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Contrasting LQC and WDW Theory Using an Exactly Solvable Model

Contrasting LQC and WDW Theory Using an Exactly Solvable Model

Contrasting LQC and WDW Theory Using an Exactly Solvable Model

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How much does the Cosmos recall?<br />

Consider a general state in the present epoch (post big b<strong>an</strong>g)<br />

describing a large classical universe at low curvature<br />

lim<br />

φ→∞<br />

<br />

(∆ˆV )<br />

〈 ˆ V 〉<br />

2<br />

Relative dispersion in curvature:<br />

= J−<br />

I 2 −<br />

− 1 =: δv ≪ 1<br />

(∆t<strong>an</strong>(λb/2)/〈t<strong>an</strong>(λb/2)〉) = √ 12πG∆x =: δb ≪ 1<br />

D = (∆V/〈ˆV 〉) 2 φ→−∞ − (∆V/〈ˆV 〉) 2 φ→∞<br />

< (1 + δv) (e 8δb − 1)<br />

Difference bounded by the relative dispersions in the initial state. A<br />

semi-classical initial state evolves to a semi-classical state after the<br />

bounce. Fluctuations are symmetric up to very small difference.<br />

Answer: Universe has a very very sharp memory.<br />

Cosmos remembers almost everything after the bounce.<br />

IGC Inaugural Conference – p.10

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