Geometrically consistent approach to stochastic DBI inflation
- Theoretical and Mathematical Physics Group, Centre for Particle Physics and Phenomenology, Louvain University, 2 Chemin du Cyclotron, 1348 Louvain-la-Neuve (Belgium)
Stochastic effects during inflation can be addressed by averaging the quantum inflaton field over Hubble-patch-sized domains. The averaged field then obeys a Langevin-type equation into which short-scale fluctuations enter as a noise term. We solve the Langevin equation for an inflaton field with a Dirac-Born-Infeld (DBI) kinetic term perturbatively in the noise and use the result to determine the field value's probability density function (PDF). In this calculation, both the shape of the potential and the warp factor are arbitrary functions, and the PDF is obtained with and without volume effects due to the finite size of the averaging domain. DBI kinetic terms typically arise in string-inspired inflationary scenarios in which the scalar field is associated with some distance within the (compact) extra dimensions. The inflaton's accessible range of field values therefore is limited because of the extra dimensions' finite size. We argue that in a consistent stochastic approach the inflaton's PDF must vanish for geometrically forbidden field values. We propose to implement these extra-dimensional spatial restrictions into the PDF by installing absorbing (or reflecting) walls at the respective boundaries in field space. As a toy model, we consider a DBI inflaton between two absorbing walls and use the method of images to determine its most general PDF. The resulting PDF is studied in detail for the example of a quartic warp factor and a chaotic inflaton potential. The presence of the walls is shown to affect the inflaton trajectory for a given set of parameters.
- OSTI ID:
- 21415218
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 82, Issue 2; Other Information: DOI: 10.1103/PhysRevD.82.023515; (c) 2010 The American Physical Society; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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