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S =<br />
⇤<br />
d 4 x ⇥<br />
g<br />
⇥<br />
R<br />
16 G + X V (⇥)<br />
Scalar perturbations <br />
Tensor perturbations <br />
ds 2 =<br />
(1 + 2A)dt 2 +2 i Bdtdx i + a 2 (t) [(1 + 2R) ij + h ij ] dx i dx j<br />
Scalar <br />
S (2)<br />
s = dtd 3 xa 3 Q s Ṙ 2 c 2 s<br />
a 2 ( R)2<br />
For standard potential-‐driven inflation <br />
Q s =<br />
˙2<br />
c 2<br />
2H 2 , s =1<br />
The amplitude of curvature perturbations <br />
can be estimated by solving <strong>the</strong> equation <br />
of motion which follows from <strong>the</strong> above <br />
action. <br />
<br />
<br />
<br />
<br />
The conditions for <strong>the</strong> avoidance <br />
of ghosts and Laplacian instabilities <br />
Q s > 0 c 2 s > 0<br />
,
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