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 .