**3.2.1. Shape Parameter of the Transfer Function**

The initial perturbations of the density fluctuation
*P(k)* =
|_{k}|^{2} ~
*k*^{n} receive a modification as *P(k)* =
|_{k}|^{2} ~
*k*^{n} *T(k)* as they grow,
where *T(k)* is called the transfer function.
Fluctuations of a small scale that enter the horizon in the radiation dominant
epoch do not grow for a while, till the universe becomes matter dominated.
The transfer function *T(k)* thus damps for small scales as ~
*k*^{-4},
whereas it stays close to unity for long-wave lengths.
The transition region is controlled by a parameter
*k* ~ 2 /
*ct*_{eq}, *ct*_{eq} being the horizon size at the
time of matter-radiation equality, i.e., a characteristic length of
6.5(*h*)^{-1}
*h*^{-1} Mpc. The parameter
=
*h* determines the
behaviour of the transfer function and
is called the shape parameter. To give a sufficient power to several
tens of Mpc, must be as small as 0.2
(Efstathiou et
al. 1990).
This small value ( = 0.15-0.25) is
supported by later analyses (e.g.,
Peacock & Dodds
1994;
Eke et al. 1998).