Does History Repeat Itself? Periodic Time Cosmology
  It has been suggested that the cosmic history might repeat in cycles, with an
infinite series of similar aeons in the past and the future. Here, we instead
propose that the cosmic history repeats itself exactly, constructing a universe
on a periodic temporal history, which we call Periodic Time Cosmology. In
particular, the primordial power spectrum, convolved with the transfer function
throughout the cosmic history, would form the next aeon's primordial power
spectrum. By matching the big bang to the infinite future using a conformal
rescaling (a la Penrose), we uniquely determine the primordial power spectrum,
in terms of the transfer function up to two free parameters. While nearly scale
invariant with a red tilt on large scales, using Planck and Baryonic Acoustic
Oscillation observations, we find the minimal model is disfavoured compared to
a power-law power spectrum at $5.1\sigma$. However, extensions of $\Lambda$CDM
cosmic history change the large scale transfer function and can provide better
relative fits to the data. For example, the best fit seven parameter model for
our Periodic Time Cosmology, with $w=-1.024$ for dark energy equation of state,
is only disfavoured relative to a power-law power spectrum (with the same
number of parameters) at $1.8\sigma$ level. Therefore, consistency between
cosmic history and initial conditions provides a viable description of
cosmological observations in the context of Periodic Time Cosmology.
