Any fundamental theory of nature which intends to succesfully generate will be confronted by the `fine tuning problem' since the currently observed value of the cosmological constant is miniscule when compared with either the Plan enormous fine tuning of initial conditions is required in order to ensure that the cosmological -term comes to dominate the expansion dynamics of the universe at precisely the current epoch, no sooner and no later.

The fine-tuning problem is rendered less acute if we relax the condition
_{} =
constant, and (taking the cue from Inflation)
try to construct dynamical models for
_{}.

Phenomenological approaches to a dynamical -term belong to three main categories [21]:

(1) *Kinematic models.*

_{} is simply
assumed to be a function of either the cosmic time *t*
or the scale factor *a*(*t*) of the FRW cosmological model.

(2) *Hydrodynamic models.*

_{} is described by
a barotropic fluid with some equation of state
*p*_{}
(_{}) (dissipative
terms may also be present).

(3) *Field-theoretic models.*
The -term is
assumed to be a new physical classical field
with some phenomenological Lagrangian.

The simplest class of kinematic models

(4) |

is equivalent to hydrodynamic models based on an ideal fluid with an equation of state

(5) |

The expansion of the
universe passes through an inflection point the moment it
stops decelerating and begins to accelerate.
If the equation of state is held constant (*w* = *P* /
< - 1/3)
then the cosmological redshift when this occurs is given by

(6) |

We find that
*z*_{a} 0.7
for the cosmological constant (*w* = - 1) with
_{}
0.7 and
_{m}
0.3.
The acceleration of the universe is therefore a *very recent*
phenomena. This fact
is related to the *cosmic coincidence* conundrum since it appears
that we live during a special era
when the density of dark matter and dark energy are comparable.
The cosmic coincidence puzzle remains in place even if we relax the
assumption *w* = - 1 and allow dark energy to be time dependent.
Indeed, it is easy to show that
the equality between dark matter and dark energy takes
place at (1 + *z*_{eq})^{3} =
(_{} /
_{m})^{-1/w}. For a cosmological constant
this gives
*z*_{eq}
0.3 and *z*_{a} > *z*_{eq}
implying that the universe
begins to accelerate even *before* it becomes
-dominated.
For *w* = - 2/3 *z*_{a} = *z*_{eq}
0.5, while for stiffer
equations of state
*z*_{a} < *z*_{eq} (*w* > - 2/3)
further exacerbating the cosmological coincidence puzzle.