Inflation drives quantum fluctuations beyond the Hubble horizon, freezing them out before the small-scale modes re-enter during the radiation dominated epoch, and subsequently decay, while large-scale modes re-enter later during the matter dominated epoch and grow. This distinction shapes the matter power spectrum and provides observational evidence in support of the standard model. In this paper, we demonstrate that another mechanism, based on the fluctuation growth in the R_h=ct universe, itself an FLRW cosmology with the added constraint of zero active mass (i.e., rho+3p=0), also accounts very well for the observed matter power spectrum, so this feature is not unique to LambdaCDM. In R_h=ct, the shape of the matter power spectrum is set by the interplay between the more rapid decay of the gravitational potential for the smaller mode wavelengths and the longer dynamical timescale for the larger wavelengths. This combination produces a characteristic peak that grows in both amplitude and mode number as a function of time. Today, that peak lies at k approx 0.02 Mpc^-1, in agreement with the Ly-alpha and Planck data. But there is no need of an inflationary expansion, and a complicated epoch dependence as one finds in LambdaCDM.
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