  We examine the power spectrum of clusters in the Press-Schechter (PS) theory
and in N-body simulations to see how the power spectrum of clusters is related
to the power spectrum of matter density fluctuations in the Universe. An
analytic model for the power spectrum of clusters for their given number
density is presented, both for real space and redshift space. We test this
model against results from N-body simulations and find that the agreement
between the analytic theory and the numerical results is good for wavelengths
$\lambda >60h^{-1}$ Mpc. On smaller scales non-linear processes that are not
considered in the linear PS approximation influence the result. We also use our
analytic model to study the redshift-space power spectrum of clusters in cold
dark matter models with a cosmological constant ($\Lambda$CDM) and with a
scale-invariant Harrison-Zel'dovich initial spectrum of density fluctuations.
We find that power spectra of clusters in these models are not consistent with
the observed power spectra of the APM and Abell-ACO clusters. One possible
explanation for the observed power spectra of clusters is an inflationary
scenario with a scalar field with the potential that has a localized steplike
feature. We use the PS theory to examine the power spectrum of clusters in this
model.
