  One of the characteristics of the "Matter Bounce" scenario, an alternative to
cosmological inflation for producing a scale-invariant spectrum of primordial
adiabatic fluctuations on large scales, is a break in the power spectrum at a
characteristic scale, below which the spectral index changes from n = 1 to n =
3. We study the constraints which current cosmological data place on the
location of such a break, and more generally on the position of the break and
the slope at length scales smaller than the break. The observational data we
use include the WMAP five-year data set (WMAP5), other CMB data from BOOMERanG,
CBI, VSA, and ACBAR, large-scale structure data from the Sloan Digital Sky
Survey (SDSS, their luminous red galaxies sample), Type Ia Supernovae data (the
"Union" compilation), and the Sloan Digital Sky Survey Lyman-\alpha forest
power spectrum (Ly\alpha) data. We employ the Markov Chain Monte Carlo method
to constrain the features in the primordial power spectrum which are motivated
by the matter bounce model. We give an upper limit on the length scale where
the break in the spectrum occurs.
