Int J Theor Phys (2012) 51:2503–2513 DOI 10.1007/s10773-012-1130-x Some Anisotropic Homogeneous Cosmological Models in Self-creation Cosmology Priyanka Rai · L.N. Rai · V.K. Singh Received: 6 January 2012 / Accepted: 5 March 2012 / Published online: 18 March 2012 © Springer Science+Business Media, LLC 2012 Abstract The paper presents an exact solution of cylindrically symmetric cosmological models which are of Petrov type-I or Petov type-D in Barber’s second self-creation theory of gravitation. Some physical and geometrical properties of these models are also discussed. Keywords Anisotropic · Cylindrically symmetric · Cosmological model · Petrov type-I · Petrov type-D · Barber’s second self-creation theory 1 Introduction Barber [1] proposed two self-creation cosmologies by modifying the Brans and Dicke [2] theory of gravitation and general theory of relativity. These modified theories create the universe out of self contained gravitational and matter fields. After that Brans [3] has pointed out that Barber’s first theory is not only in disagreement with experiment but is actually inconsistent. Barber’s second theory is a modification of general relativity to a variable G- theory. In this theory the scalar field does not directly gravitate, but simply divides the matter tensor, acting as a reciprocal gravitational constant. It is postulated that this scalar field couples to the trace of the energy-momentum tensor. Hence, the field equations in Barber’s second theory are: R ij − 1 2 g ij R =−8πφ −1 T ij (1.1) and φ = 8π 3 λT (1.2) P. Rai ( ) · L.N. Rai Dept. of Maths, Patna Science College, Patna 800005, Bihar, India e-mail: priyankarai2007@rediffmail.com L.N. Rai e-mail: lnrai_mathsc@yahoo.co.in V.K. Singh School of Physics, S. M. V. D. University, Katra, 182320, Jammu & Kashmir, India