Rescuing Palindromic Universes with Improved Recombination Modelling

In our paper, Rescuing Palindromic Universes with Improved Recombination Modelling (2111.14588), we revisit an intriguing cosmological idea: a universe that is symmetric in time. This work, led by Metha Prathaban and Will Handley, demonstrates how a more careful treatment of the universe’s thermal history can resolve critical tensions between theory and observation, potentially resurrecting the “palindromic” model as a serious contender to the standard cosmological picture.

The Palindromic Universe and its Challenge

The concept starts with the observation that our universe appears to be heading towards an asymptotically de Sitter state, which possesses a “future conformal boundary” (FCB) at a finite future conformal time. The question of what happens at and beyond this boundary has profound implications. Previous work by our group (2104.02521, 2104.01938) explored the consequences of requiring physical fields to remain well-behaved as they cross this boundary and evolve towards a future singularity, or “Big Bang 2.”

This requirement imposes strict symmetry conditions on cosmological perturbations, which leads to a remarkable prediction: the primordial power spectrum is not continuous but quantized. The allowed modes of fluctuation are discrete, analogous to the standing waves on a guitar string. While this is a fascinating theoretical prediction, initial models struggled to match the precise measurements of the Cosmic Microwave Background (CMB) from experiments like Planck (10.1051/0004-6361/201833910). The calculated spectrum, particularly the lowest allowed wavenumber ($k_0$), was in significant tension with the data, casting doubt on the entire framework.

Our Contribution: A More Sophisticated Physical Model

The discrepancy arose from a simplifying assumption in earlier models: treating post-recombination photons as an “imperfect fluid” or assuming recombination was instantaneous. In this paper, we lift these simplifications and tackle the problem with a more realistic physical model. Our key innovations are:

• Full Photonic Boltzmann Hierarchy: We include the full, infinite hierarchy of equations describing the evolution of the photon distribution after recombination, rather than truncating it at a low order. This provides a much more accurate description of the free-streaming photons that make up the CMB.

• Refined Recombination Modelling: Recognizing that recombination is not instantaneous, we treat the values of the higher-order photon modes at the end of recombination as free parameters. This accounts for their growth during the finite duration of the recombination epoch and provides the necessary degrees of freedom to satisfy the stringent symmetry conditions at the FCB.

To solve this complex boundary-value problem, we developed a new computational approach. The method involves integrating the perturbation equations both forwards from the Big Bang to recombination and backwards from the future conformal boundary. By matching these solutions, we can simultaneously solve for the allowed wavenumbers and the conditions at recombination.

Vindicating the Model: New Results

This more rigorous approach yields a new, physically-motivated quantized spectrum. We calculate a lowest allowed wavenumber of ${k_0 = 9.93 \times 10^{-5} \textrm{Mpc}^{-1}}$ and a linear spacing of ${\Delta k = 1.63 \times 10^{-4} \textrm{Mpc}^{-1}}$.

The impact of this result is significant. A primordial power spectrum constructed from these values is now largely consistent with cosmological data. It provides fits to the CMB power spectrum that are equivalent in quality to the standard $\Lambda$CDM model, effectively “rescuing” the palindromic universe from its previous observational tensions.

This work underscores a crucial theme in modern cosmology: that subtle details in our physical models can have dramatic consequences for our understanding of the universe’s fundamental nature. By combining first-principles physics with advanced computational techniques, we have shown that the elegant idea of a time-symmetric universe remains a compelling and viable possibility.

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