Context : The planning of the ESA Science Programme Voyage 2050 relies on the public discussion of open scientific questions of paramount importance for an advance of our understanding of the Laws of Nature , that can be addressed by a scientific space mission within the Voyage 2050 planning cycle , covering the period from 2035 to 2050 .
As a part of the ESA Science Programme Voyage 2050 , a new concept of high–energy mission named GrailQuest ( Gamma Ray Astronomy International Laboratory for QUantum Exploration of Space–Time ) is investigated .

Aims : The three main scientific objectives that GrailQuest wants to pursue are : i ) to probe space–time structure down to the Planck scale by measuring the delays between photons of different energies in the prompt emission of Gamma–ray Bursts ; ii ) to localise Gamma–ray Bursts prompt emission with an accuracy of few arc–seconds .
This capability is particularly relevant in light of the recent discovery that fast high energy transients are the electromagnetic counterparts of some gravitational wave events observed by the Advanced LIGO and Virgo network ; iii ) to fully exploit timing capabilities down to micro–seconds or below at X/Gamma–ray energies , by means of an adequate combination of temporal resolution and collecting area , thus allowing to effectively investigate , for the first time , the micro–second structure of Gamma–ray Bursts and other transient phenomena in the X/Gamma–ray energy window .

Methods : A significant class of theories of Quantum Gravity describing the space–time structure down to the Planck scale predict a dispersion law for the propagation of photons in vacuo that linearly depends on the ratio between the photon energy and the Planck energy .
The delays induced by this relation of light dispersion in vacuo depends linearly on the space travelled and are tiny , being in the microsecond range , for photons that travelled for ( few ) billion years .
Gamma–ray Bursts are ideal targets to test , robustly , this prediction because the prompt gamma–ray emission extends , in a detectable way , over more than six orders of magnitude in energy ( from keV to ten ( s ) of GeV ) and are among the most distant objects ever detected ( their maximum redshift measured up to date is just above z = 9 ) .
Spectral intrinsic delays due to unknown characteristics of the emission process in different energy bands , could easily dominate the delays observable between different spectral components , however these effects can be disentangled by i ) having a sufficient number of photons in sufficiently narrow energy bands , as the emission process is the same within a narrow band ; ii ) having a sufficiently rich sample of Gamma–ray Bursts at different redshift , since the delays induced by a dispersion law for the propagation of photons in vacuo scale almost linearly ( with a weak dependence on the details of the particular cosmology adopted ) with redshift .
This double linear dependence , in energy and redshift , is the characteristic signature of a Quantum Gravity effect .

GrailQuest is a mission concept based on a constellation of nano/micro/small–satellites in low ( or near ) Earth orbits , hosting fast scintillators to probe the X/gamma–ray emission of bright high–energy transients .
The main features of this proposed experiment are : temporal resolution \leq 100 nano-seconds , huge overall collecting area , \sim 100 square meters , very broad energy band coverage , \sim 1 keV– 10 MeV . GrailQuest is conceived as an all–sky monitor for fast localisation of high signal–to–noise ratio transients in the broad keV–MeV band by robust triangulation techniques with accuracies at micro–second level , and baselines of several thousand of km .
These features allow unprecedented localisation capabilities , in the keV–MeV band , of few arc–seconds or below , depending on the temporal structure of the transient event .
Despite the huge collecting area , hundred ( s ) of square meters , and the consequent number of nano/micro/small–satellites utilised ( from thousand ( s ) down to ten ( s ) , respectively ) , orbiting all–around Earth in uniformly distributed orbits , the technical capabilities and subsequent design of each base unit of the constellation are extremely simple and robust .
This allows for mass–production of the base unit of this experiment , namely a satellite equipped with a non–collimated ( half–sky field of view ) detector ( effective area in the range hundred–thousand ( s ) square centimetres ) .
The detector consists in segmented scintillator crystals coupled with Silicon Drift Detectors with broad energy band coverage ( keV–MeV range ) and excellent temporal resolution ( \leq 100 nano–seconds ) .
Very limited ( if any ) pointing capabilities are required .
We forecast that mass production of this simple unit allows a huge reduction of costs .
Moreover , the large number of satellites involved in the GrailQuest constellation make this experiment very robust against failure of one or more of its units .

GrailQuest is a modular experiment in which , for each of the detected photons , only three information are essential , namely accurate time–of–arrival of each photon ( down to 100 nano-seconds , or below ) , moderate energy resolution ( few percent ) , and detector position ( within few tens of meters ) .
This opens the compelling possibility to combine data from different kind of detectors ( aboard of different kind of satellites belonging , in principle , to different constellations ) to achieve the scientific objectives of the GrailQuest project , making GrailQuest one of the few example of modular space–based astronomy .
In past years , modular experiments , proved to be very effective in opening up new possibilities for astronomical investigation .
Just think of the Very Large Baseline Interferometry , an astronomical interferometry in the Radio Band , involving more that thirty radio telescopes all over the world and the Cluster II mission , a space mission of the European Space Agency , with NASA participation , composed of a constellation of four satellites , to study the Earth ’ s magnetosphere , launched in 2000 and recently extended to the end of 2020 .
In the near future , a constellation of three satellites in formation is planned for the LISA mission , to reveal gravitational waves from space .
Very recently , two extremely successful experiments , of paramount importance for fundamental physics , involve the combined use of several ground–based detectors .
One is the LIGO/Virgo Collaboration ( involving the two US–based LIGO and the European Virgo facilities ) that allowed for the first detection and localisation of gravitational waves .
In one case , temporal triangulation techniques , conceptually similar to those proposed for GrailQuest constellation and described in this work , effectively constrained the position of the event in the sky , allowing for fast subsequent localisation , in the electromagnetic window , of a double Neutron Star merging event .
The other is the Event Horizon Telescope ( which provides for the combined use of 8 radio/micro–wave observatories spread all over the world ) that allowed to obtain the first image of the event horizon around a black hole .
We consider these compelling results as the proof that modular astronomy , that benefits from the combined use of distributed detectors ( to increase the overall detecting area and allow for unprecedented spatial resolution , in case of the Event Horizon Telescope and the GrailQuest project ) , is the new frontier of cutting–edge experimental astronomical science that is performed by exploiting the combination of a large number of detectors distributed all over the Earth surface .
The GrailQuest project is a space–based version of this epochal revolution .

Results : We performed accurate Monte–Carlo simulations of thousands of light curves of Gamma–ray Bursts , based on true data obtained from the scintillators of the Gamma Burst Monitor on board of the Fermi Satellite .
We produced Gamma–ray Burst light curves in consecutive energy bands in the interval 10 keV–50 MeV , for a range of effective area .
We then applied cross–correlation techniques to these light curves to determine the minimum accuracy with which potential temporal delays between these light curves are determined .
As expected , this accuracy depends , in a complicated way , from the temporal variability scale of the Gamma–ray Burst considered , and scales with roughly the square root of the number of photons in the considered energy band .
We determined that , for temporal variabilities in the millisecond range ( that are expected in at least 30 % of the observed Gamma–ray Bursts ) , with an overall effective area of \sim 100 square meters the statistical accuracy of these delays is always smaller ( for redshifts \geq 0.5 ) than the delays expected by a dispersion law for the propagation of photons in vacuo that linearly depends on the ratio between the photon energy and the Planck energy .

This proves that the GrailQuest constellation is able to achieve the ambitious objectives outlined above , within the budget of a European Space Agency M–class mission .