Abstract
We show the analogy between a generalization of the Rayleigh–Plesset equation of bubble dynamics including surface tension, elasticity and viscosity effects with a reformulation of the Friedmann–Lemaître set of equations describing the expansion of space in cosmology assuming a homogeneous and isotropic universe. By comparing both fluid and cosmic equations, we propose a bold generalization of the newly-derived cosmic equation mapping three continuum mechanics contributions. Conversely, the addition of a cosmological constant-like term in the fluid equation would lead also to a new phenomenology.
References
Banerjee, S., Danielsson, U., Dibitetto, G., Giri, S., Schillo, M.: Emergent de Sitter cosmology from decaying anti-de sitter space. Phys. Rev. Lett. 121(26), 261301 (2018)
Friedmann, A.: Über die Krümmung des Raumes. Z. Phys. A 10(1), 377–386 (1922)
Lemaître, G.: Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques. Ann. Soc. Sci. Brux. 47, 49–59 (1927)
Rayleigh, Lord: On the pressure developed in a liquid during the collapse of a spherical cavity. Philos. Mag. 34, 94–98 (1917)
Minnaert, M.: On musical air-bubbles and the sounds of running water. Philos. Mag. Ser. 7 16(104), 235–248 (1933)
Plesset, M.S.: The dynamics of cavitation bubbles. J. Appl. Mech. 16, 277–282 (1949)
Noltingk, B.E., Neppiras, E.A.: Cavitation produced by ultrasonics. Proc. Phys. Soc. Lond. Sect. B 63(9), 674 (1950)
Poritsky, H.: The collapse or growth of a spherical bubble or cavity in a viscous fluid. In: Proceedings of the First U. S. National Congress on Applied Mechanics, pp. 813–821 (1952)
Franc, J.-P., Michel, J.-M.: Fundamentals of Cavitation, vol. 76. Springer, Berlin (2006)
Chaline, J.: Analogie macroscopique et acousto-mécanique d’une microbulle. Application aux agents de contraste ultrasonore. PhD Thesis of the Tours University, France (2015)
Bini, D., Succi, S.: Analogy between capillary motion and Friedmann–Robertson–Walker cosmology. Europhys. Lett. 82(3), 34003 (2008)
Kolomeisky, E.B.: Natural analog to cosmology in basic condensed matter physics. Phys. Rev. B 100(14), 140301 (2019)
Mancas, S.C., Rosu, H.C.: Evolution of spherical cavitation bubbles: parametric and closed-form solutions. Phys. Fluids 28(2), 022009 (2016)
Rosu, H.C., Mancas, S.C., Chen, P.: Barotropic FRW cosmologies with Chiellini damping in comoving time. Mod. Phys. Lett. A 30(20), 1550100 (2015)
Mancas, S.: Cavitation of spherical bubbles with surface tension and viscosity: theory and experiments, Oral Presentation at Miami 2015: A Topical Conference on Elementary Particles Astrophysics, and Cosmology, Fort Lauderdale, Florida, USA, 16–22 Dec (2015)
Faraoni, V.: Analogy between equilibrium beach profiles and closed universes. Phys. Rev. Res. 1(3), 033002 (2019)
Faraoni, V.: Analogy between freezing lakes and the cosmic radiation era. Phys. Rev. Res. 2, 013187 (2020)
Novosyadlyj, B.: Century of \(\Lambda \). Eur. Phys. J. H 43(3), 267–280 (2018)
Knobloch, E., Krechetnikov, R.: Problems on time-varying domains: formulation, dynamics, and challenges. Acta Appl. Math. 137(1), 123–157 (2015)
Sahni, V., Krasiński, A.: Republication of: the cosmological constant and the theory of elementary particles (By Ya. B. Zeldovich). Gen. Relativ. Gravity 40, 1557–1591 (2008)
Da̧browski, M.P., Stachowiak, T.: Phantom Friedmann cosmologies and higher-order characteristics of expansion. Ann. Phys. 321(4), 771–812 (2006)
Aasi, J., et al.: Constraints on cosmic strings from the LIGO-virgo gravitational-wave detectors. Phys. Rev. Lett. 112, 131101 (2014)
Icke, V.: Which side are you on? Nat. Phys. 12(4), 374–374 (2016)
Malmi-Kakkada, A., Thirumalai, D.: Generalized Rayleigh–Plesset Theory for Cell Size Maintenance in Viruses and Bacteria (2019). arXiv:1902.07329
Doinikov, A.A., Bouakaz, A.: Review of shell models for contrast agent microbubbles. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58(5), 981–993 (2011)
Weinberg, S.: Entropy generation and the survival of protogalaxies in an expanding universe. Astrophys. J. 168, 175 (1971)
Marmottant, P., Van Der Meer, S., Emmer, M., Versluis, M., De Jong, N., Hilgenfeldt, S., Lohse, D.: A model for large amplitude oscillations of coated bubbles accounting for buckling and rupture. JASA 118(6), 3499–3505 (2005)
Barceló, C.: Analogue black-hole horizons. Nat. Phys. 15, 210–213 (2019). https://doi.org/10.1038/s41567-018-0367-6
Euvé, L.-P., Robertson, S., James, N., Fabbri, A., Rousseaux, G.: Scattering of co-current surface waves on an analogue black hole. Phys. Rev. Lett. 124(14), 141101 (2020)
Kragh, H.: Cyclic models of the relativistic universe: the early history. In: Rowe, D.E., Sauer, T., Walter, S.A. (eds.) Beyond Einstein, pp. 183–204. Birkhäuser, New York (2018)
Acknowledgements
GR thanks Jennifer Chaline for providing him with the essential knowledge on the Rayleigh–Plesset equation based on her Ph.D. thesis work. He also acknowledges discussions with M. Baudoin and P. Marmottant.
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Conflict of interest
The authors report no conflict of interest.
Data Sharing
Data sharing is not applicable to this article as no new data were created or analyzed in this study.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Rousseaux, G., Mancas, S.C. Visco-elastic cosmology for a sparkling universe?. Gen Relativ Gravit 52, 55 (2020). https://doi.org/10.1007/s10714-020-02705-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10714-020-02705-y