New exact solutions for power‐law inflation Friedmann models
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- 1 January 1990
- journal article
- Published by Wiley in Astronomische Nachrichten
- Vol. 311 (3) , 165-168
Abstract
We consider the spatially flat Friedmann model For a ≈ tp, especially, if p ≥ 1, this is called power‐law inflation. For the Lagrangian L = Rm with p = − (m − 1) (2m − 1)/(m − 2) power‐law inflation is an exact solution, as it is for Einstein gravity with a minimally coupled scalar field ϕ in an exponential potential V(ϕ) = exp (μϕ) and also for the higher‐dimensional Einstein equation with a special Kaluza‐Klein ansatz. The synchronized coordinates are not adapted to allow a closed‐form solution, so we write The general solutions reads Q(a) = (ab + C)f/b with free integration constant C (C = 0 gives exact power‐law inflation) and m‐dependent values b and f: f = −2 + 1/p, b = (4m − 5)/(m − 1). Finally, special solutions for the closed and open Friedmann model are found.Keywords
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This publication has 3 references indexed in Scilit:
- Fourth-order gravity and conformal transformationsClassical and Quantum Gravity, 1989
- The equivalence of conformally and minimally coupled scalar fields in Einstein's theory of gravityPhysics Letters B, 1988
- Inflationary models with exponential potentialsNuclear Physics B, 1988