Manuscript XIX-A@1 · XIX-A.tex · section · e30d8062

The cosmological comparison background

The scalar-clock lapse and the original spatial rods › The cosmological comparison background · lines 523–545

XIX-A@1#eq:background, XIX-A@1#eq:N0

Use the displayed background of the supplied Em02-E record:

q_{0} T_{0} (t) H (t) = - d t^{2} + a (t)^{2} δ_{ij} d x^{i} d x^{j}, a (t) = a_{*} (t / t_{*})^{p}, = ϕ_{*} + 2 p M_{Pl} lo g (t / t_{*}), p > 1, = \frac{a ˙}{a} = \frac{p}{t}, v (t) = T ˙_{0} (t) = \frac{2 p M _{Pl}}{t} > 0.

Work on a fixed closed subinterval of $(t_{*} /2, 2 t_{*})$ . There is no limit toward $t = 0$ . The background lapse is

N_{0} (t) = \frac{1}{v ( t )} .

Only the displayed geometry and nondegenerate clock are needed below. We do not import an Einstein-equation theorem as a premise of a separation calculation.

Displayed formulas in this passage

XIX-A@1#eq:background · line 526
$q_{0} T_{0} (t) H (t) = - d t^{2} + a (t)^{2} δ_{ij} d x^{i} d x^{j}, a (t) = a_{*} (t / t_{*})^{p}, = ϕ_{*} + 2 p M_{Pl} lo g (t / t_{*}), p > 1, = \frac{a ˙}{a} = \frac{p}{t}, v (t) = T ˙_{0} (t) = \frac{2 p M _{Pl}}{t} > 0.$
XIX-A@1#eq:N0 · line 537
$N_{0} (t) = \frac{1}{v ( t )} .$

The cosmological comparison background

Displayed formulas in this passage

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