Scalar field cosmology in Lyra's geometry


  • V. K. Shchigolev Department of Theoretical Physics, Ulyanovsk State University
  • E. A. Semenova Department of Theoretical Physics, Ulyanovsk State University



Cosmology, Lyra's Geometry, Phantom, Scalar Field, Tachyon Field.


The new classes of homogeneous cosmological models for the scalar fields are build in the context of Lyra’s geometry. The different types of exact solution for the model are obtained by applying two procedures, viz the generating function method and the first order formalism.


[1] Agarwal S, Pandey RK, Pradhan A (2011) LRS Bianchi type II perfect fluid cosmological models in normal gauge for Lyra’s manifold. International Journal of Theoretical Physics, 50: 296-307.

[2] Bazeia A, Gomes C B, Losano L & Menezes R (2006), First-order formalism and dark energy. Physics Letters B, 633: 415.

[3] Beesham A (1986), Friedmann's cosmology in Lyra's manifold. Astrophysics and Space Science, 127: 355-359.

[4] Beesham A (1988), FLRW cosmological models in Lyra's manifold with time dependent displacement field. Australian Journal of Physics, 41: 833-842.

[5] Chimento L P, Mendez V & Zuccala N (1999), Cosmological models arising from generalized scalar field potentials. Classical & Quantum Gravity, 16: 3749.

[6] Chaubey R (2012), Kantowski-Sachs Cosmological Model in Lyra’s Geometry. International Journal of Theoretical Physics, 51:3933–3940.

[7] Diakonos FK, Saridakis EN (2009), A Statistical Solution to the Cosmological Constant Problem in the Brane world. JCAP, 0902: 030.

[8] Hoyle F, Narlikar J V (1964), a new theory of gravitation. Proceedings of the Royal Society of London Series A, 282: 191-207.

[9] Lyra G (1951), Uber eine Modifikation der riemannschen Geometric. Mathematische Zeitschrift, 54:52.

[10] Perlmutter S, et al. (1999), Measurements of Ω and Λ from 42 High-Redshift Supernovae. Astrophysical Journal, 517: 565.

[11] Pradhan A, Yadav P (2009), Accelerated Lyra's Cosmology Driven by Electromagnetic Field in Inhomogeneous Universe. International Journal of Mathematics & Mathematical Sciences,

[12] Pradhan A, Amirhashehi H, Zanuddin H (2011), A new class of inhomogeneous cosmological model with electromagnetic field in normal gauge for Lyra manifold. International Journal of Theoretical Physics, 50: 56-69.

[13] Riess AG, et al. (1998), Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant. Astronomical Journal, 116: 1009-1038.

[14] Sahni V, Sahni V, Saini T D, Starobinsky A A, Alam U (2003), Statefinder-a new geometrical diagnostic of dark energy. JETP Letters, 77 (5): 201-206.

[15] Sen D K, Dunn K A (1971), A scalar-tensor theory of gravitation in a modified Riemannian manifold. Journal of Mathematical Physics, 12: 578.

[16] Shchigolev VK (2012), Cosmological Models with a Varying Λ -Term in Lyra’s Geometry. Modern Physics Letters a, 27 (29): 1250164.

[17] Shchigolev VK (2013), Cosmology with an Effective Λ-Term in Lyra Manifold. Chinese Physics Letters, 30 (11): 119801.

[18] Soleng H H (1987), Cosmologies based on Lyra's geometry. General Relativity & Gravitation, 19: 1213.

[19] Weyl H (1918), Gravitation und Elektrizität.Sitzungsber. Preuss. Akad. d. Wiss. Teil, 1: 465-480.

[20] Zhuravlev VM, Chervon SV (2000), Cosmological Inflation Models Admitting Natural Emergence to the Radiation - Dominated Stage and the Matter Domination Era. Journal of Experimental and Theoretical Physics, 91 (2): 227–238.