cifar08/Lindefest 5-9 March, 2008. Nonlinear curvature perturbations in two-field hybrid inflation. -- d N in exactly soluble models --. Yukawa Institute (YITP) Kyoto University. Misao Sasaki. Happy Kanreki, Andrei!. kanreki = one cycle of chinese zodiacal calendar. 祝還暦. 60 yrs =
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5-9 March, 2008
-- dN in exactly soluble models --
Yukawa Institute (YITP)
kanreki = one cycle of
chinese zodiacal calendar
60 yrs =
x 5 elements
this (Andrei’s) year
mouse x earth
also, Red is a color
A person is regarded as reborn on the 60th birthday
Linde ’82, ...
explains the origin of cosmological perturbations.
finally observed by COBE & WMAP!
Inflation from string theory
KKLMMT ’03, ...
brane/DBI inflation, moduli inflation, ...
may lead to large non-Gaussianity.
−9 < fNLlocal < 111 (WMAP 5yr)
may be detected in the very near future
In this talk, I analyze full nonlinear curvature perturbations
in exactly soluble models of slow-roll inflation
Using dN formalism,
(dN··· e-folding number perturbation)
We may deepen our understanding of
Because it’s fun!
Starobinsky ‘85, MS & Stewart ‘96, MS & Tanaka '98,
Lyth, Malik & MS ‘04,....
Separate universe (gradient expansion) approach
Belinski et al. ’70, Tomita ’72, Salopek & Bond ’90, …
٠٠٠ curvature perturbation
on comoving slice
defined by an integral
→ gauge invariance
MS & Tanaka ’98, Lyth & Rodriguez ’05, ...
→ N=indep. of df/dt
where df =dfF (on flat slice) at horizon-crossing.
(e.g., power-law inflation)
Slow-roll equations of motion
e-folding number from the end of inflation
for each a
this is sufficient
new field space
··· na is conserved
solvability (n-1) constants of integration
where (q, na) and (dq, dna) are the values at horizon
crossing during inflation
perturbations orthogonal to dqa/dN
entropy perturbation during inflation
Polarski & Starobinsky ’94,
Mukhanov & Steinhardt ’97, MS & Tanaka ’98,...
entropy perturbation at the end of inflation
Bernardeau, Kofman & Uzan ‘04, Lyth ‘05, ...
inflation4. Two (plus one)-field hybrid inflation
∙ can be easily generalized to n fields
and the universe is thermalized instantaneously.
Parametrize orbits by an angle at the end of inflation
(∙∙∙ const of motion)
This determines g in terms of f1 & f2 .
(assuming instantaneous thermalization)
However, this correction is negligible
No non-Gaussianity if dfis Gaussian
“true” entropy perturbation
linear entropy perturbation
contributes at 2nd order
practically any non-Gaussianity is possible
hope you like it...
(classically. negligible quantum corrections assumed)