3.2.1. Shape Parameter of the Transfer Function

The initial perturbations of the density fluctuation P(k) = |_k|² ~ kⁿ receive a modification as P(k) = |_k|² ~ kⁿ 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).