Constraints on Equivalence Principle Violation from Gamma Ray Bursts

Abstract

Theories of gravity that obey the Weak Equivalence Principle have the same Parametrised Post-Newtonian parameter γ for all particles at all energies. The large Shapiro time delays of extragalactic sources allow us to put tight constraints on differences in γ between photons of different frequencies from spectral lag data, since a non-zero ∆γ would result in a frequency-dependent arrival time. The majority of previous constraints have assumed that the Shapiro time delay is dominated by a few local massive objects, although this is a poor approximation for distant sources. In this work we consider the cosmological context of these sources by developing a source-by-source, Monte Carlo-based forward model for the Shapiro time delays by combining constrained realisations of the local density field using the BORG algorithm with unconstrained large-scale modes. Propagating uncertainties in the density field reconstruction and marginalising over an empirical model describing other contributions to the time delay, we use spectral lag data of Gamma Ray Bursts from the BATSE satellite to constrain ∆γ < 3.4 × 10 −15 at 1σ confidence between photon energies of 25 keV and 325 keV.

Constraints on quantum gravity and the photon mass from gamma ray bursts

“…Since the redshift values are uncertain, as in [43], we draw N MC = 10 4 redshifts per source from a two-sided Gaussian with upper and lower uncertainties equal to the uncertainties calculated in [49]. Doubling N MC yields identical results, indicating that the number of samples is adequate.…”

“…As demonstrated in [43], for the WEP violation case one cannot accurately describe the alternative contributions to the time delay by a single Gaussian. Instead, we model these extra contributions, B ij , to the observed delay ∆t…”

“…As in [43], the deliberately wide priors, P (θ), in Table I lead to difficulties in interpreting the Bayes ratio. To find the maximum likelihood and thus the BIC, we first optimise using the Nelder-Mead algorithm [54] with a simplex consisting of parameters drawn randomly from the prior.…”

“…First, we address the issues highlighted when constraining E QG by constructing probabilistic source-by-source forward models of the time delays of 448 GRBs from the BATSE satellite [41,42] and marginalising over empirical noise models describing astrophysical and observational contributions to the measured time delay. These techniques were developed in Bartlett et al [43] who, using the same sources as here, constrain WEP violation to ∆γ < 2.1 × 10 −15 at 1σ confidence between photon energies of 25 keV and 325 keV. Second, we provide constraints on the photon mass that are independent of radio observations and are thus insensitive to potential systematics in modelling the propagation of photons at radio frequency.…”