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Standard slow-­‐roll inflation <br />

S =<br />

⇤<br />

d 4 x ⇥<br />

ä<br />

a = 8 G<br />

3<br />

V ( )<br />

V (⇥)<br />

Inflation occurs under <strong>the</strong> condition <br />

g<br />

⇥<br />

R<br />

16 G + X V (⇥)<br />

On <strong>the</strong> FLRW background, <strong>the</strong> scale factor obeys <br />

˙2<br />

˙⇥2 ⇥<br />

X = 1 (⇥ )2<br />

2<br />

V ( )<br />

Slow-­‐roll <br />

The field evolves slowly along a <br />

nearly flat potential (slow-­‐roll). <br />

In this case <br />

H<br />

Cosmic acceleration <br />

ȧ<br />

a ⇥ const. a e H inf t

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