Quantum Tide from the Future: Accelerating the Universe Without Dark Energy ✛ ✦

For almost a century, cosmologists have been grappling with the mystery: what makes the Universe expand ever faster? The standard answer — dark energy — creates a monstrous discrepancy between the theoretical vacuum density and observations. But there's another path, one that turns causality on its head. Just as the final note of a symphony, not yet played, can govern the tempo of the entire piece, a quantum condition imposed from the distant future rewrites the expansion history. The idea, going back to Georges Lemaître and Edwin Hubble, takes a new twist: what if the dynamics of spacetime are determined not only by the initial Big Bang, but also by a final state selected from a quantum superposition of possible worlds?

Imagine a flat Universe filled with radiation, with no dark energy. In such a minisuperspace model, physicists specify the wave function not only at the Big Bang but also in the far future — as a Chern-Simons soliton. This is a purely quantum configuration with no classical analogue, localized on the trajectory b ∝ $T^{1/3}$. Two waves — forward and time-reversed — interfere, and their conditional amplitude yields an unexpected effect. The probability peak for the scale factor no longer follows the radiation deceleration b ∝ $T^{-1/5}$, but suddenly takes off, like a sailboat caught by a wind from a harbor that doesn't yet exist.

The key equation — the peak shift: b_{\text{peak}} \approx $b_r$ + \frac{\epsilon^2}{\sigma_X^2} $b_r^2$ b_{\text{CS}}^5, where ε ≪ 1 is the half-width of the forward wave packet, and $σ_X$ is the width of the soliton. At sufficiently large times, the correction starts to dominate, and the effective equation of state slides toward dark energy with w ≈ –1, then to phantom w < –1. This dramatic finale is not the true end, but a signal: the classical interpretation breaks down, giving way to a full quantum description. Like the collapse of the wave function in the lab, post-selection creates the illusion of 'unmotivated' acceleration — but now on the scale of the entire observable Universe.

The shift in perspective is radical: the cosmological constant problem becomes a question of boundary conditions. Stephen Hawking insisted on the wave function of the Universe as the central object — and now it really begins to work. Moreover, the choice of a different final state, say with quantum entanglement on the horizon, can change the picture — just as the choice of vacuum near a black hole redefines Hawking radiation. Tests are already being planned using subtle features of the cosmic microwave background and large-scale structure, which will help distinguish post-selection acceleration from conventional dark energy models. Thus, the future, physically encoded in the wave function, ceases to be an abstraction and becomes a tool for reading the past — and the present expansion. Perhaps our experiments today already bear the imprint of cosmic events yet to come: the Universe, like a book being read, remembers its ending on every page.