Multifield models of inflation with nonminimal couplings are in excellent agreement with the recent results from Planck. Across a broad range of couplings and initial conditions, such models evolve along an effectively single-field attractor solution and predict values of the primordial spectral index and its running, the tensor-to-scalar ratio, and non-Gaussianities squarely in the observationally most-favored region. Such models can also amplify isocurvature perturbations, which could account for the low power recently observed in the cosmic microwave background power spectrum at low multipoles. Future measurements of primordial isocurvature perturbations could distinguish between the currently viable possibilities.

Realistic models of high-energy physics include multiple scalar fields. Renormalization requires that the fields have nonminimal couplings to the spacetime Ricci curvature scalar, and the couplings can be large at the energy scales of early-universe inflation. The nonminimal couplings induce a nontrivial field-space manifold in the Einstein frame, and they also yield an effective potential in the Einstein frame with nontrivial curvature. The ridges or bumps in the Einstein-frame potential can lead to primordial non-Gaussianities of observable magnitude. We develop a covariant formalism to study perturbations in such models and calculate the primordial bispectrum. As in previous studies of non-Gaussianities in multifield models, our results for the bispectrum depend sensitively on the fields’ initial conditions.

This is the first of a three-part series of papers, in which we study the preheating phase for multifield models of inflation involving nonminimal couplings. In this paper, we study the single-field attractor behavior that these models exhibit during inflation and quantify its strength and parameter dependence. We further demonstrate that the strong single-field attractor behavior persists after the end of inflation. Preheating in such models therefore generically avoids the “dephasing” that typically affects multifield models with minimally coupled fields, allowing efficient transfer of energy from the oscillating inflaton condensate(s) to coupled perturbations across large portions of parameter space. We develop a doubly covariant formalism for studying the preheating phase in such models and identify several features specific to multifield models with nonminimal couplings, including effects that arise from the nontrivial field-space manifold. In papers II and III, we apply this formalism to study how the amplification of adiabatic and isocurvature perturbations varies with parameters, highlighting several distinct regimes depending on the magnitude of the nonminimal couplings ${\xi }_I$.

We study derivatively coupled fermions in axion-driven inflation, specifically m 2 φ φ 2 and monodromy inflation, and calculate particle production during the inflationary epoch and the post-inflationary axion oscillations. During inflation, the rolling axion acts as an effective chemical potential for helicity which biases the gravitational production of one fermion helicity over the other. This mechanism allows for efficient gravitational production of heavy fermion states that would otherwise be highly suppressed. Following inflation, the axion oscillates and fermions with both helicities are produced as the effective frequency of the fermion field changes non-adiabatically. For certain values of the fermion mass and axionfermion coupling strength, the two helicity states are produced asymmetrically, resulting in unequal number-densities of left-and right-helicity fermions.