Constraining Temporal Oscillations of Cosmological Parameters Using Type
  Ia Supernovae
  The existing set of type Ia supernovae (SNe Ia) is now sufficient to detect
oscillatory deviations from the canonical $\Lambda$CDM cosmology. We determine
that the Fourier spectrum of the Pantheon data set of spectroscopically
well-observed SNe Ia is consistent with the predictions of $\Lambda$CDM. We
also develop and describe two complementary techniques for using SNe Ia to
constrain those alternate cosmological models that predict deviations from
$\Lambda$CDM that are oscillatory in conformal time. The first technique uses
the reduced $\chi^2$ statistic to determine the likelihood that the observed
data would result from a given model. The second technique uses bootstrap
analysis to determine the likelihood that the Fourier spectrum of a proposed
model could result from statistical fluctuations around $\Lambda$CDM. We
constrain three oscillatory alternate cosmological models: one in which the
dark energy equation of state parameter oscillates around the canonical value
of $w_{\Lambda} = -1$, one in which the energy density of dark energy
oscillates around its $\Lambda$CDM value, and one in which gravity derives from
a scalar field evolving under an oscillatory coupling. We further determine
that any alternate cosmological model that produces distance modulus residuals
with a Fourier amplitude of $\simeq 36$ millimags is strongly ruled out, given
the existing data, for frequencies between $\simeq 0.08\ \textrm{Gyr}^ {-1}
h_{100}$ and $\simeq 80\ \textrm{Gyr}^ {-1} h_{100}$.
