No Arabic abstract
We propose a new technique to study fast transitions during inflation, by studying the dynamics of quantum quenches in an $O(N)$ scalar field theory in de Sitter spacetime. We compute the time evolution of the system using a non-perturbative large-$N$ limit approach. We derive the self-consistent mass equation for several physically relevant transitions of the parameters of the theory, in a slow motion approximation. Our computations reveal that the effective mass after the quench evolves in the direction of recovering its value before the quench, but stopping at a different asymptotic value, in which the mass squared is strictly positive. Furthermore, we tentatively find situations in which the effective mass squared can be temporarily negative, thus breaking the $O(N)$ symmetry of the system for a certain time, only to then come back to a positive value, restoring the symmetry. We argue the relevance of our new method in a cosmological scenario.
We show how the choice of an inflationary state that entangles scalar and tensor fluctuations affects the angular two-point correlation functions of the $T$, $E$, and $B$ modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, tensor-tensor, and scalar-tensor power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate how such a state would modify the angular correlations in the CMB with a simple example where the initial state is a small perturbation away from the Bunch-Davies state. Because the state breaks some of the rotational symmetries, the angular power spectra no longer need be strictly diagonal.
We discuss and clarify the validity of effective single field theories of inflation obtained by integrating out heavy degrees of freedom in the regime where adiabatic perturbations propagate with a suppressed speed of sound. We show by construction that it is indeed possible to have inflationary backgrounds where the speed of sound remains suppressed and slow-roll persists for long enough. In this class of models, heavy fields influence the evolution of adiabatic modes in a manner that is consistent with decoupling of physical low and high energy degrees of freedom. We emphasize the distinction between the effective masses of the isocurvature modes and the eigenfrequencies of the propagating high energy modes. Crucially, we find that the mass gap that defines the high frequency modes increases with the strength of the turn, even as the naive heavy (isocurvature) and light (curvature) modes become more strongly coupled. Adiabaticity is preserved throughout, and the derived effective field theory remains in the weakly coupled regime, satisfying all current observational constraints on the resulting primordial power spectrum. In addition, these models allow for an observably large equilateral non-Gaussianity.
We study the structure of multi-field inflation models where the primordial curvature perturbation is able to vigorously interact with an ultra-light isocurvature field -- a massless fluctuation orthogonal to the background inflationary trajectory in field space. We identify a class of inflationary models where ultra-light fields can emerge as a consequence of an underlying scaling transformation that rescales the entire systems action and keeps the classical equations of motion invariant. This scaling invariance ensures the existence of an ultra-light fluctuation that freezes after horizon crossing. If the inflationary trajectory is misaligned with respect to the scaling symmetry direction, then the isocurvature field is proportional to this ultra-light field, and becomes massless. In addition, we find that even if the isocurvature field interacts strongly with the curvature perturbation --transferring its own statistics to the curvature perturbation-- it is unable to induce large non-Gaussianity. The reason is simply that the same mechanism ensuring a suppressed mass for the isocurvature field is also responsible for suppressing its self-interactions. As a result, in models with light isocurvature fields the bispectrum is generally expected to be slow-roll suppressed, but with a squeezed limit that differs from Maldacenas consistency relation.
We derive the stochastic description of a massless, interacting scalar field in de Sitter space directly from the quantum theory. This is done by showing that the density matrix for the effective theory of the long wavelength fluctuations of the field obeys a quantum version of the Fokker-Planck equation. This equation has a simple connection with the standard Fokker-Planck equation of the classical stochastic theory, which can be generalised to any order in perturbation theory. We illustrate this formalism in detail for the theory of a massless scalar field with a quartic interaction.
We use the Wilsonian functional Renormalisation Group (RG) to study quantum corrections for the Higgs inflationary action including the effect of gravitons, and analyse the leading-order quantum gravitational corrections to the Higgs quartic coupling, as well as its non-minimal coupling to gravity and Newtons constant, at the inflationary regime and beyond. We explain how within this framework the effect of Higgs and graviton loops can be sufficiently suppressed during inflation, and we also place a bound on the corresponding value of the infrared RG cut-off scale during inflation. Finally, we briefly discuss the potential embedding of the model within the scenario of Asymptotic Safety, while all main equations are explicitly presented.