 16ε_1 emerges from slow-roll dynamics. The analysis classifies major inflationary potentials (large-field, small-field, linear, exponential, hybrid) and compares their predictions with WMAP data, revealing which models are favored or disfavored and highlighting the role of the number of e-folds N_*. The discussion also addresses open issues such as embedding inflation in high-energy theories and the trans-Planckian problem, emphasizing how future observations could constrain new physics using cosmology.

Abstract

A brief review of inflation is presented. After having demonstrated the generality of the inflationary mechanism, the emphasize is put on its simplest realization, namely the single field slow-roll inflationary scenario. Then, it is shown how, concretely, one can calculate the predictions of a given model of inflation. Finally, a short overview of the most popular models is given and the implications of the recently released WMAP data are briefly (and partially) discussed.

Figures (5)

• Figure 1: Left panel: Sketch of the evolution of the horizon. The origin of the coordinates is chosen to be Earth. The red circles represent the size of the horizon at the time of equality, $z_{\rm eq} \simeq 10^4$. The green circles represent the horizon at the time of recombination $z_{\rm rec}\simeq 1100$. The black circle represents the horizon today. The dotted blue circle represents the surface of last scattering viewed from Earth. The angle $\Delta \Omega$ is the angular size of the horizon at recombination viewed from Earth. Right panel: Sketch of the evolution of the horizon in an inflationary universe. The conventions are the same as in the left panel. The horizon at recombination now includes the last scattering surface and there is no horizon problem anymore
• Figure 2: Evolution of the Hubble radius and of three physical wavelengths with different comoving wavenumbers during the inflationary phase and the subsequent radiation and matter dominated epochs. Without inflation, the wavelengths of the mode are super-Hubble initially whereas in the case where inflation takes place, they are sub-Hubble which permits to set up sensible initial conditions.
• Figure 3: Sketch of the effective potential of Eqs. (\ref{['eomscalar']}) and (\ref{['eomtensor']}). During the inflationary phase the effective potential behaves as $U\simeq \eta ^{-2}$ while during the radiation dominated era it goes to zero. A smooth transition between these two epochs has been assumed which does not take into account the details of the reheating (and preheating) process.
• Figure 4: The various models discussed in this article represented in the plan $(\epsilon _1,\epsilon _2)$. The dotted lines are the lines of constant spectral index. The full lines represent the location of the large field models. The small field models are concentrated along the $\epsilon _1=0, \epsilon _2>0$ axis whereas the exponential models are along the $\epsilon _2=0$ line. Hybrid models have $n_{_{\mathrm{S}}}>1$ and $\epsilon _2<0$.
• Figure 5: Left panel: allowed region in the plan $(\epsilon _1,\epsilon _2)$ coming from the recently released WMAP data as analyzed in Ref. LL. Right panel: zoom of the left panel. The model $V(\phi _{_0} ) \propto \phi _{_0} ^4$ is now under big observational pressure. These two figures are from Ref. LL.