Testing Einstein’s Equivalence Principle With Fast Radio Bursts

The accuracy of Einstein’s equivalence principle (EEP) can be tested with the observed time delays between correlated particles or photons that are emitted from astronomical sources. Assuming as a lower limit that the time delays are caused mainly by the gravitational potential of the Milky Way, we prove that fast radio bursts (FRBs) of cosmological origin can be used to constrain the EEP with high accuracy. Taking FRB 110220 and two possible FRB/gamma-ray burst (GRB) association systems (FRB/GRB 101011A and FRB/GRB 100704A) as examples, we obtain a strict upper limit on the differences of the parametrized post-Newtonian parameter $\gamma$ values as low as $[\gamma (1.23\mathrm{GHz})-\gamma (1.45\mathrm{GHz})]<4.36\times {10}^{-9}$. This provides the most stringent limit up to date on the EEP through the relative differential variations of the $\gamma$ parameter at radio energies, improving by 1 to 2 orders of magnitude the previous results at other energies based on supernova 1987A and GRBs.

Figure 1

Limits on the differences of the $\gamma$ values for three FRB observations. The dots represent the conservative upper limits on $\mathrm{\Delta }\gamma$ by taking the inferred redshifts from Method 1 or 2, and assuming $\mathrm{\Delta }{t}_{\text{obs}}\gg \mathrm{\Delta }{t}_{\mathrm{DM}}$. The red lines show the test results from considering different $\mathrm{\Delta }{t}_{\mathrm{DM}}$ contributions. From top to bottom, the red error bars correspond to the case of $\mathrm{\Delta }{t}_{\mathrm{DM}}=0.001\mathrm{\Delta }t$ and $\mathrm{\Delta }{t}_{\mathrm{DM}}=0.999\mathrm{\Delta }t$, respectively. The constraints on $\mathrm{\Delta }\gamma$ from varying the values of redshifts are presented as the blue lines. From top to bottom, the blue error bars correspond to the cases of 1 Mpc, $0.5z$, $2z$, and $3z$, respectively.