Clocks in the Universe are tricky things. Usually, in calculations of the birth of the world, a special scalar field plays the role of a clock — something like an invisible fluid filling all of space. It ticks, and physicists watch how the world changes relative to that ticking. But these clocks are man-made, introduced for convenience.
The authors of the new work took a different path. They based their approach on unimodular loop quantum cosmology — a framework where spacetime curvature itself sets the rhythm. Here, time is not tied to any particular substance but emerges from geometry. It's as if the course of events were determined not by the hands on a dial, but by the very movement of the mechanism. This step makes the theory cleaner: no need to invent a special clock field; the fabric of the cosmos suffices.
The researchers derived simplified equations for the early Universe and found solutions for several cases. For example, for a constant field energy, like a flat landscape, they obtained exact formulas. For more realistic scenarios, such as a quadratic potential and Starobinsky inflation, they had to resort to numerical calculations. In all variants, the Universe undergoes a 'bounce': contraction gives way to expansion without a singularity — a point of infinite density.
The main takeaway is that this approach is not only more elegant but also leaves potential traces in the observable sky. If quantum gravitational effects indeed influenced the early Universe, their imprints may survive in the large-scale structure of the cosmos. The geometry of time might not be just a mathematical trick, but a key to testing the theory.
as written by the authors arXiv:2607.27344
We study inflation in the setting of unimodular loop quantum cosmology, where time evolution is defined in unimodular time rather than with respect to a free, massless scalar field as is standard in loop quantum cosmology. The unimodular setting leads to a natural Schr\"odinger time evolution in a time coordinate with clear geometric meaning, defined independently of any particular matter content; an inflaton can be included but is not needed as a clock. We review the unimodular version of loop quantum cosmology and comment on possible connections to full (unimodular) loop quantum gravity. Then, focusing on semiclassical effective equations, we derive analytical solutions in simple cases such as a constant potential, emphasising the use of a unimodular time coordinate. We also discuss numerical solutions for phenomenologically interesting cases such as a quadratic potential and Starobinsky inflation, comparing different possible choices of initial conditions. In particular, we show that choosing an $$\alpha$$-attractor potential allows for models of a bounce either dominated by kinetic or potential energy, which are compatible with observations while potentially including observable imprints of the quantum-gravity regime.
In unimodular gravity, the cosmological constant, the very one responsible for the accelerated expansion of the Universe, arises not as mysterious energy but as a natural parameter of the theory, almost like a fixed sum in the cosmic ledger.
In the novel 'The End of Eternity,' Isaac Asimov describes a world where time is merely a product of engineering manipulations; here, time ceases to be an external tool and becomes an inherent property of space.