1. New Inflation Amy Bender 05/03/2006

2. Inflation Basics Perturbations from quantum fluctuations of scalar field Fluctuations are: –Gaussian –Scale Invariant Spectrum (almost) k 3 P Φ (k) ~ constant –Adiabatic –Scalar & Tensor Matter/radiation anisotropies & gravity waves N > 50 - 60 e-foldings

3. 3 Parameters n s : Scalar spectral index –Scale free  n s =1 r: ratio of amplitude of tensor to scalar fluctuations (δ H /A T ) dn s /dlnk: running of scalar spectral index WMAP 3 year data –n s ~ 0.951 ± 0.02 –r < 0.28 –dn s /dlnk < 0

4. Single Field Inflation Effective Lagrangian –Potential dominates KE Evolution Equations (from energy momentum tensor & Friedmann Eqn) Slow Roll Approximation –Inflation field & Hubble parameter vary slowly –Parameters in terms of derivatives of the potential

5. New Inflation Vega & Sanchez, astro-ph/0604136 Quartic Trinomial Potential –y is coupling parameter, h is asymmetry parameter χ ω ω 0 =0 h=y=1

6. Energy Scale of Inflation Scalar perturbation amplitude From WMAP: = 4.67  10 -5 With N=50, find M ~ 0.77  10 16 GeV GUT scale ~ 10 16 GeV—physics?

8. Calculation of Parameters From limits of y & h, can constrain cosmology n s : limit on the maximum value –n s,max = 0.96 r < 0.16 for all coupling parameters dn s /dlnk: depends on coupling (or other params) WMAP n s = 0.95 –0.03 < r < 0.04 –-0.00070 < dn s /dlnk < -0.00055 Consistent!!!

9. Other Scenarios Hybrid Inflation –Inflation field is coupled to another scalar field Chaotic Inflation –V(φ)=λφ 4, initial ‘chaotic’ distribution of φ ≠ 0 Future of New Inflation –Need to constrain r & running parameter better observationally –What does this mean for GUT theory?