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Register a new userScaling attractors in multi-field inflation
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Multi-field inflation with a curved scalar geometry has been found to support background trajectories that violate the slow-roll, slow-turn conditions and thus have the potential to evade the swampland constraints. In order to understand how generic this novel behaviour is and what conditions lead to it, we perform a classification of dynamical attractors of two-field inflation that are of the scaling type. Scaling solutions form a one-parameter generalization of De Sitter solutions with a constant value of the first Hubble flow parameter $epsilon$ and, as we argue and demonstrate, form a natural starting point for the study of non-slow-roll slow-turn behaviour. All scaling solutions can be classified as critical points of a specific dynamical system. We recover known multi-field inflationary attractors as approximate scaling solutions and classify their stability using dynamical system techniques. In particular, we discover that dynamical bifurcations play an integral role in the transition between geodesic and non-geodesic motion and discuss the ability of scaling solutions to describe realistic multi-field models. We revisit the criteria for background stability and show cases where the usual criteria found in the literature do not capture the background evolution of the system.
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We explore the dynamics of multi-field models of inflation in which the field-space metric is a hyperbolic manifold of constant curvature. Such models are known as $alpha$-attractors and their single-field regimes have been extensively studied in the context of inflation and supergravity. We find a variety of multi-field inflationary trajectories in different regions of parameter space, which is spanned by the mass parameters and the hyperbolic curvature. Amongst these is a novel dynamical attractor along the boundary of the Poincare disc which we dub angular inflation. We calculate the evolution of adiabatic and isocurvature fluctuations during this regime and show that, while isocurvature modes decay during this phase, the duration of the angular inflation period can shift the single-field predictions of $alpha$-attractors.
We analyze and compare the multi-field dynamics during inflation and preheating in symmetric and asymmetric models of $alpha$-attractors, characterized by a hyperbolic field-space manifold. We show that the generalized (asymmetric) E- and (symmetric) T-models exhibit identical two-field dynamics during inflation for a wide range of initial conditions. The resulting motion can be decomposed in two approximately single-field segments connected by a sharp turn in field-space. The details of preheating can nevertheless be different. For the T-model one main mass-scale dominates the evolution of fluctuations of the spectator field, whereas for the E-model, a competing mass-scale emerges due to the steepness of the potential away from the inflationary plateau, leading to different contributions to parametric resonance for small and large wave-numbers. Our linear multi-field analysis of fluctuations indicates that for highly curved manifolds, both the E- and T-models preheat almost instantaneously. For massless fields this is always due to efficient tachyonic amplification of the spectator field, making single-field results inaccurate. Interestingly, there is a parameter window corresponding to $r={cal O}(10^{-5})$ and massive fields, where the preheating behavior is qualitatively and quantitatively different for symmetric and asymmetric potentials. In that case, the E-model can completely preheat due to self-resonance for values of the curvature where preheating in the T-model is inefficient. This provides a first distinguishing feature between models that otherwise behave identically, both at the single-field and multi-field level. Finally, we discuss how one can describe multi-field preheating on a hyperbolic manifold by identifying the relevant mass-scales that control the growth of inflaton and spectator fluctuations, which can be applied to any $alpha$-attractor model and beyond.
In this PhD thesis, we investigate generic features of inflation which are strictly related to fundamental aspects of UV-physics scenarios, such as string theory or supergravity. After a short introduction to standard and inflationary cosmology, we present our research findings. On the one hand, we show that focusing on universality properties of inflation can yield surprisingly stringent bounds on its dynamics. This approach allows us to identify the regime where the inflationary field range is uniquely determined by both the tensor-to-scalar ratio and the spectral index. Then, we derive a novel field-range bound, which is two orders of magnitude stronger than the original one derived by Lyth. On the other hand, we discuss the embedding of inflation in supergravity and prove that non-trivial hyperbolic Kahler geometries induce an attractor for the inflationary observables: the spectral tilt tends automatically to the center of the Planck dome whereas the amount of primordial gravitational waves is directly controlled by curvature of the internal manifold. We identify the origin of this attractor mechanism in the so-called $alpha$-scale supergravity model. Finally, we show how the inclusion of a nilpotent sector, allowing for a unified description of inflation and dark energy, implies an enhancement of the attractor nature of the theory. The main results of this thesis have been already published elsewhere. However, here we pay special attention to present them in a comprehensive way and provide the reader with the necessary background.
We study the consequences of spatial coordinate transformation in multi-field inflation. Among the spontaneously broken de Sitter isometries, only dilatation in the comoving gauge preserves the form of the metric and thus results in quantum-protected Slavnov-Taylor identities. We derive the corresponding consistency relations between correlation functions of cosmological perturbations in two different ways, by the connected and one-particle-irreducible Greens functions. The lowest-order consistency relations are explicitly given, and we find that even in multi-field inflation the consistency relations in the soft limit are independent of the detail of the matter sector.
Moduli with flat or run-away classical potentials are generic in theories based on supersymmetry and extra dimensions. They mix between themselves and with matter fields in kinetic terms and in the nonperturbative superpotentials. As the result, interesting structure appears in the scalar potential which helps to stabilise and trap moduli and leads to multi-field inflation. The new and attractive feature of multi-inflationary setup are isocurvature perturbations which can modify in an interesting way the final spectrum of primordial fluctuations resulting from inflation.
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