The quadratic approximation for quintessence with arbitrary initial conditions
Swaney, Jeffrey
:
2014-04
Abstract
We examine models of quintessence in which a minimally-coupled scalar field
phi evolves near a
local extremum of its potential V ( phi) at phi_*. Assuming that (1/V
)(dV/dphi) is small and w ~ -1, we
Taylor expand the potential about phi_* and derive a general expression for
w(a). The dynamics of this
field are determined by the initial and final equation of state parameters
w_i and w_0, the quantity
V''( phi_*)/V(phi_*), and the direction of \dot\phi_i in relation to
\dot\phi _0. This approximation is then tested for six
values of V''( phi_*)/V(phi_*) and shown to lie within 2% of the exact
solution for five of these cases.
However, the model becomes less precise near certain values of V''(
phi_*)/V(phi_*) where \dot\phi
becomes very large.
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