Asymptotically locally AdS and asymptotically flat black hole solutions are found for a particular case of the Horndeski action. The action contains the Einstein-Hilbert term with a cosmological constant, a real scalar field with a non minimal kinetic coupling given by the Einstein tensor, the minimal kinetic coupling and the Maxwell term. There is no scalar potential. The solution has two integration constants related with the mass and the electric charge. The solution is given for all dimensions. A new class of asymptotically locally flat spherically symmetric black holes is found when the minimal kinetic coupling vanishes and the cosmological constant is present. In this case we get a solution which represents an electric Universe. The electric field at infinity is only supported by Λ. When the cosmological constant vanishes the black hole is asymptotically flat.

This paper is concerned with the construction and analysis of boson stars in the context of nonminimal derivative coupling theories. In particular we embed our model in the biscalar extension of Horndeski gravity, considering a scalar field theory displaying a nonminimally coupled kinetic term given by the Einstein tensor. We focus on the case where the potential is given by a mass term only, and when a six order self-interaction is included. In the latter case we consider specific couplings in the self-interacting terms in such a way that our self-interaction is given by a positive definite potential presenting two degenerate local vacua. We show how solutions can be obtained and we compare its principal properties with standard configurations constructed with the usual minimally coupled kinetic term.Comment: Published in Phys. Rev.

We construct cubic gravity and its f (P ) extension and we investigate their early-and late-time cosmological applications. Cubic gravity is based on a particular invariant P , constructed from cubic contractions of the Riemann tensor, under three requirements: (i) the resulting theory possesses a spectrum identical to that of general relativity, (ii) it is neither topological nor trivial in four dimensions, and (iii) it is defined such that it is independent of the dimensions. Relaxing the last condition and restricting the parameters of cubic gravity we can obtain second-order field equations in a cosmological background. We show that at early times one can obtain inflationary, de Sitter solutions, which are driven by an effective cosmological constant constructed purely from the cubic terms of the simple cubic or f (P ) gravity. Concerning late-time evolution, the new terms constitute an effective dark-energy sector and we show that the Universe experiences the usual thermal history and the onset of late-time acceleration. In the case of f (P ) gravity, depending on the choice of parameters, we find that the dark-energy equation-of-state parameter can be quintessencelike, phantomlike or it can experience the phantom-divide crossing during the evolution, even if an explicit cosmological constant is absent. PACS numbers: 98.80.-k, 95.36.+x, 04.50.Kd I. INTRODUCTIONHigher-order gravities have been introduced in the general framework of modified theories of gravity, with the aim to describe in a uniform way the history of the Universe; to account for the early-time inflation, the late-time acceleration, and the presence of dark matter; and to be consistent with observations [1][2][3][4][5]. A more theoretical motivation in studying higher-order corrections to the Einstein-Hilbert term is that these theories arise naturally in the gravitational effective action of a complete string theory [6] and they result in a renormalizable and thus quantizable gravitational theory [7]. Additionally, in such considerations one can construct theories which possess general relativity as a particular limit [8]. Moreover, certain higher-order gravities are equivalent to Einstein gravity at the linearized level in the vacuum, and the only physical mode propagated by the metric perturbation is a transverse and massless graviton. Such theories are certain f(Lovelock) theories [9].Higher-order gravities and more generally modified theories of gravity provide a deeper understanding of Einstein gravity theory itself. The construction of modified theories of gravity starts from the Einstein-Hilbert Lagrangian and includes extra terms, such as in f (R) gravity [3,[10][11][12], f (G) gravity [13,14], Lovelock gravity [9,15], Weyl gravity [16,17], Galileon theory [18][19][20][21][22][23][24], etc. More radical modifications of Einstein gravity theory are provided by the introduction of torsion terms in f (T ) gravity [25][26][27][28] or f (T, T G ) gravity [29,30]. These modified theories of gravity allow us to unveil what features of a grav...