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 $\simeq 80\ \textrm{Gyr}^ {-1} h_{100}$.