Croatian Science Foundation Research Project

Project: Towards quantum gravity: noncomutative geometry, field theory and cosmology

Principal Investigator (PI): Stjepan Meljanac, - senior scientist, Rudjer Bošković Institute (RBI)

Starting date: 1.09.2015.

Ending date: 31.8.2017.

Project proposal summary

The proposed project aims at carrying out research on various aspects of quantum gravity, related areas of mathematical physics, certain topics in cosmology, astroparticle physics and physics of black holes. Whereas a satisfactory theory of quantum gravity still remains elusive, some of the assessed properties revealing a nonlocal character of such a theory (i.e. noncommutativity of spacetime coordinates, ultraviolet/infrared (UV/IR) mixing and the holographic principle) has already changed our perspective upon reconciliation of the quantum field theory (QFT) framework with general relativity. A particular attention will be paid to construction, classification and unification of noncomutative (NC) spaces. In this regard, a procedure can be defined by making use of rigorous quantum deformation techniques as well as some well-known differential algebra concepts such as the Hopf algebra. This permits formulation and study of the twist-deformed Riemannian geometry, the twisted version of Einstein's equations and the algebraic structure on kappa-deformed Minkowski space. A further extension of these ideas opens a possibility to study NC effect in black holes. Furthermore, using the tools of QFT in curved spacetime, several aspects of modern cosmology will be covered including those based on the most successful realization of the holographic principle - the AdS/CFT duality. Finally, a class of quantum gravity models will be tested by probing Lorentz violation in observations of rapidly-varying astrophysical sources of high-energy gamma-rays. This requires a full-fledged field-theoretical model with a trouble-free and meaningful quantum loop results, with all UV and IR pathologies being under control.

Objectives of the proposed research

  1. NC differential geometry on deformed spaces
  2. NC metric
  3. NC fields in BTZ background
  4. NC gravity
  5. NC physics and near horizon geometries
  6. θ-exact covariant NCQFT
  7. New couplings/new processes
  8. Limit on the non-commutative scale
  9. Application to Astroparticle physics
  10. Hadronic fluid and AdS/CFT
  11. K-essence unification and De Sitter invariant propagators


  1. N. Bilić, "Randall-Sundrum versus holographic cosmology", Phys. Rev. D 93, no. 6, 066010 (2016) doi:10.1103/PhysRevD.93.066010 [arXiv:1511.07323 [gr-qc]].
  2. N. Bilić and D. Tolić, "Cosmological particle creation in a hadronic fluid", Phys. Rev. D 91, no. 10, 104025 (2015) doi:10.1103/PhysRevD.91.104025 [arXiv:1412.3977 [gr-qc]].
  3. N. Bilić, S. Domazet and D. Tolić, "Analog geometry in an expanding fluid from AdS/CFT perspective", Phys. Lett. B 743, 340 (2015) doi:10.1016/j.physletb.2015.03.009 [arXiv:1410.0263 [hep-th]].
  4. T. Jurić, S. Meljanac, D. Pikutić and R. Štrajn,"Toward the classification of differential calculi on κ-Minkowski space and related field theories", JHEP 1507, 055 (2015)
  5. K. S. Gupta, E. Harikumar, T. Jurić, S. Meljanac and A. Samsarov,"Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole", JHEP 1509, 025 (2015)
  6. T. Jurić, S. Meljanac and A. Samsarov, "Light-like κ-deformations and scalar field theory via Drinfeld twist", J.Phys.Conf.Ser. 634, no. 1, 012005 (2015)
  7. T. Juric, S. Meljanac and D. Pikutić, "Realizations of kappa-Minkowski space, Drinfeld twists and related symmetry algebras", Eur. Phys. J. C 75, no. 11, 528 (2015)
  8. S. Meljanac, A. Pachoł and D. Pikutić, "Twisted conformal algebra related to kappa-Minkowski space", Phys. Rev. D 92, no. 10, 105015 (2015)
  9. S. Meljanac, S. Krešić-Jurić and T. Martinić, "The Weyl realizations of Lie algebras and left-right duality, arXiv:1511.03936 [math-ph]
  10. T. Jurić, S. Meljanac and A. Samsarov, "Twist deformations leading to kappa-Poincare Hopf algebra and their application to physics", arXiv:1511.05592 [hep-th]
  11. A. Géré, T. Jurić and J. C. Wallet, "Noncommutative gauge theories on ${\mathrm{\mathbb{R}}}_{\lambda}^3$: perturbatively finite models", JHEP 1512, 045 (2015)
  12. B. Ivetić, S. Mignemi and A. Samsarov, "Spectrum of the hydrogen atom in Snyder space in a semiclassical approximation", arXiv:1510.06196 [hep-th]
  13. J. Trampetić and J. You, "theta-exact Seiberg-Witten maps at order e^3", Phys. Rev. D 91, no. 12, 125027 (2015)
  14. R. Horvat, J. Trampetić and J. You, "Photon polarization tensor on deformed spacetime: A four-photon-tadpole contribution", Phys. Rev. D 92, 125006 (2015)
  15. R. Horvat, J. Trampetić and J. You, "Photon self-interaction on deformed spacetime", Phys. Rev. D 92, no. 12, 125006 (2015)
  16. R. Horvat, "Avoiding Boltzmann Brain domination in holographic dark energy models", Phys.Lett. B 750, 181 (2015)
  17. N. Bilić, S. Domazet and D. Tolić, "Analog geometry in an expanding fluid from AdS/CFT perspective", Phys. Lett. B 743, 340 (2015)
  18. N. Bilić and D. Tolić, "Cosmological particle creation in a hadronic fluid", Phys. Rev. D 91, no. 10, 104025 (2015)
  19. N. Bilić, "Randall-Sundrum vs holographic cosmology", arXiv:1511.07323 [gr-qc]
  20. A. Borowiec, T. Juric, S. Meljanac, A. Pachoł, "Noncommutative tetrads and quantum spacetimes", arXiv:1602.01292
  21. T. Jurić, A. Samsarov, "Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry", arXiv:1602.01488

External colaborators


Job openings

A call for a position of research associate is open.
Call description:
Research in theoretical and mathematical physics, in particular on quantum gravity and quantum field theory with the emphasis on the use of methods of noncommutative geometry and quantum symmetry.

The deadline is until March 3. For all informations please contact

There will be a call for a postdoc position within the project. It will be announced in September/October 2016. The position is for 6 months and it starts on March 1, 2017. For more information contact

Activities within the HRZZ-project and other activities of the Group for Theoretical and Mathematical physics (conferences, talks, visits)

September 2015:
October 2015:
November 2015:
December 2015:
February 2016:
March 2016:
April 2016:

Contact info

Stjepan Meljanac
senior scientist, Head of Theoretical and mathematical physics group
Phone: +385 1 456 1121