New InflationAmy Bender

05/03/2006

Inflation Basics• Perturbations from quantum fluctuations of

scalar field

• Fluctuations are:– Gaussian– Scale Invariant Spectrum (almost)

• k3PΦ(k) ~ constant

– Adiabatic– Scalar & Tensor

• Matter/radiation anisotropies & gravity waves

• N > 50 - 60 e-foldings

3 Parameters

• ns: Scalar spectral index– Scale free ns=1

• r: ratio of amplitude of tensor to scalar fluctuations (δH/AT)

• dns/dlnk: running of scalar spectral index

• WMAP 3 year data– ns ~ 0.951 ± 0.02– r < 0.28– dns/dlnk < 0

2

1

03

1)( H

ns

H

k

kkP

1)( TnTh kAkP

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

)(2

2

VL

02 2

d

dVaaH

Va

GH 222

2

1

3

8

negligible~

New Inflation Vega & Sanchez, astro-ph/0604136

• Quartic Trinomial Potential

– y is coupling parameter, h is asymmetry parameter

)(2

32232

1)( 432 hF

y

yyhw

)()( 4 wMNV foldse

0.5 1 1.5 2 2.5c

-0.2

-0.1

0.1

0.2

0.3

w 8w vs c<

χ

ωω 0=0

h=y=1

Energy Scale of Inflation

• Scalar perturbation amplitude

• From WMAP: = 4.67 10-5

• With N=50, find M ~ 0.77 1016

GeV• GUT scale ~ 1016 GeV—physics?

)(

)(

12 2'

34

2

22

w

w

M

MN

plk

GeVM pl18104.2

)1(~)('~)( Oww

k

Calculation of Parameters

• From limits of y & h, can constrain cosmology

• ns: limit on the maximum value

– ns,max = 0.96

• r < 0.16 for all coupling parameters

• dns/dlnk: depends on coupling (or other params)

• WMAP ns = 0.95– 0.03 < r < 0.04

– -0.00070 < dns/dlnk < -0.00055

• Consistent!!!

Other Scenarios

• Hybrid Inflation– Inflation field is coupled to another scalar field

• Chaotic Inflation– V(φ)=λφ4, 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?