[Paper Review] Upper limits on Einstein's weak equivalence principle placed by uncertainties of dispersion measures of fast radio bursts

T. Hashimoto, Tomotsugu Goto+8 more|arXiv (Cornell University)|Nov 22, 2021

Pulsars and Gravitational Waves Research49 references8 citations

TL;DR

This paper uses dispersion measure uncertainties in fast radio bursts (FRBs) to place stringent upper limits on violations of Einstein's weak equivalence principle (WEP), testing whether photons of different energies experience different Shapiro time delays in gravitational fields. By analyzing FRB 121002 (z = 1.6 ± 0.3) and FRB 180817.J1533+42 (z = 1.0 ± 0.2), the study derives log ∆γ < −20.8 ± 0.1 and log(∆γ/rE) < −20.9 ± 0.2, representing the tightest constraints to date using astrophysical sources under consistent Shapiro delay modeling.

ABSTRACT

Fast radio bursts (FRBs) are astronomical transients with millisecond timescales occurring at cosmological distances. The observed time lag between different energies of each FRB is well described by the inverse-square law of the observed frequency, i.e., dispersion measure. Therefore, FRBs provide one of the ideal laboratories to test Einstein's weak equivalence principle (WEP): the hypothetical time lag between photons with different energies under a gravitational potential. If WEP is violated, such evidence should be exposed within the observational uncertainties of dispersion measures, unless the WEP violation also depends on the inverse-square of the observed frequency. In this work, we constrain the difference of gamma parameters ($\Delta\gamma$) between photons with different energies using the observational uncertainties of FRB dispersion measures, where $\Delta\gamma=0$ for Einstein's general relativity. Adopting the averaged 'Shapiro time delay' for cosmological sources, FRB 121002 at $z=1.6\pm0.3$ and FRB 180817.J1533+42 at $z=1.0\pm0.2$ place the most stringent constraints of $\log\Delta\gamma<-20.8\pm0.1$ and $\log(\Delta\gamma/r_{E}) < -20.9\pm0.2$, respectively, where $r_{E}$ is the energy ratio between the photons. The former is about three orders of magnitude lower than those of other astrophysical sources in previous works under the same formalization of the Shapiro time delay while the latter is comparable to the tightest constraint so far.

Motivation & Objective

• To test Einstein’s weak equivalence principle (WEP) using fast radio bursts (FRBs) as probes of gravitational time delays.
• To constrain the difference in gamma parameters (∆γ) between photons of different energies, where ∆γ = 0 in general relativity.
• To improve upon previous astrophysical limits by using cosmological FRBs and a consistent cosmological Shapiro time delay model.

Proposed method

• Model the observed time delay (∆tobs) as the sum of dispersion measure delay (∆tDM), intrinsic delay (∆tint), and gravitational Shapiro delay (∆tgra), with other effects negligible.
• Use a cosmological analytic solution for the averaged Shapiro time delay (tgra,ave) based on Planck15 cosmology, decomposed into Λ and matter terms.
• Derive ∆tgra from the matter contribution term (tmatter) and the γ parameter, assuming γ = 1 for general relativity.
• Apply the constraint ∆γ < (∆tobs − ∆tDM) × (6c³)/(ΩmH₀²dₛ³) to bound WEP violation using observational uncertainties in DM.
• Use the observed frequency dependence ν⁻²_obs of ∆tDM to argue that any WEP violation not following the same ν⁻²_obs law would be detectable within DM uncertainty.
• Apply the method to FRB 121002 and FRB 180817.J1533+42, using their redshifts and dispersion measure uncertainties to derive bounds on ∆γ.

Experimental results

Research questions

• RQ1 Can fast radio bursts (FRBs) be used to place tighter constraints on violations of Einstein’s weak equivalence principle (WEP)?
• RQ2 How do observational uncertainties in dispersion measures (DM) of FRBs limit the difference in gamma parameters (∆γ) between photons of different energies?
• RQ3 What are the implications of using cosmological Shapiro time delay models instead of local approximations for WEP testing with FRBs?
• RQ4 How do the resulting bounds on ∆γ compare to those from other astrophysical sources like pulsars or gravitational waves?

Key findings

• For FRB 121002 at z = 1.6 ± 0.3, the study places the tightest constraint to date: log ∆γ < −20.8 ± 0.1.
• For FRB 180817.J1533+42 at z = 1.0 ± 0.2, the constraint log(∆γ/rE) < −20.9 ± 0.2 is comparable to the tightest limit reported so far.
• The constraint from FRB 121002 is approximately three orders of magnitude lower than previous astrophysical limits using the same Shapiro delay formalism.
• The method relies on the assumption that WEP violation does not follow the same ν⁻²_obs frequency dependence as dispersion measure delay, otherwise the effects would be degenerate.
• The analysis uses a cosmologically consistent model for the averaged Shapiro time delay, accounting for matter and dark energy contributions.
• The results demonstrate that FRBs at cosmological distances provide a uniquely powerful probe for testing WEP due to their high redshift and high-precision DM measurements.