Energy densities offer new path to resolving the Hubble tension

Researchers from the University of Waterloo have proposed a new method to measure the Hubble constant that could help resolve one of modern cosmology’s pressing puzzles: the Hubble tension.

The study published in Physical Review Letters aims to resolve the Hubble tension, a discrepancy between the value of the Hubble constant (H₀) from the local (distance ladder) method and the cosmic microwave background (CMB) method.

Phys.org spoke to the first author of the study, Dr. Alex Krolewski, a postdoctoral researcher at the University of Waterloo.

“The Hubble tension between early-time, large-scale, and local, late-time measurements of the universe’s expansion rate has now reached the 5-sigma level! This is a probability of less than 0.0000003 of occurring by chance,” explained Dr. Krolewski.

The distance ladder method gives a value of 73 km/s/Mpc (kilometers per second per megaparsec), whereas the CMB method gives 67 km/s/Mpc. This difference is significant and indicates a gap in our understanding.

The sound horizon

The distance ladder method uses nearby objects like Cepheid variable stars and Type 1a supernovas as candles, i.e., objects whose brightness is known to us. The distances to these objects and their redshifts are measured, which can be used to calculate the Hubble constant.

On the other hand, methods using CMB rely on sound horizon, a standard measure in cosmology. It is a measure of the maximum distance traveled by sound waves in the early universe before the decoupling of light and matter.

These approaches require researchers to make assumptions about the ΛCDM model, the best cosmological model of the universe today.

This has led researchers to modify early universe physics to reduce the sound horizon, which increases the Hubble constant’s value derived from CMB data, lowering the discrepancy. The issue here is the reliance on the sound horizon and therefore, the ΛCDM model. Dr. Krolewski and his team aimed to eliminate this issue.

“Our new method instead estimates the total energy density of the universe or the critical density, which is directly related to the expansion rate. As John Archibald Wheeler famously put it, ‘Spacetime tells matter how to move; matter tells spacetime how to curve,'” explained Dr. Krolewski.

Baryonic fraction measurements

The researchers’ approach is a completely new method to measure the Hubble constant from low-redshift, large-scale structure observations independent of the sound horizon.

Their method combines four independent measurements to calculate the Hubble constant.

These are the physical photon density from the CMB temperature, the baryon-to-photon ratio derived from primordial deuterium abundance, the baryon fraction from the amplitude of baryon acoustic oscillations in galaxy clustering, and the geometrical matter density from Alcock-Paczynski measurements.

“Our method is based on bootstrapping from the well-known energy densities of photons and ordinary matter to the total energy density of the universe,” said Dr. Krolewski.

The innovation in their method lies in extracting the baryon fraction from galaxy clustering data, a parameter that is generally overlooked in standard analyses.

This measurement denotes the ratio of ordinary (or baryonic) matter to total matter (which includes dark matter) in the universe. This parameter would be unity if all the matter in the universe was baryonic and zero if all the matter was dark matter.

The sound horizon approach utilizes data about the distribution of baryon acoustic oscillations (BAO), which are ripples in matter distribution. On the other hand, the baryonic fraction measurement focuses on the strength of these ripples, making it independent of the sound horizon.

Tightening constraints

The researchers used their sound horizon-free approach and tested it on the Sloan Digital Sky Survey’s Baryon Oscillation Spectroscopic Survey (BOSS DR12) data.

Their method yielded a Hubble constant value of 67.1 km/s/Mpc with an uncertainty of +6.3/−5.3. This value is consistent with both measurements, and therefore not favoring either side of the tension.

“We tested our method on mock galaxy surveys with different cosmological models and found that we were always able to recover the correct value of the expansion rate. Overall, our method is very robust to systematic uncertainties,” noted Dr. Krolewski.

While their findings do not definitively resolve the Hubble tension, future surveys like the Dark Energy Spectroscopic Instrument (DESI) and the Euclid satellite are expected to improve constraints.

“DESI and Euclid will measure the BAO feature in the galaxy distribution at sub-percent precision. At this precision, we can measure the amplitude of the BAO with much better accuracy than today. With the full data from DESI and Euclid, we can differentiate between the local and CMB values for the Hubble rate,” concluded Dr. Krolewski.

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