Induced Superfluid Cosmology: A Theoretical Framework for Emergent Gravity and Dark Matter

TungLam  Trinh

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Induced Superfluid Cosmology: A Theoretical Framework for Emergent Gravity and Dark Matter

T. Trinh

2026-01-06

https://doi.org/10.24108/preprints-3114222

Abstract: Induced Gravity and Harmonic Mass Spectrum in a Superfluid Vacuum We present a theoretical framework for emergent spacetime based on chiral symmetry breaking in a Planck-scale fermion condensate. Using a topological field theory approach on a torus manifold $T^2$, we derive the mass spectrum of elementary particles as resonant breathing modes of vortex loops. This yields a Master Spectral Law: $m(p,q) = M^(1/p + 1/q)$, where $M^ \approx 365$ GeV is the symmetry-breaking scale. This framework offers a unified resolution to several open problems: Hierarchy Problem: The weak scale emerges naturally via a BCS-type dimensional transmutation mechanism ($\Lambda_{UV} \to M^*$). Mode Selection: We prove that the observed particle spectrum (Higgs, W, Z) corresponds to the lowest-complexity topological sectors ($p=5$ and $p=q$), uniquely determined by constrained optimization. Dark Sector: The model predicts a specific "Dark Tower" of high-winding composite solitons ($p=q=2^n$) that function as Self-Interacting Dark Matter (SIDM), consistent with formation structure and Vainshtein screening in the solar system.

Ссылка для цитирования:

Trinh T. 2026. Induced Superfluid Cosmology: A Theoretical Framework for Emergent Gravity and Dark Matter. PREPRINTS.RU. https://doi.org/10.24108/preprints-3114222

Список литературы

1. References

2. [1] Kiefer, C. (2007). Quantum Gravity. Oxford University Press.

3. [2] Sakharov, A. D. (1968). “Vacuum quantum fluctuations in curved space and the theory of

4. gravitation”. Sov. Phys. Dokl. 12, 1040.

5. [3] Volovik, G. E. (2003). The Universe in a Helium Droplet. Oxford University Press.

6. [4] Bardeen, J., Cooper, L. N., & Schrieffer, J. R. (1957). “Theory of Superconductivity”.

7. Phys. Rev. 108, 1175.

8. [5] Particle Data Group (2022). Prog. Theor. Exp. Phys. 2022, 083C01.

9. [6] Lelli, F. et al. (2016). “SPARC: A High-Quality Rotation Curve Sample”. Astron. J. 152,

10. [7] Vainshtein, A. I. (1972). “To the problem of nonvanishing gravitation mass”. Phys. Lett.

11. B 39, 393.

12. [8] Clowe, D. et al. (2006). “A Direct Empirical Proof of the Existence of Dark Matter”.

13. Astrophys. J. 648, L109.

14. [9] Abbott, B. P. et al. (LIGO/Virgo) (2017). “GW170817: Observation of Gravitational

15. Waves from a Binary Neutron Star Inspiral”. Phys. Rev. Lett. 119, 161101.

16. [10] Riess, A. G. et al. (SH0ES) (2022). “A Comprehensive Measurement of the Local Value

17. of the Hubble Constant”. Astrophys. J. Lett. 934, L7.

18. [11] KATRIN Collaboration (2022). “Direct neutrino-mass measurement with sub-electronvolt

19. sensitivity”. Nature Phys. 18, 160.

20. [12] LZ Collaboration (2023). “First Dark Matter Search Results from the LUX-ZEPLIN Ex-

21. periment”. Phys. Rev. Lett. 131, 041002.

22. [13] XENON Collaboration (2023). “First Dark Matter Search with Nuclear Recoils from the

23. XENONnT Experiment”. Phys. Rev. Lett. 131, 041003.

24. [14] CRESST Collaboration (2019). “Results on light dark matter from CRESST-III”. Phys.

25. Rev. D 100, 102002.

26. [15] SuperCDMS Collaboration (2020). “Constraints on low-mass dark matter from Super-

27. CDMS HVeV”. Phys. Rev. D 102, 091101.

28. [16] PandaX-4T Collaboration (2022). “Dark Matter Search Results from the PandaX-4T

29. Commissioning Run”. Phys. Rev. Lett. 129, 121801.

30. [17] CDF Collaboration (2022). “High-precision measurement of the W boson mass with the

31. CDF II detector”. Science 376, 170.

32. [18] ATLAS Collaboration (2024). “Measurement of the W-boson mass in pp collisions at

33. √s = 7 TeV with the ATLAS detector”. Eur. Phys. J. C 84, 1309. (Note: See also ATLAS-

34. CONF-2023-004 for updated combination.)

35. [19] Nicolis, A., Rattazzi, R., & Trincherini, E. (2009). “The Galileon as a local modification

36. of gravity”. Phys. Rev. D 79, 064036.

37. [20] de Rham, C. (2014). “Massive Gravity”. Living Rev. Relativ. 17, 7.

38. [21] Berezhiani, L. & Khoury, J. (2015). “Theory of dark matter superfluidity”. Phys. Rev. D

39. 92, 103510.

40. [22] Khoury, J. (2016). “Another path for the emergence of modified galactic dynamics from

41. dark matter superfluidity”. Phys. Rev. D 93, 103533.

42. [23] Liberati, S. (2013). “Tests of Lorentz invariance: a 2013 update”. Class. Quantum Grav.

43. 30, 133001.

44. [24] Fermi-LAT Collaboration (2009). “A limit on the variation of the speed of light arising

45. from quantum gravity effects”. Nature 462, 331.

46. [25] Muon g-2 Collaboration (2023). “Measurement of the Positive Muon Anomalous Mag-

47. netic Moment to 0.20 ppm”. Phys. Rev. Lett. 131, 161802.

48. [26] LEP Electroweak Working Group (2006). “Precision electroweak measurements on the Z

49. resonance”. Phys. Rept. 427, 257.

50. [27] Kaloper, N. & Padilla, A. (2014). “Sequestering the Standard Model Vacuum Energy”.

51. Phys. Rev. Lett. 112, 091304.

52. [28] Planck Collaboration (2020). “Planck 2018 results. VI. Cosmological parameters”. As-

53. tron. Astrophys. 641, A6.

54. [29] Belle II Collaboration (2023). “Search for an invisible Z’ in a final state with two muons

55. and missing energy”. Phys. Rev. Lett. 130, 181801.

56. [30] Tulin, S. & Yu, H.-B. (2018). “Dark Matter Self-interactions and Small Scale Structure”.

57. Phys. Rept. 730, 1.

58. [31] Horndeski, G. W. (1974). “Second-order scalar-tensor field equations in a four-

59. dimensional space”. Int. J. Theor. Phys. 10, 363.

60. [32] Bertotti, B., Iess, L., & Tortora, P. (2003). “A test of general relativity using radio links

61. with the Cassini spacecraft”. Nature 425, 374.

62. [33] Spergel, D. N. & Steinhardt, P. J. (2000). “Observational evidence for self-interacting cold

63. dark matter”. Phys. Rev. Lett. 84, 3760.

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