Photon rest mass from localized fast radio bursts with improved distribution of dispersion measure from extragalactic gas

Technical Summary: Photon Rest Mass Constraints from Localized Fast Radio Bursts

Problem Statement
The assumption that photons are massless is a foundational postulate of modern physics, specifically Einstein's special relativity, which posits the invariance of the speed of light. However, this hypothesis remains subject to experimental verification. A non-zero photon rest mass ($m_\gamma$) would induce a frequency-dependent group velocity, causing higher-frequency components of a signal to travel faster than lower-frequency ones. This results in a measurable time delay for photons emitted simultaneously from a distant source. While ground tests and astrophysical observations (e.g., gamma-ray bursts) have constrained photon mass, Fast Radio Bursts (FRBs) offer a unique laboratory due to their cosmological distances and precise dispersion measurements.

A critical challenge in using FRBs to constrain $m_\gamma$ is the accurate modeling of the dispersion measure (DM) arising from extragalactic gas ($DM_{cosmic}$). Previous studies relied on distribution functions (e.g., Macquart et al. [38]) that were later found to misestimate statistical moments or lacked explicit cosmological information (Konietzka et al. [56]). Furthermore, recent Dark Energy Spectroscopic Instrument (DESI) observations favor dynamical dark energy over the standard cosmological constant ($\Lambda$), necessitating a re-evaluation of photon mass constraints within models accommodating dynamical dark energy ($w$CDM and $w_0w_a$CDM).

Methodology
The authors propose a refined approach to constrain $m_\gamma$ by integrating improved statistical modeling of extragalactic gas with a multi-probe cosmological analysis.

1. Improved $DM_{cosmic}$ Distribution:
   The authors construct an improved probability distribution function (PDF) for the extragalactic dispersion measure. This model:

   • Restores a missing normalization factor ($1/\langle DM_{cosmic} \rangle$) present in previous formulations.
   • Allows the shape parameters $\alpha$ and $\beta$ to vary with redshift, rather than treating them as fixed constants.
   • Is calibrated against mock data, where the Kolmogorov–Smirnov test confirms that varying all three parameters ($\alpha, \beta, \sigma_{cosmic}$) provides a significantly better fit than fixed-parameter models.

2. Theoretical Framework:
   The time delay induced by a non-zero photon mass is interpreted as an effective dispersion measure ($DM_\gamma$). The total observed dispersion is modeled as:
   $$DM_{obs} = DM_{MW}^{ISM} + DM_{MW}^{halo} + DM_{cosmic} + \frac{DM_{host}}{1+z} + DM_\gamma$$
   The analysis employs three flat cosmological models: $\Lambda$CDM, $w$CDM, and $w_0w_a$CDM (the latter favored by recent DESI BAO data). The dimensionless Hubble parameter $\tilde{E}(z)$ is defined differently for each model to account for dynamical dark energy.

3. Data Sets and Likelihood:
   The study combines four distinct datasets to break degeneracies between cosmological parameters and the photon mass:

   • FRBs: A sample of 104 localized FRBs (selected from a compilation of 115, excluding outliers and those with ambiguous host localization).
   • SN Ia: 1,590 Type Ia supernovae from the Pantheon+ compilation.
   • CMB: Planck 2018 derived parameters ($l_A, R, \Omega_b h^2$).
   • BAO: Latest measurements from DESI Data Release 2 (DR2).

   A joint log-likelihood function is constructed, and Markov Chain Monte Carlo (MCMC) simulations are performed using the emcee package.

4. Host Galaxy Treatment:
   The host galaxy dispersion measure ($DM_{host}$) is modeled as a log-normal distribution. The authors perform two analyses: one where the host parameters ($\mu_{host}, \sigma_{host}$) are fixed based on IllustrisTNG simulations (which assume $\Lambda$CDM), and another where these parameters are treated as free variables to assess potential biases.

Key Results
The analysis yields the following 1$\sigma$ upper limits on the photon rest mass ($m_\gamma$):

• $\Lambda$CDM Model: $m_\gamma \leq 4.83 \times 10^{-51}$ kg
• $w$CDM Model: $m_\gamma \leq 4.71 \times 10^{-51}$ kg
• $w_0w_a$CDM Model: $m_\gamma \leq 4.86 \times 10^{-51}$ kg

When treating the host galaxy parameters ($\mu_{host}, \sigma_{host}$) as free parameters rather than fixing them to IllustrisTNG values, the constraints become slightly tighter:

• $\Lambda$CDM: $m_\gamma \leq 4.28 \times 10^{-51}$ kg
• $w$CDM: $m_\gamma \leq 4.26 \times 10^{-51}$ kg
• $w_0w_a$CDM: $m_\gamma \leq 4.22 \times 10^{-51}$ kg

Cosmological parameters ($H_0, \Omega_{m0}, \Omega_{b0}h^2$) derived in this study are consistent with previous determinations from Planck, DESI, and ACT. The analysis also finds a preference for dynamical dark energy in the $w_0w_a$CDM model, with $w_0$ noticeably larger than $-1$ and $w_a$ deviating from zero at $>2\sigma$, aligning with recent DESI findings.

Significance and Claims
The paper claims to provide the most stringent constraints on the photon mass derived from FRBs to date. The authors emphasize that their results offer robust and reliable empirical support for the massless nature of the photon.

A crucial aspect of the paper's significance is the correction of the $DM_{cosmic}$ distribution function. The authors note that previous studies (e.g., [46, 57, 59]) which reported tighter limits (e.g., $m_\gamma \leq 3.1 \times 10^{-51}$ kg) utilized the uncorrected distribution from Macquart et al. [38], which omitted the normalization factor. The authors argue that this omission significantly biased previous constraints. By incorporating the corrected distribution and utilizing a comprehensive dataset (FRB + SN Ia + CMB + BAO) across multiple cosmological models, this work establishes a more reliable baseline for testing the photon mass hypothesis.

The authors modestly note that the inferred photon mass limits show little sensitivity to the assumed background cosmological model or the treatment of host galaxy parameters, though they caution that the current FRB sample is dominated by low-redshift sources, which may limit the sensitivity to high-redshift cosmological effects.