Constraints on equivalence principle violation from gamma ray bursts

Theories of gravity that obey the Weak Equivalence Principle have same Parametrised Post-Newtonian parameter $\gamma$ for all particles at energies. The large Shapiro time delays extragalactic sources allow us to put tight constraints on differences in between photons different frequencies from spectral lag data, since a non-zero $\Delta \gamma$ would result frequency-dependent arrival time. majority previous assumed delay is dominated by few local massive objects, although this poor approximation distant sources. In work we consider cosmological context these developing source-by-source, Monte Carlo-based forward model combining constrained realisations density field using Bayesian origin reconstruction galaxies algorithm with unconstrained large-scale modes. Propagating uncertainties and marginalising over an empirical describing other contributions delay, use data Gamma Ray Bursts BATSE satellite constrain \gamma < 2.1 \times 10^{-15}$ $1 \sigma$ confidence photon energies $25 {\rm \, keV}$ $325 keV}$.