Comparative Analysis of Standard ΛCDM and ΛCS Models


  • V.E. Kuzmichev Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
  • V.V. Kuzmichev Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine





We draw a comparison of time-dependent cosmological parameters calculated in the standard ΛCDM model with those of the model of a homogeneous and isotropic Universe with non-zero cosmological constant filled with a perfect gas of low-velocity cosmic strings (ΛCS model). It is shown that pressure-free matter can obtain the properties of a gas of low-velocity cosmic strings in the epoch, when the global geometry and the total amount of matter in the Universe as a whole obey an additional constraint. This constraint follows from the quantum geometrodynamical approach in the semiclassical approximation. In terms of general relativity, its effective contribution to the field equations can be linked to the time evolution of the equation of state of matter caused by the processes of redistribution of the energy between matter components. In the present article, the exact solutions of the Einstein equations for the ΛCS model are found. It is demonstrated that this model is equivalent to the open de Sitter model. After the scale transformation of the time variable of the ΛCS model, the standard ΛCDM and ΛCS models provide the equivalent descriptions of cosmological parameters as functions of time at equal values of the cosmological constant. The exception is the behavior of the deceleration parameter in the early Universe.


K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010).

A. Riotto, CERN Yellow Report CERN-2010-01, 315 (2010), arXiv:1010.2642 [hep-ph] (2010).

E. Bianchi and C. Rovelli, arXiv:1002.3966 [astro-ph.CO] (2010).

L. Perivolaropoulos, arXiv:1104.0539 [astro-ph.CO] (2011)

L. Perivolaropoulos, in The Problems of Modern Cosmology, edited by P.M. Lavrov (Tomsk State Pedagogical Univ., Tomsk, 2009), arXiv:0811.4684 [astro-ph] (2008)

P. Kroupa et al., Astron. Astrophys. 523, A32 (2010), arXiv:1006.1647 [astro-ph.CO] (2010).

E.W. Kolb, Astrophys. J. 344, 543 (1989).

E.W. Kolb and M.S. Turner, The Early Universe (Addison-Wesley, Redwood City, 1990).

G.J. Whitrow and D.G. Randall, MNRAS 111, 455 (1951).

D. Meschini, Found. Sci. 12, 277 (2007), arXiv:gr-qc/0601097 (2006)

C. Kiefer and B. Sandhoefer, in Beyond the Big Bang, edited by R. Vaas (Springer, Heidelberg, 2008), arXiv:0804.0672 [gr-qc] (2008).

V.V. Kuzmichev, Ukr. J. Phys. 43, 896 (1998)

V.V. Kuzmichev, Phys. Atom. Nucl. 62, 708 (1999), arXiv:gr-qc/0002029 (2000)

V.V. Kuzmichev, Phys. Atom. Nucl. 62, 1524 (1999), arXiv:gr-qc/0002030 (2000)

V.E. Kuzmichev and V.V. Kuzmichev, Eur. Phys. J. C 23, 337 (2002), arXiv:astro-ph/0111438 (2001).

V.E. Kuzmichev and V.V. Kuzmichev, Acta Phys. Pol. B 39, 979 (2008), arXiv:0712.0464 [gr-qc] (2007); V.E. Kuzmichev and V.V. Kuzmichev, Acta Phys. Pol. B 39, 2003 (2008), arXiv:0712.0465 [gr-qc] (2007); V.E. Kuzmichev and V.V. Kuzmichev, Acta Phys. Pol. B 40, 2877 (2009), arXiv:0905.4142 [gr-qc] (2009); V.E. Kuzmichev and

V.V. Kuzmichev, Ukr. J. Phys. 55, 626 (2010).

F. Lund, Phys. Rev. D 8, 3247 (1973)

V.G. Lapchinskii and V.A. Rubakov, Theor. Math. Phys. 33, 1076 (1977)

F.J. Tipler, Rep. Prog. Phys. 68, 897 (2005).

R.C. Tolman, Relativity, Thermodynamics and Cosmology (Clarendon Press, Oxford, 1969).

A.G. Riess et al., Astrophys. J. 730, 119 (2011), arXiv:1103.2976 [astro-ph.CO] (2011).

D. Larson et al., Astrophys. J. Suppl. 192, 16 (2011), arXiv:1001.4635 [astro-ph.CO] (2010)

N. Jarosik et al., Astrophys. J. Suppl. 192, 14 (2011), arXiv:1001.4744 [astro-ph.CO] (2010).

A. Benoit-Levy and G. Chardin, arXiv:0903.2446 [astro-ph.CO] (2009)

arXiv:0811.2149 [astro-ph] (2008).

J.R. Gott and M.J. Rees, MNRAS 227, 453 (1987).

Ø. Grøn, Eur. J. Phys. 23, 135 (2002), arXiv:0801.0552 [astro-ph] (2008).

A. Vilenkin, Phys. Rep. 121, 263 (1985).

M. Rowan-Robinson, Cosmology (Clarendon Press, Oxford, 2004).

D.W. Sciama, MNRAS 113, 34 (1953).

D.W. Sciama, Modern Cosmology (Cambridge Univ. Press, Cambridge, 1971).

E. Mach, Die Mechanik in Ihrer Entwickelung: Historisch-Kritisch Dargestellt (F.A. Brockhaus, Leipzig, 1897).

H. Bondi and J. Samuel, Phys. Lett. A 228, 121 (1997), arXiv:gr-qc/9607009 (1996).

J. Barbour, Found. Phys. 40, 1263 (2010), arXiv:1007.3368 [gr-qc] (2010).

J.A. Wheeler, in Gravitation and Relativity, edited by Hong-Yee Chiu and W.F. Hoffmann (Benjamin, New York, 1964).

C.H. Brans and R.H. Dicke, Phys. Rev. 124, 925 (1961).

M. Heller, Acta Phys. Pol. B 1, 123 (1970).

P.A.M. Dirac, Nature 139, 323 (1937).

P.A.M. Dirac, Proc. Roy. Soc. London A 333, 403 (1973).

S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972).

J.P. Petit, Mod. Phys. Lett. A 3, 1527 (1988)

J.W. Moffat, Int. J. Mod. Phys. D 2, 351 (1993), arXiv:gr-qc/9211020 (1992)

A. Albrecht and J. Magueijo, Phys. Rev. D 59, 043516 (1999), arXiv:astro-ph/9811018 (1998).

T. Chiba, Prog. Theor. Phys. 126, 993 (2011), arXiv:1111.0092 [gr-qc] (2011).

I. Prigogine, J. Geheniau, E. Gunzig, and P. Nardone, Gen. Relativ. Gravit. 21, 767 (1989); J.A.S. Lima, M.O. Calvao, and I. Waga, Cosmology, Thermodynamics and Matter Creation in Frontier Physics, Essays in Honor of Jaime Tiomno, edited by S. MacDowel, H.M. Nussenzweig, and R.A. Salmeron (World Scientific, Singapore,

; arXiv:0708.3397 [astro-ph] (2007); A. de Roany and J.A. de Freitas Pacheco, Gen. Relativ. Gravit. 43, 61 (2011).

L.D. Landau and E.M. Lifshitz, The Classical Theory of Fields (Butterworth-Heinemann, Amsterdam, 1975).




How to Cite

Kuzmichev, V., & Kuzmichev, V. (2021). Comparative Analysis of Standard ΛCDM and ΛCS Models. Ukrainian Journal of Physics, 57(11), 1169.



Astrophysics and cosmology

Most read articles by the same author(s)