We perform analytical and numerical study of static spherically symmetric solutions in the context of Brans-Dicke-like cosmological model by Elizalde et al. [1] with an exponential potential. In this model the phantom regime arises without the appearance of any ghost degree of freedom due to the specific form of coupling. For the certain parameter ranges the model contains a regular solution which we interpret as a wormhole in an otherwise dS Universe. We put several bounds on the parameter values: ω < 0, α 2 /|ω| < 10 −5 , 22.7 φ 0 25 . The numerical solution could mimic the Schwarzschild one, so the original model is consistent with astrophysical and cosmological observational data. However differences between our solution and the Schwarzschild one can be quite large, so black hole candidate observations could probably place further limits on the φ 0 value.

In shift-symmetric Horndeski theories, a static and spherically symmetric black hole can support linearly time-dependent scalar hair. However, it was shown that such a solution generically suffers from ghost or gradient instability in the vicinity of the horizon. In the present paper, we explore the possibility to avoid the instability, and present a new example of theory and its black hole solution with a linearly time-dependent scalar configuration. We also discuss the stability of solutions with static scalar hair for a special case where nonminimal derivative coupling to the Einstein tensor appears.

Abstract. We discuss a Brans-Dicke model with a cosmological constant, negative value of the w parameter and an arbitrary (in general non-vanishing) scale factor at the Big Bang. The Friedman equations for a flat universe are considered. The current observational values for Hubble constant H 0 and deceleration parameter q 0 play the role of initial conditions. We follow the approach of [1] in order to solve field equations analytically. In Ref.[1] only positive values of w were considered, we extend the study to a complete set of possible w values. Our main result is that the scale factor (during it's evolution back in time direction) may not vanish, unlike in the standard ΛCDM case. In other words, the considered model demonstrates a cosmological bounce instead of the initial singularity. The famous formula (4.6), that leads to the bounce, is valid only for the dust-filled universe with p = 0 and, therefore, is not adequate for the Early Universe hot stage when the bounce happens. So, our results are qualitative in nature and must be used to obtain initial values for the hot stage of the Universe.

Abstract:In this review, we focus our attention on scalar-tensor gravity models and their empirical verification in terms of black hole and wormhole physics. We focus on black holes, embedded in an expanding universe, describing both cosmological and astrophysical scales. We show that in scalar-tensor gravity it is quite common that the local geometry is isolated from the cosmological expansion, so that it does not backreact on the black hole metric. We try to extract common features of scalar-tensor black holes in an expanding universe and point out the issues that are not fully investigated.

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