  Power spectra always play an important role in the theory of inflation. In
particular, the ability to reproduce the galaxy matter power spectrum and the
CMB temperature angular power spectrum coefficients to high accuracy is often
considered a triumph of inflation. In our previous work, we presented an
alternative explanation for the matter power spectrum based on nonperturbative
quantum field-theoretical methods applied to Einstein's gravity, instead of
inflation models based on scalar fields. In this work, we review the basic
concepts and provide further in-depth investigations. We first update the
analysis with more recent data sets and error analysis, and then extend our
predictions to the CMB angular spectrum coefficients, which we did not consider
previously. Then we investigate further the potential freedoms and
uncertainties associated with the fundamental parameters that are part of this
picture, and show how recent cosmological data provides significant constraints
on these quantities. Overall, we find good general consistency between theory
and data, even potentially favoring the gravitationally-motivated picture at
the largest scales. We summarize our results by outlining how this picture can
be tested in the near future with increasingly accurate astrophysical
measurements.
