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H. V. Grushevskaya, N. G. Krylova

Belarusian State University, Minsk, Belarus

**Part of the book: **Future Relativity, Gravitation, Cosmology

While within the minimal Standard Model the electroweak phase transition is considered to be the second order, the first-order electroweak phase transitions proposed in the background of beyond Standard Models may solve some cosmological problems, like the generation of the baryon asymmetry of the universe. We develop a geometrothermodynamic model of cosmological first-order vacuum-phase transition based on a theory of the first-order phase transition in a contact statistical manifold. Nucleation of true-vacuum bubbles with axially symmetric generalized Newman– Unti–Tamburino (NUT)-like metrics have been considered. A manifold of evolving bubbles is a pseudo-Finsler statistical manifold of such thermodynamic system. Finsler-Lagrange dynamics has been studied taking into account the heterogeneity of nucleation processes, notably a relaxation times distribution for bubbles. We has shown that a NUT-like variable parameter n in the theory is the gauge parameter of the scalar field which plays a role of fifth dimension and the transition of which from the steady state into strongly oscillating state is accompanied by the first-order phase transition between true and false vacua.

**Keywords:** cosmological first-order phase transitions, Newman–Unti–Tamburino metric,

geometrothermodynamics, pseudo-Finsler statistical manifold

[1] Gogberashvili M. (2018) J. Advances in High Energy Physics 2018, 4653202.

[2] Ghosh B. (2016) Pramana 87, 43.

[3] Gurtler M, Ilgenfritz E-M, Schiller A. (1997) Phys. Rev. D 56, 3888.

[4] Csikor F, Fodor Z, Heitger J. (1999) Phys. Rev. Lett. 82, 21.

[5] Witten E. (1984) Phys. Rev. D 30, 272.

[6] Kamionkowski M, Kosowsky A, Turner M S. (1994) Phys. Rev. D 49, 2837

[7] Anderson G W, Hall L J. (1992) Phys. Rev. D 45(8), 2685

[8] Brauner T, Tenkanen T V I, Tranberg A, Vuorinen A, Weir D J. (2017) JHEP 1703, 007.

[9] Linde A D. (1990) Physics of elementary particles and inflationary cosmology

(Moscow: Science)

[10] Zeldovich Y B, Kobzarev I Y, Okun L B. (1974) J. Exper. Theor. Phys. (Zh. Eksp.

Teor. Fiz.) 67, 3.

[11] Kempfer B, Lukash B, Paal G. (1990) Physics of elementary particles and atomic

nucleus 22, 63.

[12] Rao V U M, Suryanarayana G, Aditya Y. (2016) Advances in Astrophysics 1, 62.

[13] Dutta S, Jain A, Soni R. (2013) JHEP 2013, 060.

[14] Padmanabhan T. (2003) Phys. Rept. 380, 235.

[15] Banerjee R, Modak S K, Roychowdhury D. (2012) JHEP 1210, 125.

[16] Chaturvedi P, Das A, Sengupta G. (2017) Eur. Phys. J. C 77, 110.

[17] Sahay A, Sarkar T, Sengupta G. (2010) JHEP 10, 118.

[18] Avrami M. (1939) J. Chem. Phys. 7, 1103; (1940) J. Chem. Phys. 8, 212; (1941) J.

Chem. Phys. 9, 177.

[19] Jinno R, Leeb S, Seong H, Takimoto M. (2017) CTPU-17-28 KEK-TH-1990;

arXiv:1708.01253v2.

[20] Megevand A, Ramirez S. (2018) arXiv:1710.06279v2.

[21] Weir D J. (2018) HIP-2017-06/TH; arXiv:1705.01783v2.

[22] Balazs C, Fowlie A, Mazumdar A, White G. (2017) Phys. Rev. D 95, 043505.

[23] Ivanov I P. (2017) Prog. Part. Nucl. Phys. 95, 160.

[24] Turner M S, Weinberg E J, Widrow L M. (1992) Phys. Rev. D 46, 2384.

[25] Hiramatsu T, Kawasaki M, Saikawa K. (2014) J. Cosmol. Astropart. Phys. 2014, 31.

[26] Vladimirov Y S. Geometrophysics (BINOM, Moscow, 2010).

[27] Vilenkin A, Ford L H. (1982) Phys. Rev. D 26, 1231.

[28] Starobinsky A A. (1982) Phys. Lett. 117, 175.

[29] Ken’ichi Saikawa. (2017) Universe 3, 40.

[30] Hawking S W. (1975) Commun. Math. Phys. 43, 199.

[31] Bekenstein J D. (1973) Phys. Rev. D 7, 2333.

[32] Hawking S W, Page Don N. (1983) Commun. Math. Phys. 87, 577.

[33] Cvetic M, Gubser S S. (1999) JHEP 07, 010.

[34] Chaturvedi P, Sengupta G. (2015) Preprint arXiv:1501.07748v1.

[35] Simovic F, Mann R B. (2018) arXiv:1807.11875v1.

[36] Xu Z, Hou X, Wang J. (2018) arXiv:1711.04538v2.

[37] Multamki T, Vilja I .(2006) Phys. Rev. D 74, 064022.

[38] Gutirrez-Pieres A C., Lopez-Monsalvo C S (2013) Phys. Lett. B 718, 1493.

[39] Nashed G G L, Bamba K. (2019) arXiv:1902.08020v1.

[40] Sakti M F A R, Suroso A, Zen F P. (2019) arXiv:1901.09163v1.

[41] Schaf J. (2018) J. Modern Physics 9, 1883.

[42] Bravetti A, Lopez-Monsalvo C S, Nettel F, Quevedo H. (2014) J. Geom. Phys. 81, 1.

[43] Bravetti A, Lopez-Monsalvo C S, Nettel F. (2015) Entropy 17, 6150.

[44] Hawking S. (1966) Astrophys. J. 145, 544.

[45] Bittencourt E, Salim J, dos Santos G B. (2014) Int. J. Nonlin. Phenom. in Complex

Sys. 17, 352.

[46] Balan V, Grushevskaya H V, Krylova N G, Neagu M. (2016) Int. J. Nonlin. Phenom.

in Complex Sys. 19, 223.

[47] Quevedo H. (2007) J. Math. Phys. 48, 13506.

[48] Quevedo H, Quevedo M N. (2011) EJTP – Zacatecas Proc. II, 1.

[49] Quevedo H, Sanchez A, Taj S, Vazquez A. (2011) Gen. Rel. Grav. 43 1153.

[50] Boyer C P. (2011) SIGMA 7, 058.

[51] Arnold V I, Novikov S P. Dynamical Systems IV: Symplectic Geometry and Its Applications (Springer, Berlin, 2001).

[52] Mrugała R. (2000) Rep. Math. Phys. 46, 461.

[53] Krylova N G. (2017) Proceedings of NAS of Belatus. Ser. Phys.-Math. 53(3), 66. (in

Russian)

[54] Krylova N G, Grushevskaya H V. (2018) Proceedings of NAS of Belatus. Ser. Phys.-

Math. 54(1), 84. (in Russian)

[55] Nemilov S V. Optical study of materials (SPbSU ITMO Publishing, Saint-Petersburg,

2009). (in Russian)

[56] Kuni F, Shchekin A K, Grinin A P. (2009) Physics-Uspekhi (Advances in Physical

Sciences) 171, 345. (in Russian)

[57] Gitterman M, Halpern V. Phase Transitions(World Scientific, London, 2004).

[58] Grushevskaya H V, Krylova N G. (2018) J. of Phys. CS 1051, 012013.

[59] Thompson J M T. Instabilities and Catastrophes in Science and Engineering (Wiley,

New York, 1982).

[60] Bravetti A, Nettel F. (2014) Phys. Rev. D 90, 044064; arXiv:1208.0399v2.

[61] Voicu N. (2011) Progress In Electromagnetics Research. 113, 83.

[62] Landau L D, Lifshits E M. Statistical physics (Science, Moscow, 1976).

[63] Bao D, Chern S S, Shen Z. An introduction to Riemann-Finsler geometry (Springer,

Berlin, 2000).

[64] Balan V, Grushevskaya H, Krylova N, Neagu M, Oana A. (2013) Applied Sciences 15, 30.

[65] Neagu M., Krylova N G, Grushevskaya H V. (2013) J. Math. Phys. 54, 031508.

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