  I present a simple analytical model describing the normal state of a
superconductor with a pseudogap in the density of states, such as in underdoped
cuprates. In nearly two-dimensional systems, where the superconducting
transition temperature is reduced from the mean-field BCS value, Cooper pairs
may be present as slow fluctuations of the BCS pairing field. Using the
self-consistent T-matrix (fluctuation exchange) approach I find that the
fermion spectral weight exhibits two BCS-like peaks, broadened by fluctuations
of the pairing field amplitude. The density of states becomes suppressed near
the Fermi energy, which allows for long-lived low-energy Cooper pairs that
propagate as a sound-like mode with a mass. A self-consistency requirement,
linking the width of the pseudogap to the intensity of the pairing field,
determines the pair condensation temperature. In nearly two-dimensional
systems, it is proportional to the degeneracy temperature of the fermions, with
a small prefactor that vanishes in two dimensions.
