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Register a new userRacetrack inflation and assisted moduli stabilisation
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Authors
Zygmunt Lalak
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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.
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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.
Inflation and moduli stabilisation mechanisms work well independently, and many string-motivated supergravity models have been proposed for them. However a complete theory will contain both, and there will be (gravitational) interactions between the two sectors. These give corrections to the inflaton potential, which generically ruin inflation. This holds true even for fine-tuned moduli stabilisation schemes. Following a suggestion by 0712.3460, we show that a viable combined model can be obtained if it is the Kahler functions (G= K+ln |W|^2) of the two sectors that are added, rather than the superpotentials (as is usually done). Interaction between the two sectors does still impose some restrictions on the moduli stabilisation mechanism, which are derived. Significantly, we find that the (post-inflation) moduli stabilisation scale no longer needs to be above the inflationary energy scale.
We study the cosmological properties of a metastable de Sitter vacuum obtained recently in the framework of type IIB flux compactifications in the presence of three D7-brane stacks, based on perturbative quantum corrections at both world-sheet and string loop level that are dominant at large volume and weak coupling. In the simplest case, the model has one effective parameter controlling the shape of the potential of the inflaton which is identified with the volume modulus. The model provides a phenomenological successful small-field inflation for a value of the parameter that makes the minimum very shallow and near the maximum. The horizon exit is close to the inflection point while most of the required e-folds of the Universe expansion are generated near the minimum, with a prediction for the ratio of tensor-to-scalar primordial fluctuations $r sim 4 times 10^{-4}$. Despite its shallowness, the minimum turns out to be practically stable. We show that it can decay only through the Hawking-Moss instanton leading to an extremely long decay rate. Obviously, in order to end inflation and obtain a realistic model, new low-energy physics is needed around the minimum, at intermediate energy scales of order $10^{12}$ GeV. An attractive possibility is by introducing a waterfall field within the framework of hybrid inflation.
A spectral index n_s < 0.95 appears to be a generic prediction of racetrack inflation models. Reducing a general racetrack model to a single-field inflation model with a simple potential, we obtain an analytic expression for the spectral index, which explains this result. By considering the limits of validity of the derivation, possible ways to achieve higher values of the spectral index are described, although these require further fine-tuning of the potential.
The one-loop vacuum energy is explicitly computed for a class of perturbative string vacua where supersymmetry is spontaneously broken by a T-duality invariant asymmetric Scherk-Schwarz deformation. The low-lying spectrum is tachyon-free for any value of the compactification radii and thus no Hagedorn-like phase-transition takes place. Indeed, the induced effective potential is free of divergence, and has a global anti de Sitter minimum where geometric moduli are naturally stabilised.
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