Quantum gravity with THESEUS

In this paper we explore the possibility to search for a dispersion law for light propagation in vacuo with a sample of Gamma-Ray Bursts detected by the THESEUS satellite. Within Quantum Gravity theories, different models for space-time quantization predict relative discrepancies of the speed of photons w.r.t. the speed of light that (in a series expansion) depend on a given power of the ratio of the photon energy to the Planck energy. This ratio is as small as 10− 23 for photons in the soft γ −ray band (100 keV). The dominant effect is determined by the first significant term of this expansion. If the first order in this expansion is relevant, these theories imply a Lorentz Invariance Violation (LIV hereafter) and are generally dubbed LIV-theories. Therefore, to detect this effect, light must propagate over enormous distances and the experiment must have extraordinary sensitivity. Gamma-Ray Bursts, occurring at cosmological distances, could be used to detect this tiny signature of space-time granularity. Once the photons of a Gamma-Ray Burst are emitted at a given (cosmological) distance, they arrive on the detector with relative delays that linearly depends on the energy differences and on the distance travelled, that, given a set of cosmological parameters, is a unique function of the redshift. The strong temporal variability of the Gamma-Ray Bursts light-curves allows, with different techniques (e.g. cross-correlations), to compute these delays by comparing light-curves of Gamma-Ray Bursts for which the redshift is known, in adjacent energy bands covering a sufficiently wide energy range. In this way, LIV-theories can be effectively constrained. THESEUS offers the opportunity to collect a homogeneous set of GRBs for which the redshift is known, with a signal to background ratio sufficient to compute delays through cross correlation techniques, and covering an energy band (from few keV to few MeV) wide enough to produce significant delays. In this article we explore the possibility to constrain LIV-theories with THESEUS by means of Monte Carlo simulations. In summary, within the nominal duration of 3 years, THESEUS could constrain (or detect) Quantum Gravity Lorentz Invariance Violation effects at al level of 17 times the Planck Length (1.6 × 10− 33 cm); if the mission is extended up to 7 years, this constrain is improved down to a level of 11 times the Planck Length.