Single Field Models of Inflation after WMAP5

1. Single Field Models of Inflation after WMAP5 • Laila Alabidi, QMUL • Cosmo’08 • 26th of August 2008 “The Inflationary Universe” by Harry St. Ours

2. Overview • Review I: Action of a scalar field • Review II: Parameterising inflation. • Canonical Models • A non-Canonical Model: Dirac Born Infeld Models in the Ultra Violet Regime • Results • Questions & Comments

3. The Action of the Scalar Field • The action of a scalar field looks something like this: • X is the kinetic terms and is given by , R is the Ricci scalar and g is the metric. • In the canonical case the pressure term is given by: • The non-canonical case is a bit more complicated, and we will present the DBI case in a later section.

4. Parametrising Inflation • Sound speed of inflaton fluctuations is defines as: • The inflationary parameters are then: • both of which must be < 1 for the universe to inflate. • Specializing to , these parameters reduce to the slow roll parameters constrained solely by the inflationary potential: • How much inflation?

5. Observable Parameters Curvature Perturbation scale • The spectrum is defined as: • The spectral index defines the scale dependence of the spectrum: • The tensor fraction is defined as: spectrum of gravitational waves

6. The Non-Gaussianity Parameter • This definition will be needed to comprehend the results for the non-canonical model that we consider. • Usually we take the easy route and assume that the perturbations are gaussian, however not necessarily 100% true, the curvature perturbation ζ may deviate slightly from gaussianity. • To quantify, we split ζ into a guassian (ζg) and a non-gaussian (ζng) part. We define the non-gaussian part as the square of the gaussian part: • So far: canonical models seem to predict fNL<<1. • The observational limits on fNL for the equilateral configuration (where the three wavenumbers are roughly equal) and which is predicted by DBI models is:

7. Small Field Models Canonical Models I p>0, inflaton rolls away from the origin • The tree level potential: • The logarithmic Potential: • The exponential potential: Taylor expand about the vacuum, then assume one of the p’s dominates. p<0, inflaton rolls towards the origin p<0 & logarithmic, inflaton rolls towards the origin p<0, logarithmic and exponential , inflaton rolls towards the origin *not so if μ>mpl

8. Canonical Models II • The monomial potential: • α is a positive integer: chaotic. • α <1: Monodromy Large Field Models • The sinusoidal potential: Hilltop regime Chaotic regime

9. A non-canonical model

10. The Calabi Yau Manifold Bulk Brane escaping throat (IR) Brane falling into throat (UV) Warped throat where inflation takes place. This image is taken from a talk by Henry Tye @ the VEU 25 conference

11. Basically a direct relation between observables and string theoretic parameters The DBI model The pressure term is given by: is the tension of the brane. Modified consistency relation: is the base volume of the throat, is the string coupling, is related to the topology of the throat and is the wrapped volume

12. Results

13. Small Field Models p=0 p<0 |p|→∞ p>0

15. Large Field Model N=61 N=30 N=47 η=0 Axion Monodromy Limit of of constant warp factor in the (UV) DBI model Planck sensitivity

17. Single Brane Single Brane, either wrapped around throat base or wound around the throat Multiple branes (UV) DBI Expected values p is winding number. q is the symmetry level n is the number of branes (n<10) branes are randomly spaced. So, for example, the single unwound D5 then requires either

18. UV DBI: inconsistency with data. Need geometry which allows for a larger Euler number or which motivates a tiny base volume. Tree level potential: either reject the tree level potential with p>0 or find solid reason for suppressing lower order terms.