The Power-Law Cosmology

From Universe in Problems
Revision as of 04:22, 23 May 2014 by Cosmo All (Talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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 \[w=\frac{2-q}{3q}=const.\]