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Cosmological Model Independent Constraints on Lorentz Invariance Violation with Updated Gamma-Ray Burst Observations: An Artificial Neural Network Approach

Jun Tian, Yu Pan, Shuo Cao, Qing-Quan Jiang, Wei-Liang Qian

TL;DR

This work tackles the dependence of Lorentz Invariance Violation (LIV) constraints on cosmological priors by using an artificial neural network (ANN) to reconstruct the expansion history $H(z)$ in a model-independent way, thereby avoiding biases from specific cosmological priors. It analyzes 74 GRB time-delay measurements, including 37 from GRB 160625B at $z=1.41$, paired with a power-law intrinsic time delay model and an ANN-based $H(z)$ reconstruction trained on 32 cosmic chronometer data. Through joint fits, it derives tight LIV bounds for linear and quadratic terms: $E_{ m QG,1} \,\ge 2.60 \times 10^{15}$ GeV and $E_{ m QG,2} \,\ge 1.21 \times 10^{10}$ GeV (1σ), with the linear limit close to four orders of magnitude below the Planck scale. The approach yields robust, cosmology-independent LIV constraints using a large GRB sample and demonstrates parity with Gaussian Process methods, while noting limitations from the restricted redshift range of the ANN-based $H(z)$. This framework sets a practical path for future quantum gravity tests as more high-quality $H(z)$ data become available.

Abstract

Searching for Lorentz invariance violation (LIV) using astrophysical sources such as gamma-ray bursts (GRBs) is crucial for probing quantum gravity. However, the dependence of LIV constraints on assumed cosmological models has been largely overlooked. In this work, we present a model-independent reconstruction of the cosmic expansion history using artificial neural networks (ANN), thereby avoiding biases from specific cosmological priors. We analyze 74 GRB time delays, including 37 measurements from GRB~160625B across multiple energy bands at $z = 1.41$, and 37 additional bursts spanning redshifts $0.117 \leq z \leq 1.99$. Our analysis yields stringent constraints on both linear and quadratic LIV, with $E_{\mathrm{QG},1} \geq 2.60 \times 10^{15}~\mathrm{GeV}$ and $E_{\mathrm{QG},2} \geq 1.21 \times 10^{10}~\mathrm{GeV}$. The linear limit is within four orders of magnitude of the Planck scale. By leveraging a large sample of GRBs, our approach significantly enhances the robustness of LIV constraints, providing a powerful, cosmological-independent framework for future tests of quantum gravity.

Cosmological Model Independent Constraints on Lorentz Invariance Violation with Updated Gamma-Ray Burst Observations: An Artificial Neural Network Approach

TL;DR

This work tackles the dependence of Lorentz Invariance Violation (LIV) constraints on cosmological priors by using an artificial neural network (ANN) to reconstruct the expansion history in a model-independent way, thereby avoiding biases from specific cosmological priors. It analyzes 74 GRB time-delay measurements, including 37 from GRB 160625B at , paired with a power-law intrinsic time delay model and an ANN-based reconstruction trained on 32 cosmic chronometer data. Through joint fits, it derives tight LIV bounds for linear and quadratic terms: GeV and GeV (1σ), with the linear limit close to four orders of magnitude below the Planck scale. The approach yields robust, cosmology-independent LIV constraints using a large GRB sample and demonstrates parity with Gaussian Process methods, while noting limitations from the restricted redshift range of the ANN-based . This framework sets a practical path for future quantum gravity tests as more high-quality data become available.

Abstract

Searching for Lorentz invariance violation (LIV) using astrophysical sources such as gamma-ray bursts (GRBs) is crucial for probing quantum gravity. However, the dependence of LIV constraints on assumed cosmological models has been largely overlooked. In this work, we present a model-independent reconstruction of the cosmic expansion history using artificial neural networks (ANN), thereby avoiding biases from specific cosmological priors. We analyze 74 GRB time delays, including 37 measurements from GRB~160625B across multiple energy bands at , and 37 additional bursts spanning redshifts . Our analysis yields stringent constraints on both linear and quadratic LIV, with and . The linear limit is within four orders of magnitude of the Planck scale. By leveraging a large sample of GRBs, our approach significantly enhances the robustness of LIV constraints, providing a powerful, cosmological-independent framework for future tests of quantum gravity.

Paper Structure

This paper contains 7 sections, 13 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology and Datasets
  3. Lorentz Invariance Violation
  4. Observational Data
  5. Artificial Neural Network Method
  6. Results and Discussion
  7. Conclusions

Figures (3)

  • Figure 1: The reconstructed $H(z)$ (shown as a red curve) using ANN, along with the corresponding $1\sigma$ error (depicted as a sky-blue area), and the CC $H(z)$ data (represented by black dots with error bars). Additionally, the green curve represents the theoretical prediction of the standard cosmological model.
  • Figure 2: The 1D probability distribution of each parameter and the 2D confidence contours for the parameters $a_{\mathrm{LIV},1}$, $\tau$, and $\alpha$ (the linear LIV case, i.e., n = 1). The blue dashed line delineates the $1\sigma$ confidence interval, whereas the red dashed line highlights the best-fit estimate.
  • Figure 3: The 1D probability distribution of each parameter and the 2D confidence contours for the parameters $a_{\mathrm{LIV},2}$, $\tau$, and $\alpha$ (the quadratic LIV case, i.e., n = 2).