A Smooth Landscape: Ending Saddle Point Inflation Requires Features to be Shallow

Abstract

We consider inflation driven near a saddle point in a higher dimensional field space, which is the most likely type of slow roll inflation on the string theoretical landscape; anthropic arguments need to be invoked in order to find a sufficiently flat region. To give all inflatons large masses after inflation and yield a small but positive cosmological constant, the trajectory in field space needs to terminate in a hole on the inflationary plateau, introducing a curved end-of-inflation hypersurface. We compute non-Gaussianities (bi- and tri-spectrum) caused by this curved hyper-surface and find a negative, potentially large, local non-linearity parameter. To be consistent with current observational bounds, the hole needs to be shallow, i.e. considerably wider than deep in natural units. To avoid singling out our vacuum as special (i.e. more special than a positive cosmological constant entails), we deduce that all features on field space should be similarly shallow, severely limiting the type of landscapes one may use for inflationary model building. We justify the use of a truncated Fourier series with random coefficients, which are suppressed the higher the frequency, to model such a smooth landscape by a random potential, as is often done in the literature without a good a priory reason.

23 pages, 2 figures; v2: slightly extended to match JCAP version (conclusions unchanged)

References in corpus (25)

• Planck 2013 results. XVI. Cosmological parameters
• Flux Compactification
• The Anthropic Landscape of String Theory
• Non-Gaussianity in the modulated reheating scenario
• Mass hierarchies and non-decoupling in multi-scalar field dynamics
• Heavy fields, reduced speeds of sound and decoupling during inflation
• CMB Constraints on Primordial non-Gaussianity from the Bispectrum (f_{NL}) and Trispectrum (g_{NL} and τ_{NL}) and a New Consistency Test of Single-Field Inflation
• Measure and Probability in Cosmology
• On Classification of Models of Large Local-Type Non-Gaussianity
• Cosmology From Random Multifield Potentials
• Accidental Inflation in String Theory
• Tumbling through a landscape: Evidence of instabilities in high-dimensional moduli spaces
• Search for stopped long-lived particles produced in pp collisions at sqrt(s) = 7 TeV
• Exploring a string-like landscape
• A non-Gaussian landscape
• Rapid Tunneling and Percolation in the Landscape
• Small Steps and Giant Leaps in the Landscape
• Probing Two-Field Open Inflation by Resonant Signals in Correlation Functions
• On the Unlikeliness of Multi-Field Inflation: Bounded Random Potentials and our Vacuum
• Star Formation in the Multiverse
• The Scale of Inflation in the Landscape
• A Renormalization Group Approach to the Cosmological Constant Problem
• Folded Inflation, Primordial Tensors, and the Running of the Scalar Spectral Index
• Eternal inflation and localization on the landscape
• The instability of orientifolds and the end of the (string) landscape as we know it

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• Untangling features in the primordial spectra
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• Classical transitions with the topological number changing in the early Universe
• Local random potentials of high differentiability to model the Landscape
• What Planck does not tell us about inflation
• Particle Production during Inflation in Light of PLANCK
• Cosmological Formation of (2+1)-Dimensional Soliton Structures in Models Possessing Potentials with Local Peaks
• Analytic results in aligned axion inflation