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Register a new userModuli and multi-field inflation
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Authors
Zygmunt Lalak
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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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Fluxbrane inflation is a stringy version of D-term inflation in which two fluxed D7-branes move towards each other until their (relative) gauge flux annihilates. Compared to brane-antibrane inflation, the leading-order inflationary potential of this scenario is much flatter. In the present paper we first discuss a new explicit moduli stabilisation procedure combining the F- and D-term scalar potentials: It is based on fluxed D7-branes in a geometry with three large four-cycles of hierarchically different volumes. Subsequently, we combine this moduli stabilisation with the fluxbrane inflation idea, demonstrating in particular that CMB data (including cosmic string constraints) can be explained within our setup of hierarchical large volume CY compactifications. We also indicate how the eta-problem is expected to re-emerge through higher-order corrections and how it might be overcome by further refinements of our model. Finally, we explain why recently raised concerns about constant FI terms do not affect the consistent, string-derived variant of D-term inflation discussed in this paper.
We present a model of inflation based on a racetrack model without flux stabilization. The initial conditions are set automatically through topological inflation. This ensures that the dilaton is not swept to weak coupling through either thermal effects or fast roll. Including the effect of non-dilaton fields we find that moduli provide natural candidates for the inflaton. The resulting potential generates slow-roll inflation without the need to fine tune parameters. The energy scale of inflation must be near the GUT scale and the scalar density perturbation generated has a spectrum consistent with WMAP data.
Hybrid inflation can be realised in low-energy effective string theory, as described using supergravity. We find that the coupling of moduli to F-term hybrid inflation in supergravity leads to a slope and a curvature for the inflaton potential. The epsilon and eta parameters receive contributions at tree and one loop level which are not compatible with slow roll inflation. Furthermore the coupling to the moduli sector can even prevent inflation from ending at all. We show that introducing shift symmetries in the inflationary sector and taking the moduli sector to be no-scale removes most of these problems. If the moduli fields are fixed during inflation, as is usually assumed, it appears that viable slow-roll inflation can then be obtained with just one fine-tuning of the moduli sector parameters. However, we show this is not a reasonable assumption, and that the small variation of the moduli fields during inflation gives a significant contribution to the effective inflaton potential. This typically implies that eta is approximately -6, although it may be possible to obtain smaller values with heavy fine-tuning.
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.
We develop the path integral formalism for studying cosmological perturbations in multi-field inflation, which is particularly well suited to study quantum theories with gauge symmetries such as diffeomorphism invariance. We formulate the gauge fixing conditions based on the Poisson brackets of the constraints, from which we derive two convenient gauges that are appropriate for multi-field inflation. We then adopt the in-in formalism to derive the most general expression for the power spectrum of the curvature perturbation including the corrections from the interactions of the curvature mode with other light degrees of freedom. We also discuss the contributions of the interactions to the bispectrum.
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