Inflationary model in Brans-Dicke theory

In this paper, we present a model of inflation in the original form of Brans-Dicke (BD) theory without any modification and without adding any dark energy candidate. We consider a log function of the scale factor in the BD scalar field to discuss the inflationary era of the universe. We obtain the expressions for the deceleration parameter and the equation of state parameter, and plot their graphs against the cosmic scale factor. We observe that the universe starts with decelerated expansion and experiences an early time phase transition from a decelerated phase to an accelerated phase. After a very short period, the accelerated expansion ends in a decelerated expansion, showing the inflationary era of the cosmic evolution. To analyze the model on thermodynamic ground, we consider generalized second law of thermodynamics and observe that the law is satisfied within the model. Further, we study the stability of the model using the squared sound speed method. We plot the squared sound speed against cosmic time t and discuss the effects of the parameters on the stability of the model. We observe that for suitable values of the model parameters our model is stable.