Gauge Fields and Inflation

TL;DR

This review examines how gauge fields can influence inflation by appearing in the background or at the level of perturbations. It surveys two broad avenues: (i) background gauge fields leading to anisotropic or isotropic inflation with potential no-hair violations, and (ii) perturbation-level gauge fields generating seeds for primordial magnetic fields, statistical anisotropy, and non-Gaussianity, including gravitational waves. It then details two concrete frameworks: anisotropic inflation with a gauge-kinetic function f(\phi)^2 F^2 and gauge-flation, where non-Abelian gauge fields (SU(2)) drive nearly de Sitter expansion via F^2 and a higher-order F^4-like κ-term, with isotropy preserved by a triad and stability analyzed. The work highlights observational probes such as direction-dependent power spectra, anisotropic NG, TB/EB correlations in the CMB, and potential parity-violating gravitational waves, while discussing backreaction, backreaction-induced attractor behavior, and the cosmic minimum-hair conjecture. Overall, the paper provides a cohesive framework connecting high-energy gauge theories to inflationary dynamics and observable signatures.

Abstract

The isotropy and homogeneity of the cosmic microwave background (CMB) favors "scalar driven" early Universe inflationary models. Non-scalar fields, and in particular gauge fields, are on the other hand commonplace in all high energy particle physics models proposed to be at work at the upper bound on energy scale of inflation set by the current CMB observations. In this review we consider the role and consequences, theoretical and observational, that gauge fields can have during inflationary era. Gauge fields may be turned on in the background during inflation, or may become relevant at the level of cosmic perturbations. There have been two main class of models with gauge fields in the background, models which show violation of cosmic no-hair theorem and those which lead to isotropic FLRW cosmology, respecting the cosmic no-hair theorem. Models in which gauge fields are only turned on at the cosmic perturbation level, may source primordial magnetic fields. We also review specific observational features of these models on the CMB and/or the primordial cosmic magnetic fields. Our discussions will be mainly focused on the inflation period, with only a brief discussion on the post inflationary (p)reheating era.

Figures (23)

• Figure 1: In this figure, we have the $1\sigma$ and $2\sigma$ observational contour bounds from the combined data of 7-year WMAP+BAO+H0. The points here represent the theoretical predictions of inflation models with monomial potentials, $V (\varphi)=V_0\varphi^n$ . The solid line represents the model with $n$ = 4, the dashed line has $n$= 2 and the dotted line denotes the multi-axion field models with $n$= 2 and $\beta$= 1/2 in Easther:2005zr, with e-folds $N_e=50$ and $60$ (from top to bottom). This figure is taken from Komatsu:2010fb.
• Figure 2: Trajectory of the inflaton field $\phi$ in phase space. This trajectory is drawn for parameters $c=2$ and $m=10^{-5}$ and with initial conditions $\phi_i=12$ and $\dot{\phi}_i=0$. There are two different slow-roll phases, namely isotropic and anisotropic inflation. The transition occurs around $\phi= 9$.
• Figure 3: The time evolutions of the anisotropy $\Sigma/H$ for various $c$ with respect to the number of $e$-folds. The anisotropic inflation phase can be sufficiently long.
• Figure 4: Several trajectories in $X$-$Y$-$Z$ space are shown for $\lambda = 0.1, \rho=50$. The trajectories converge to the attractor corresponding to anisotropic inflation.
• Figure 5: For a uniform coupling $g=5$, we plotted time evolutions of anisotropic expansion rate normalized by the Hubble parameter with respect to the e-fold number time $\tau$. The components $\Sigma_+$, $\Sigma_-$, $\Sigma_{23}$, $\Sigma_{13}$, and $\Sigma_{12}$ correspond to thick, dashed, blue, red, and green lines, respectively.