The effect of backreaction of non-minimally coupled massless quintom fields in FLRW universe

Abstract

In this paper the quantum backreaction of non-minimally coupled massless quintom fields in FLRW universe has been discussed. quintom model contains two massless scalar fields where one of scalar fields has positive kinetic energy and another one has negative kinetic energy term. In this model, we obtain the vacuum expectation value of the full energy–momentum tensor in different cosmological eras including inflation, radiation and matter dominated eras on FRLW universe with constant \(\epsilon \). This quantity is divergent in different cases. In order to renormalize it, we separate the vacuum expectation values of the full energy–momentum tensor to the UV and IR parts by using \(\mu \) cutoff. Then we eliminate the UV divergences by introducing a counterterm action and adding it to the action of the model. Also we calculate the IR part of the energy–momentum tensor during inflation and different transitions. For this purpose, we assume that the transition from one period to the next happens fast. Therefore we use a sudden transition approximation at matching time. In order to study behavior of the backreaction, we obtain the ratio of the dominant contribution of quantum energy density to the corresponding background quantity in different cosmological eras. Moreover, we show that the one-loop fluctuations of quintom model on de Sitter space give a contribution to the cosmological constant. Finally we obtain the effect of the quantum backreaction on the background geometry leading to new scale factor for cosmological eras.