We study antigravity, that is, having an effective gravitational constant with a negative sign, in scalar-tensor theories originating from theory and in a Brans-Dicke model with cosmological constant. For the theory case, we obtain the antigravity scalar-tensor theory in the Jordan frame by using a variant of the Lagrange multipliers method and we numerically study the time dependent effective gravitational constant. As we will demonstrate by using a specific model, although there is no antigravity in the initial model, it might occur or not in the scalar-tensor counterpart, mainly depending on the parameter that characterizes antigravity. Similar results hold true in the Brans-Dicke model. 1. Introduction During the last two decades our perception about the universe has changed drastically owing to the discovered late time acceleration that our universe has. Particularly, it can be thought as one of the most striking astrophysical observations with another striking observation being the verification of the inflating period of our universe. Actually, moving from time zero to present time, inflation came first, with the late time acceleration occurring at present epoch. One of the greater challenges in cosmology is to model this late time acceleration in a self-consistent way. According to the new Planck telescope observational data for the present epoch, the universe is consistently described by the model, according to which the universe is nearly spatially flat and consists of ordinary matter (~4.9%), cold dark matter (~26.8%), and dark energy (~68.3%). The dark energy is actually responsible for late time acceleration and current research on the field is mostly focused on this issue. One of the most promising and theoretically appealing descriptions of dark energy and late time acceleration issues is provided by the modified theories of gravity and related modifications. For important review articles and papers on the vast issue of theories, the reader is referred to [1–19] and references therein. For some alternative theories to modified gravity that model dark energy, see [5, 20–24]. The most appealing characteristic of modified gravity theories is that what is actually changed is not the left hand side of the Einstein equations, but the right hand side. Late time acceleration then requires a negative fluid, which can be consistently incorporated in the energy momentum tensor of these theories. This feature naturally appears in theories and also late time acceleration solutions of the Friedmann-Robertson-Walker equations naturally occur in these
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