Constraining the curvature-induced quantum gravity scales via gamma-ray bursts

Abstract: We constrain the parameters that govern curvature-induced quantum gravity time-of-flight (TOF) effects. These TOF delays, which occur due to modified dispersion relations of particles in the vacuum, could be a phenomenological signature of quantum gravity. Gamma-ray bursts (GRBs), short, high-energy events from distant galaxies, offer a unique opportunity to impose observational limits on TOF delays and, by extension, on the energy scales of quantum gravity. Using the standard Jacob-Piran relation, which assumes a locally-flat spacetime, the analysis of quantum gravity-induced TOF effects establishes a lower limit of approximately $10 E_{\rm Pl}$ on the energy scale of these effects. However, curvature-induced quantum gravity effects may introduce additional contributions. From current GRB observations, we find that, at a 95% credibility level, in the symmetry-deformed scenario, curvature-induced TOF effects may only arise at energies above $0.04 E_{\rm Pl}$. If we consider only curvature-induced effects, this limit is an order of magnitude stronger. Observing more GRBs at different redshifts could improve the constraints on the curvature-induced QG phenomena. However, given the capabilities of current telescopes and the current understanding of GRBs, it is unlikely that these constraints will be significantly extended beyond the present level.

• The paper constrains curvature-induced quantum gravity (QG) energy scales by analyzing time-of-flight delays of high-energy photons from gamma-ray bursts (GRBs).
• The study finds that QG effects are constrained to be significant above approximately 10 times the Planck scale for locally flat space and above 0.04 times the Planck scale when considering space-time curvature.
• Analyzing data from several bright GRBs, especially GRB 221009A and 090510, provides stringent empirical limits near or above the Planck energy, guiding future QG theories.

Curvature-Induced Quantum Gravity Scales and Gamma-Ray Bursts

The paper "Constraining the curvature-induced quantum gravity scales via gamma-ray bursts" by D. D. Ofengeim and T. Piran offers a rigorous investigation into quantum gravity (QG) effects using gamma-ray bursts (GRBs) as observable markers. The study focuses on the time-of-flight (TOF) delays of photons hypothesized to arise from modifications in dispersion relations due to quantum gravitational phenomena.

Gamma-ray bursts, due to their high-energy emissions over cosmological distances, serve as effective tools for testing the upper bounds of TOF delays caused by QG effects. The authors utilize the standard Jacob-Piran relation, which considers space as locally flat, to analyze these TOF effects and place constraints on the energy scale associated with QG phenomena. Through their analysis, they estimate that these effects become significant at an energy scale that is approximately ten times the Planck scale (10 $E_{\text{Pl}}$). However, when considering the impact of space-time curvature within QG frameworks, they propose a more stringent lower limit of $0.04E_{\text{Pl}}$.

The GRB observations analyzed include prompt emissions as well as afterglows, with the latter involving higher photon energies. This study integrates various GRB data with differing redshifts to mitigate systematic uncertainties, such as intrinsic lags in emissions of different energies that complicate isolation of QG-induced delays. Data from six notable GRBs—221009A, 190114C, 090510, 090902B, 090926A, and 080916C—were utilized, each providing unique constraints, with GRB 221009A and 090510 delivering the most stringent constraints.

By employing both Bayesian statistical methods and the previously established frameworks by Amelino-Camelia et al., the analysis evaluates both locally-flat and curvature-induced QG parameters. Among the findings, the scales for these effects are constrained to $QG^{(\text{lf})}$ for locally-flat cases and $QG^{(\text{ci})}$ for curvature-induced cases, revealing the parameters' interdependencies.

The theoretical implications are profound, creating a detailed parameter space to test future QG theories. Moreover, bounding these scales near or above the Planck energy not only solidifies the limits of current theoretical models but also guides future research into gravitational theories beyond General Relativity.

Practically, this research emphasizes the utility of prolonged gamma-ray observation for tightening QG parameters' constraints. Future improvements in observational techniques, particularly in capturing high-energy photons from GRBs, may present opportunities to explore beyond the current energy scale limits. Additionally, exploring the interplay between curvature-induced effects and cosmological evolution models may yield further insights.

In conclusion, the findings of the study underscore the delicate balance between theoretical adaptability and empirical constraints in the field of quantum gravity, utilizing gamma-ray bursts as a cosmic laboratory to push the boundaries of our understanding of the universe. The prospect of more detailed measurements in higher energy domains could refine these findings and drive future theoretical advancements.