Conformally coupled massless scalar field in semi-classical gravity and its cosmological consequences

Recent observations predict accelerated expansion of the universe. To explain this scenario of the universe, different cosmological models have been developed. Initially, General Relativity (GR) theory which is governed by the Einstein field equations was considered to counter this issue. But later on some unexplained issues led the researchers to explore other avenues and as a result they have tried to modify the GR. Einstein’s field equation comprises of mainly two parts namely matter part and gravity part. Some of the scientists have modified the matter part, others have modified the gravity part and some of them have modified both. Semi-classical gravity essentially approximates quantum gravity. In semi classical gravity, gravity is assumed to be classical and matter is described using quantum mechanics. In this framework, matter is represented by quantum field in curved spacetime and gravity is modeled by spacetime metric that follows field equations, developed by Einstein. In semi classical gravity, the matter part in the field equations is typically the probabilistic expected value of the energy-momentum tensor operator. In this work, we have contemplated a homogeneous and isotropic FRW model of the universe with dark matter and dark energy. Choosing the dark energy in the form of mass less conformally coupled scalar field in semi classical gravity, we have got the evolution equations which have been transformed into an autonomous system by considering suitable dimensionless variables. We have tried to look into the stability criterion of universe around the critical points and finally cosmological implications of the behaviour of the critical points have been discussed.