1. The role of conformal-coupled scalar field in cosmology   R. Avakyan   G. Harutyunyan   E. Chubaryan   A. Piloyan Yerevan State University

2. Let us rewrite conformal respective space in accordance with And for last action we obtain where Corresponding equations:

3. Cosmological scalar in the theory of JBD. Following by analogy of a introducing of cosmological constant in GR we rewrite action of Theory of JBD:

4. where In Einstein frame

5. Field equations in Jordan proper frame Field equations in Einstein frame n = 0, 3, 4, 6

6. In Einstein frame: a)the solutions for vacuum model (n=0), b)for others models (n=3, 4, 6) when

7. In the Einstein frame, when k = 0, we have eventually we have for Einstein frame when Expansion in power series of t give (n=0, 3, 6 )

8. The existence of transition from decelerated phase to acceleration mean that in any point q is going to zero. Modern state is according to P=0 case. It is can be seen from eq., that for certain conditions we can have above mentioned transition.

9. The solutions in the proper frame of the JBD theory with a dominating non minimally coupled scalar field. It is shown that only by advent of the cosmological scalar, with corresponding to the usual cosmological constant in the Einstein frame, the possibility arises for the evolution phase with transition uniform and further accelerated expansion of the Universe during cosmological time scales.

10. Then a) Consider the case q=0 only, but in that case the theory of JBD is unclear. Note, that when b) Let us consider the case

11. Eventually in a result of analysis deceleration coefficient for expanding Universe in the framework of the Theory of JBD we have: a)if dominated non-minimally coupled scalar field it is possible only decelerated expansion b) in the presence of cosmological constant in the case of non- minimally coupled scalar field arises a possibility of evolution of the Universe with transition from zer0 accelerated phase to accelerated phase in time order of 10 mld. yr. Lets construct the cosmological model non-minimally coupled scalar field in the presence of cosmological constant in the by taking into account the radiation.

12. The solutions in the Jordan proper frame The solutions in the Einstein frame

13. The condition of accelerated expansion So we have: The presence of cosmological constant takes a way for possibility of accelerated expansion of the Universe also in radiation epoch

14. The action which correspond to following eq.: where

15. for accelerated expansion we have Then For the values of, typical in cosmology, the factor is expressed as follows: vacuum model matter dominated radiation dominated scalar field dominated stiff fluid

16. a)In the case of scalar field domination or in the case of for too large a we have b)in the case of radiation c) matter dominated era as can be seen for For accelerated solution we get for following times q = - 1

17. d) and q=1 Accelerated expansion can be possible only in the case of and P=0 when the energy density satisfied toand

18. Conclusion When we considered JBD theory in the Jordan proper frame and Einstein frame acceleration was possible only when we introduced cosmological constant by analogy of GR. For last action, which we can get by certain conformal transformation, acceleration is possible in vacuum and dust cases.