Astron. Nachr./AN 323 (2002) 5, 494–498 Some cosmological models with perfect fluid, scalar field and heat flux in rotating universe I. TARHAN C ¸ anakkale Onsekiz Mart University, Arts and Sciences Faculty, Department of Physics, Terzio˜ glu Campus, 17100, C ¸ anakkale, Turkey Received 2001 July 20; accepted 2002 May 21 Abstract. The dynamics of a radiating perfect fluid universe coupled with scalar field and heat flux are studied in the non- static G¨ odel-type universe including the cosmological constant and obtained some exact solutions of Einstein field equations. The solutions have nonzero expansion, shear, and rotating universe. Various physical and geometrical properties of the model are also discussed and the temperature distribution is also given explicitly. Key words: cosmology: theory – cosmological constant 1. Introduction It is well known that, as a first approach, the astrophysical object is composed of a perfect fluid. On the other hand, the objects with large energy output, either in the form of pho- ton or neutrinos or both, in some phase of their evolution are very much known to exist. A non-static distribution would be radiating energy and therefore, it would be surrounded by an ever-expanding zone of radiation. The early universe was a differentiated soup of matter and radiation in a state of non-thermal equilibrium. Gamow pointed out that the uni- verse was dominated by radiation in the distant past. During the photon decoupling stage, part of electromagnetic radia- tion behaved as a perfect fluid co-moving with matter, while a part of it behaved like a unidirectional stream moving with fundamental velocity. Again during the neutrino decoupling stage, a similar situation arose in which, apart from stream- ing neutrinos, moving with fundamental velocity (Singh & Bahamra, 1990). In recent years, there has been a considerable interest in cosmology with scalar field. The study of scalar meson fields in general relativity has drawn the attention of many work- ers. On the other hand, scalar fields, namely a scalar meson field which is of zero-mass type and characterizes long-range interactions, as they help in explaining the creation of matter in cosmological theories, represent matter fields with spin- less quanta and can describe gravitational fields. The scalar meson field is a matter field and is associated with zero-spin chargeless particles like and mesons. Meson particles Correspondence to: I. Tarhan, ismailtarhan@physics.comu.edu.tr with the charge of electron and masses of the order of mag- nitude of 200 electron masses are found in cosmic rays. The study of a such field in general relativity has been initiated to provide an understanding of the nature of space-time and the gravitational field associated with neutral elementary par- ticles of zero spin. The concept of scalar fields was intro- duced by Dirac (1938) in trying to explore the idea of Mach’s principle, and he thereby obtained a theory in which gravi- tational constant is no longer a constant, but is dependent of time. Thereafter Das (1962), Hyade (1963), Penney (1969), Das & Agarwal (1974), Rao et al., (1976) and G ¨ urses (1977) investigated physically realistic solutions on the behavior of the scalar fields. Banerjee & Santosh (1981), Froyland (1982) and Accioly et al. (1984) discussed and obtained useful so- lutions for the coupled gravitational and scalar fields. The different aspects and outcomes of the interactions of viscous fluid distribution with a scalar field were studied by Singh & Bhamra (1987). Modern astrophysical or high energy astrophysical and particle physics observations indicate that the universe is ro- tating (Birch, 1982 & 1983). The concept of a rotating uni- verse with vanishing expansion and shear appeared with the advent of G¨ odel’s universe (G¨ odel, 1949). Chakraborty & Bandopadhyay (1983) have given a stationary generalization of G¨ odel’s universe with perfect fluid and a scalar field. But it is well known that the universe is expanding. Therefore, the study of non-static rotating world models is important. Here it should be noted that the non-static G¨ odel-type cosmological models admitting scalar field and heat flux both are very few in the literature. Rotating cosmological mod- els with viscous fluid and heat flux have been studied by c 2002 WILEY-VCHVerlag Berlin GmbH & Co. KGaA, Weinheim 2002 0004-6337/02/0510-0494 $ 17.50+.50/0