Optimal estimation of parameters for scalar field in an expanding spacetime exhibiting Lorentz invariance violation

  • Xiaobao Liu
  • Jiliang JingEmail author
  • Jieci Wang
  • Zehua TianEmail author


We address the optimal estimation of quantum parameters, in the framework of local quantum estimation theory, for a massive scalar quantum field in the expanding Robertson–Walker universe exhibiting Lorentz invariance violation (LIV). We find that, in the estimation of cosmological parameters, the ultimate bounds to the precision of the Lorentz-invariant massive scalar field can be improved due to the effects of LIV under some appropriate conditions. We also show that, in the Lorentz-invariant massive scalar field and massless scalar field due to LIV backgrounds, the optimal precision can be achieved by choosing the particles with some suitable LIV, cosmological and field parameters. Moreover, in the estimation of LIV parameter during the spacetime expansion, we prove that the appropriate momentum mode of field particles and larger cosmological parameters can provide us a better precision.


Lorentz invariance violation Expanding universe Local quantum estimation theory 



This work was supported by the National Natural Science Foundation of China under Grant Nos. 11875025 and 11675052. Hunan Provincial Natural Science Foundation of China under Grant No. 2018JJ1016. The project was funded by the CAS Key Laboratory for Research in Galaxies and Cosmology, Chinese Academy of Science (No. 18010203). Young Scientific Talents growth project of the Department of Education of Guizhou Province under Grant no. QJHKYZ[2019]129. The talent recruitment program of Liupanshui Normal University of China under Grant no. LPSSYKYJJ201906.


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Authors and Affiliations

  1. 1.Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education and Synergetic Innovation Center for Quantum Effects and ApplicationsHunan Normal UniversityChangshaPeople’s Republic of China
  2. 2.Department of Physics and Electrical EngineeringLiupanshui Normal UniversityLiupanshuiChina
  3. 3.CAS Key Laboratory of Microscale Magnetic Resonance and Department of Modern PhysicsUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China
  4. 4.Hefei National Laboratory for Physical Sciences at the MicroscaleUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China
  5. 5.Synergetic Innovation Center of Quantum Information and Quantum PhysicsUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China
  6. 6.Key Laboratory for Research in Galaxies and CosmologyChinese Academy of ScienceHefeiPeople’s Republic of China

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