Constraining Temporal Oscillations of Cosmological Parameters Using Type Ia Supernovae. (arXiv:1806.07797v2 [astro-ph.GA] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Brownsberger_S/0/1/0/all/0/1">Sasha R. Brownsberger</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Stubbs_C/0/1/0/all/0/1">Christopher W. Stubbs</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Scolnic_D/0/1/0/all/0/1">Daniel M. Scolnic</a>
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 $simeq 80 textrm{Gyr}^ {-1} h_{100}$.
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 $simeq 80 textrm{Gyr}^ {-1} h_{100}$.
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