Gravitational Fluctuations as an Alternative to Inflation
  The ability to reproduce the observed matter power spectrum $P(k)$ to high
accuracy is often considered as a triumph of inflation. In this work, we
explore an alternative explanation for the power spectrum based on
nonperturbative quantum field-theoretical methods applied to Einstein's
gravity, instead of ones based on inflation models. In particular the power
spectral index, which governs the slope on the $P(k)$ graph, can be related to
critical scaling exponents derived from the Wilson renormalization group
analysis. We find that the derived value fits favorably with the Sloan Digital
Sky Survey telescope data. We then make use of the transfer functions, based
only on the Boltzmann equations which describe states out of equilibrium, and
Einstein's General Relativity, to extrapolate the power spectrum to the Cosmic
Microwave Background (CMB) regime. We observe that the results fit rather well
with current data. Our approach contrasts with the conventional explanation
which uses inflation to generate the scale invariant Harrison-Zel'dovich
spectrum on CMB scales, and uses the transfer function to extrapolate it to
galaxy regime. The results we present here only assume quantum field theory and
Einstein's Gravity, and hence provide a competing explanation of the power
spectrum, without relying on the assumptions usually associated with
inflationary models. At the end, we also outline several testable predictions
in this picture that deviate from the conventional picture of inflation, and
which hopefully will become verifiable in the near future with increasingly
accurate measurements.
