Volume 142, number 6,7 PHYSICS LETTERS A 18 December 1989 COSMOLOGICAL CONSTANT AND REGULAR BlANCH! TYPE-I MODELS WITH RADIATION IN THE MINIMUM QUADRATIC GAUGE THEORY OF GRAVITY Hong Chuong NGUYEN Institute of Theoretical Physics, Academy ofSciences of Vietnam, P.O. Box 429, Bo Ho, Hanoi 10000, Vietnam Received 20 December 1988; revised manuscript received 25 September 1989; accepted for publication 20 October 1989 Communicated by J.P. Vigier Itis shown that within the framework of the minimum quadratic gauge theory of gravity in the Riemann—Cartan space by including a cosmological term we can construct regular homogeneous anisotropic Bianchi type-I cosmological methods with spinless as well as spinning radiation. 1. Introduction eluding terms quadratic in the curvature and torsion tensors in the gravitational Lagrangian. The simplest Within the framework of Poincaré gauge field the- generalization of ECT, which satisfies the restric- ory (PGT) gravity is described by the tetrad fields tions following from the simultaneous consideration h’ 1, and the Lorentz connection coefficients A~k~ ~. of the cancelling cosmological singularity problem, Due to the dynamical independence of the fields h’0 the quantization, and Birkhoff’s theorem, is the and A°’~~ the space—time continuum in the PGT is minimum quadratic gauge theory of gravity represented by a four-dimensional differentiable (MQGT) with the gravitational Lagrangian Riemann—Cartan manifold U4 [1—4]. The corre- Lg=h(foF+aF 2). F —‘ , F=F°~. (3) /~P’ ~litfr sponding field strength tensors are the torsion where h=det(h’~), f~= ( l6itG)~ (G is Newton’s S’ 0V=8[Ph 1~] ~hk[~A~kpJ, (l) gravitational constant), and a<0 [6]. It was shown and the curvature that the MQGT equations for the metric can be rep- resented in the form of the Einstein equations with F°~ —2ô Atk +2AI~i~Ak 1ii~1 , (2) an effective EMT T~ constructed from t/ 1 and Jjk~ p” [o vi respectively. The sources of the gravitational field in [6]. On the basis of these equations the various this theory are the canonical energy—momentum ten- physical consequences of MQGT were investigated sor (EMT) t/’ and the tetrad spin current (TSC) Jjk~. [6—9], in particular, regular homogeneous aniso- The simplest PGT is the Einstein—Cartan theory tropic Bianchi type-i cosmological models were con- (ECT) in which the gravitational Lagrangian is given structed in refs. [7,9]. in the form of the scalar curvature F. Because of the According to the modern point of view the cos- algebraic dependence between the spin angular mo- mological constant is connected with the vacuum en- mentum and the torsion for spinless matter from ECT ergy density. It is therefore very interesting to study general relativity (GR) is recovered. However, as the role of the cosmological constant in PGT [10,11]. was shown in ref. [51, the torsion of the space—time In ref. [11], for example, the influence of the cos- can play an important role in the case of spinless mological term on the dynamics of homogeneous matter with extreme high energy densities by in- isotropic perfect-fluid cosmological models was considered. ~ i, k= 0, 1,2,3, are anholonomic Lorentz indices, ~, ~= 0, 1,2, 3 In the present paper within the framework of are holonomic coordinate indices. MQGT by including a cosmological term we con- 326