In the first moments after its birth, the universe expanded faster than a match lights. This process is called inflation. It explains why today's cosmos is so homogeneous and flat. But what happened before it? Perhaps the laws of quantum gravity were at work then, and their traces can be found in the data.
The authors took an inflationary model with a special type of gravity where the curvature of space is linked to matter (known as f(R,T) gravity). They added a field that drives the expansion, the inflaton, and the Chern–Simons correction. This correction is like a quiet whisper from quantum particles that alters the expansion scenario. The scientists calculated two versions of the correction: trigonometric and exponential.
Then they computed key parameters: how much the density of matter fluctuated (the scalar spectral index) and how strongly inflation generated gravitational waves (the tensor spectral index and the tensor-to-scalar ratio). They compared the results with data from the Planck satellite from 2018. It turned out that the exponential correction is particularly good at constraining gravitational waves and agrees with the combined data from Planck, BK15, and BAO.
To check, the authors considered a model without the Chern–Simons correction, without linear f(R,T) gravity, and with a nonlinear version. The conclusion: the quantum correction indeed refines predictions, bringing them closer to what the telescope sees. This is not just playing with formulas: it's a bridge between the quantum world and the vast universe. Perhaps the first moments of the cosmos were more complex than we thought, and that complexity left its imprint in the sky.
Inflation lasted about 10⁻³⁵ seconds — during which the universe expanded by a factor of 10²⁶, as if a grain of sand became the size of a galaxy.