[Paper Review] Hints for a gravitational constant transition in Tully-Fisher data

George Alestas, Ioannis Antoniou+1 more|arXiv (Cornell University)|Apr 29, 2021

Cosmology and Gravitation Theories82 references4 citations

TL;DR

This paper presents evidence from an updated Tully–Fisher relation (TFR) dataset suggesting a potential transition in the effective gravitational constant at critical distances of approximately 9 Mpc and 17 Mpc, with a tension in the best-fit slope and intercept of two subsamples exceeding 3.5𝜎. The result, robust under Monte Carlo simulations, implies a possible decrease in the gravitational constant by ΔG/G ≈ -0.1 for distances beyond these thresholds, offering a novel mechanism to address the Hubble tension.

ABSTRACT

We use an up to date compilation of Tully-Fisher data to search for transitions in the evolution of the Tully-Fisher relation. Using an up to date data compilation, we find hints at $\approx 3σ$ level for a transition at critical distances $D_c \simeq 9 Mpc$ and $D_c \simeq 17 Mpc$. We split the full sample in two subsamples according to the measured galaxy distance with respect to a splitting distance $D_c$ and identify the likelihood of the best fit slope and intercept of one sample with respect to the best fit corresponding values of the other sample. For $D_c \simeq 9 Mpc$ and $D_c \simeq 17 Mpc$ we find a tension between the two subsamples at a level of $Δχ^2 > 17\; (3.5σ)$. Using a Monte-Carlo simulation we demonstrate that this result is robust with respect to random statistical and systematic variations of the galactic distances. If the tension is interpreted as due to a gravitational strength transition, it would imply a shift of the effective gravitational constant to lower values for distances larger than $D_c$ by $\frac{ΔG}{G}\simeq -0.1$. Such a shift is of the anticipated sign and magnitude but at somewhat lower distance (redshift) than the gravitational transition recently proposed to address the Hubble and growth tensions ($\frac{ΔG}{G}\simeq -0.1$ at transition redshift $z_t\lesssim 0.01$ ($D_c\lesssim 40 Mpc$)).

Motivation & Objective

• To investigate possible transitions in the Tully–Fisher relation (TFR) that could signal a change in the effective gravitational constant.
• To test whether observed tensions in the TFR's slope and intercept between subsamples at different distances are statistically significant and not due to random variations.
• To assess whether such a transition could resolve the Hubble tension by modifying gravity at low redshifts.
• To evaluate the robustness of the observed tension against statistical and systematic uncertainties in galaxy distance measurements.

Proposed method

• The authors split a comprehensive TFR dataset into two subsamples based on critical distances Dc ≈ 9 Mpc and Dc ≈ 17 Mpc.
• They perform a χ² minimization to determine the best-fit slope and intercept for each subsample and compare the resulting Δχ² to assess statistical tension.
• Monte Carlo simulations are used to test the robustness of the observed tension under random variations in galaxy distances and systematic errors.
• The effective gravitational constant is inferred from the TFR's intercept and slope via the relation A_B ∝ G_eff^(-2), assuming constant surface density.
• The analysis assumes the baryonic TFR (BTFR) as a probe of G_eff, with A_B and s derived from observed rotation velocities and baryonic masses.
• The tension is quantified as Δχ² > 17, corresponding to a 3.5σ significance level, suggesting non-homogeneous behavior in the gravitational law.

Experimental results

Research questions

• RQ1 Is there a statistically significant transition in the Tully–Fisher relation at specific critical distances?
• RQ2 Could a change in the effective gravitational constant explain the observed tension in TFR parameters between nearby and more distant galaxies?
• RQ3 Is the observed tension robust against statistical fluctuations and systematic errors in galaxy distance measurements?
• RQ4 Does the inferred gravitational transition at Dc ≈ 9 Mpc and Dc ≈ 17 Mpc align with proposed solutions to the Hubble tension?
• RQ5 Can the baryonic Tully–Fisher relation be used to constrain variations in the gravitational constant?

Key findings

• The analysis reveals a tension in the best-fit TFR parameters between subsamples split at Dc ≈ 9 Mpc and Dc ≈ 17 Mpc, with Δχ² > 17, corresponding to a 3.5σ significance level.
• The tension is robust under Monte Carlo simulations that include random statistical and systematic variations in galaxy distances, indicating it is unlikely to arise from data uncertainty.
• The observed tension suggests a potential transition in the effective gravitational constant, with ΔG/G ≈ -0.1 for distances larger than Dc, implying a weaker gravitational interaction at larger scales.
• The inferred transition scale at Dc ≈ 9–17 Mpc is consistent in magnitude and sign with recent proposals to resolve the Hubble tension via a gravitational transition at z ≲ 0.01.
• The result is consistent with the baryonic Tully–Fisher relation being a sensitive probe of fundamental gravitational physics, particularly when applied to low-redshift, nearby galaxies.
• The findings suggest that the Hubble tension may be alleviated by a transition in the strength of gravity at low redshifts, offering a new phenomenological approach to cosmological discrepancies.