Quantum cosmology with final states can explain the accelerated expansion of the universe

Teleology is the idea that some processes in nature are directed toward a goal or an end. Today, it is commonly asserted that teleology is a remnant of antiquated ways of thinking about causation, and that it is not compatible with modern science, because it is fundamentally untestable.

In my opinion, such claims fail to take modern physics into account. Quantum theory involves a complex notion of causation, and it can naturally incorporate final conditions. However, to work with final conditions that are not imposed by external agents, we need to move into the realm of quantum cosmology, in which the whole universe is treated as a quantum system.

With this issue in mind, I studied final conditions in quantum cosmology. I found that cosmologies with such conditions generally predict a universe with accelerated expansion. Cosmic acceleration is a well-established fact, and also one of the most puzzling features of modern cosmology.

Its explanation requires controversial assumptions about new physics: either a very small but non-zero cosmological constant, an exotic form of matter (dark energy), or a radical modification to our theory of gravity. The postulate of a final quantum cosmological condition provides a novel explanation that requires no new physics.

Ever since Newton, time evolution in physics has been understood as an initial value problem. This means that we identify the initial positions and momenta of all particles in the system and then we solve Newton’s equations of motion to obtain the positions and momenta at any future (or past) time.

The same applies to relativistic theories, with one exception: the cosmological singularities of general relativity. In cosmology, the solution of the equations of motion toward the past stops abruptly after a finite time, at the Big Bang singularity. Since nothing can be defined at the singularity, there is literally no initial condition to evolve forward in time.

A major motivation for quantum cosmology research is to resolve the singularities through quantum effects. But quantum theory brings its own bag of problems. The time evolution of the quantum state is very different from the causal evolution of classical physics, because quantum states do not express properties of individual quantum systems.

In most interpretations of quantum theory, the quantum state is solely an informational object for probabilistic bookkeeping. Furthermore, quantum probabilities have a natural generalization with both an initial and a final quantum state describing a physical system.

This generalization is well confirmed experimentally, and it has found many applications. In experiments, final states are implemented via post-selection, i.e., we keep only runs of the experiment that satisfy a specific final condition.

In quantum cosmology, we treat the universe as a single, closed quantum system, so any initial or final state must be viewed as a component of the fundamental probability assignment. They are laws of nature that fix how the universe starts and how it ends.

The majority of work on quantum cosmology focuses on specifying an initial state and ignores the possibility of a final state. One notable exception was Steven Hawking’s research in the 1980s, which suggested final conditions for a Big Crunch that fully mirror initial conditions at the Big Bang.

He wanted to show that the thermodynamic arrow of time coincides with the arrow of cosmological expansion. This did not work, and eventually, the discovery of cosmic acceleration in the late 1990s made cosmologies with a Big Crunch implausible.

My analysis started from the derivation of the “deterministic limit” of quantum probabilities with both initial and final conditions, which is obtained by averaging microscopic quantum processes. If we only have initial conditions, the deterministic limit gives the equations of classical physics, for example, Newton’s laws.

I derived the corresponding equations in the presence of quantum final conditions. These equations are novel, but they can still be expressed with the mathematics of classical physics, and they are largely independent of the properties of the underlying quantum theory. The latter result is both fortunate and unexpected: It enables specific cosmological predictions with no reference to highly speculative quantum gravity theories. These findings are published in the journal Physical Review D.

It turns out that the deterministic limit of teleological quantum cosmologies (i.e., quantum cosmological models with both initial and final conditions) generically describes a universe undergoing accelerated expansion.

The universe transitions from a nonaccelerating to an accelerating epoch, in agreement with recent observations. No cosmological constant, dark energy or modified gravity needs be involved. Cosmic acceleration is generated solely by the imposition of final conditions at the quantum level. In this sense, cosmic acceleration is a genuine macroscopic quantum effect.

Further research is needed in order to see how teleological quantum cosmology fares observationally versus the alternative accounts of cosmic acceleration. A limitation of the existent analysis is that the deterministic limit does not work near the Big Bang.

To probe the early universe, we need the full quantum description. Even a simplified model will enable us to analyze cosmological inhomogeneities in the early universe, and thereby to connect with observations of the cosmic microwave background and of primordial gravitational waves.

This story is part of Science X Dialog, where researchers can report findings from their published research articles. Visit this page for information about Science X Dialog and how to participate.

Charis Anastopoulos is an associate professor on Quantum Foundations at the University of Patras, Greece. Anastopoulos has a Ph.D. on theoretical physics from Imperial College, London, and has worked as a researcher at the universities of Barcelona, Maryland, and Utrecht. Anastopoulos is the chair of the EU-funded Action “Relativistic Quantum Information,” a network of more than 250 researchers to explore the implications of quantum information to fundamental physics, and is the author of the books “Particle or Wave: The evolution of the concept of matter in modern physics” (Princeton University Press, 2008), and “Quantum Theory, a Foundational Approach” (Cambridge University Press, 2023).