Conservation of the non-linear curvature perturbation in generic single-field inflation. Yukawa Institute for Theoretical Physics Atsushi Naruko. In Collaboration with Misao Sasaki Based on : Class. Quantum Grav. 28 072001. The contents of talk.
Yukawa Institute for Theoretical Physics
In Collaboration with Misao Sasaki
Based on : Class. Quantum Grav. 28 072001
1, curvature perturbation and non-Gaussianity
2, gradient expansion approach
3, conservation of non-linear curvature perturbation
3.1, G = 0 (for canonical, k-essential scalar)
3.2, G ≠ 0 (for Galileon scalar) in Einstein gravity
potential, therefore it gives the initial condition for
Cosmic Microwave Background (CMB).
we can subtract the information of primordial universe.
as a new window for primordial universe.
temperature fluctuations in CMB are scale invariant and
are Gaussianly distributed.
we have to make a analysis beyond linear order.
1. the standard perturbative approach.
2. the gradient expansion approach
in powers of spatial gradients, therefore, it is applicable
only to perturbations on superhorizon scales.
→ However, the full nonlinear effects are taken into account.
Mizuno-san and De Felice-san,
we know well about the perturbation
in Galileon field at horizon exit.
and write down the energy conservation law,
the rhs become a function of t
if P is the function of ρ
curvature per. is conserved
curvature perturbation is conserved on uniform energy density
slice regardless of gravity theory.
satisfied is not so trivial because the relation between P and ρ
Galileon : very much complicated…
on superhorizon scales in rather generic single-feild inflation
using gradient expansion approach.
by using scalar field equation.
is conserved in the case of scalar field.
t = const.
Again, in the attractor stage, we can show the conservation of
curvature perturbation on the uniform scalar field slice.
the evolution of curvature perturbation on superhorizon scales
in the case of single scalar field inflation.
shown without invoking gravity theory because there appear
a second derivative of Ψ in the scalar field equation.
second derivative by first derivative and we can show the
conservation of curvature perturbation in the attractor stage.