Alleviating the Hubble Tension with Torsion Condensation (TorC)

Abstract

Constraints on the cosmological parameters of Torsion Condensation (TorC) are investigated using Planck 2018 Cosmic Microwave Background data. TorC is a case of Poincaré gauge theory---a formulation of gravity motivated by the gauge field theories underlying fundamental forces in the standard model of particle physics. Unlike general relativity, TorC incorporates intrinsic torsion degrees of freedom while maintaining second-order field equations. At specific parameter values, it reduces to the \(\Lambda\)CDM model, providing a natural extension to standard cosmology. The base model of TorC introduces two parameters beyond those in \(\Lambda\)CDM: the initial value of the torsion scalar field and its time derivative---one can absorb the latter by allowing the dark energy density to float. To constrain these parameters, PolyChord nested sampling algorithm is employed, interfaced via Cobaya with a modified version of CAMB. Our results indicate that TorC allows for a larger inferred Hubble constant, offering a potential resolution to the Hubble tension. Tension analysis using the R-statistic shows that TorC alleviates the statistical tension between the Planck 2018 and SH0Es 2020 datasets, though this improvement is not sufficient to decisively favour TorC over \(\Lambda\)CDM in a Bayesian model comparison. This study highlights TorC as a compelling theory of gravity, demonstrating its potential to address cosmological tensions and motivating further investigations of extended theories of gravity within a cosmological context. As current and upcoming surveys---including Euclid, Roman Space Telescope, Vera C. Rubin Observatory, LISA, and Simons Observatory---deliver data on gravity across all scales, they will offer critical tests of gravity models like TorC, making the present a pivotal moment for exploring extended theories of gravity.

Summary

In modern cosmology, we are facing a persistent \(5\sigma\) disagreement known as the Hubble Tension.

The problem is a conflict between two numbers: \(H_0\), the rate at which the universe is expanding today. When we look at the early universe via the Planck satellite, the inferred expansion rate is \(67.4 \pm 0.5\) km/s/Mpc. However, when we look at the local universe using the SH0ES project's measurements of exploding stars, we see a significantly faster rate of \(73.04 \pm 1.04\) km/s/Mpc.

Einstein's General Relativity explains gravity through the curvature of spacetime. But in the Standard Model of particle physics, forces are described by "gauge theories." If we apply that same logic to gravity, spacetime shouldn't just curve—it should also be able to twist. This twist is known as Torsion.

In our TorC model, torsion behaves dynamically. It "condenses" into the background of the universe. While the model eventually settles down to look like standard Einsteinian gravity today, its behavior in the early universe offers a natural exit from the Hubble crisis.

The Secret Ingredient: Early Dark Radiation

Our model introduces two new "knobs" that we can turn to adjust our understanding of the universe:

• \(\varpi_r\): The value of the torsion scalar field in the early universe.
• \(\Omega_\Lambda\): The "bare" density of dark energy. Unlike in the standard model, this is a free parameter because the dynamic torsion terms break the usual requirement that all densities must sum to unity.

The most exciting find is how early-universe torsion acts like "dark radiation." By adding a bit of this torsional energy to the young universe, it pushes the expansion rate up during the first few hundred thousand years.

Why does this matter? If the early universe expanded faster, the "sound waves" in the primordial plasma couldn't travel quite as far before the universe became transparent. This makes the "ruler" we use to measure the universe (the sound horizon) smaller. To make a smaller ruler fit the data we see today, the calculated expansion rate of the current universe (\(H_0\)) has to go up—shifting the CMB prediction from 67.4 toward the 73.0 range.

Does it actually work?

We put TorC to the test using data from the Planck 2018 cosmic microwave background and the SH0ES 2020 supernova measurements.

• Bridging the Gap: Under standard gravity (\(\Lambda\)CDM), the Planck and SH0ES data are in "strong tension," with an agreement score (the \(R\)-statistic) of \(-5.60\). Under TorC, this score rises to \(+0.70\), meaning the two datasets become statistically consistent. The "crisis" effectively disappears.
• The Occam's Razor Problem: While TorC fits the data beautifully, it is a more complex theory than \(\Lambda\)CDM. In the world of Bayesian statistics, we penalize models for being too "complicated" unless they provide a massive improvement. Currently, TorC is a "statistical tie" with the standard model—it explains the discrepancy, but the complexity penalty means it isn't yet decisively proven to be the superior explanation.

Why this is a "Pivotal Moment"

We are entering a golden age of observation. With new data pouring in from the Euclid space telescope, the Vera C. Rubin Observatory, and the Simons Observatory, we will soon have the precision needed to see if the universe truly has a "twist."

As these surveys deliver data on gravity across all scales, they will offer critical tests for models like TorC. If torsion is real, it wouldn't just solve the Hubble tension; it would provide a vital link between the gravitational force and the gauge theories that underlie the rest of particle physics.