The Power-Law Cosmology

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Problem 1

problem id: PWL_1

Show that for power law $a(t)\propto t^n$ expansion slow-roll inflation occurs when $n\gg1$.


Problem 2

problem id: PWL_2

Show that in the power-law cosmology the scale factor evolution $a\propto\eta^q$ in conformal time transforms into $a\propto t^p$ in physical (cosmic) time with \[p=\frac{q}{1+q}.\]


Problem 3

problem id: PWL_3

Show that if $a\propto\eta^q$ then the state parameter $w$ is related to the index $q$ by the following \[w=\frac{2-q}{3q}=const.\]