In this paper we approach to Horndeski and beyond Horndeski theories from the effective fluid perspective. We make explicit the formal equivalence between these theories and general relativity with an effective imperfect fluid. It is shown that, for the viable Horndeski theories, in the general case (arbitrary geometry) the nonvanishing contribution from the higher-order derivative terms to the imperfect fluidlike behavior affects only the heat flux vector but not the anisotropic stresses. The only contribution to the anisotropic stress tensor is due to the nonminimal coupling of the scalar field to the curvature as it is in standard scalar-tensor theories. For the viable beyond Horndeski theories the higher-order derivatives contribute both to the heat flux and to the anisotropic stresses. The effective fluid description is applied to several particular cases of interest. It is corroborated that, in Friedmann-Robertson-Walker background space, due to the underlying symmetries, the effective stress-energy tensor of viable Horndeski and beyond Horndeski theories is formally equivalent to that of a perfect fluid. This result might not be true for other less symmetric backgrounds such as the anisotropic Bianchi I space.

In this paper we investigate the cosmological dynamics of geometric inflation by means of the tools of the dynamical systems theory. We focus on the study of two explicit models where it is possible to sum the infinite series of higher curvature corrections that arise in the formalism. These would be very interesting possibilities since, if we regard gravity as a quantum effective theory, a key feature is that higher powers of the curvature invariants are involved at higher loops. Hence, naively, consideration of the whole infinite tower of curvature invariants amounts to consideration of all of the higher-order loops. The global dynamics of these toy models in the phase space is discussed and the quantum origin of primordial inflation is exposed.

We apply the tools of the dynamical system theory in order to revisit and uncover the structure of a nongravitational interaction between pressureless dark matter and dark energy described by a scalar field $$\phi $$ϕ . For a coupling function $$Q = -(\alpha d\rho _m/dt + \beta d\rho _\phi /dt )$$Q = - ( α d ρ m / d t + β d ρ ϕ / d t ) , where t is the cosmic time, we have found that it can be rewritten in the form $$Q = 3H (\alpha \rho _m + \beta (d\phi /dt)^2 )/(1-\alpha +\beta )$$Q = 3 H ( α ρ m + β ( d ϕ / d t ) 2 ) / ( 1 - α + β ) , so that its dependence on the dark matter density and on the kinetic term of the scalar field is linear and proportional to the Hubble parameter. We analyze the scenarios $$\alpha =0$$α = 0 , $$\alpha = \beta $$α = β and $$\alpha = -\beta $$α = - β , separately and in order to describe the cosmological evolution we have calculated various observables. A notable result of this work is that, unlike for the noninteracting scalar field with exponential potential where five critical points appear, in the case studied here, with the exception of the matter dominated solution, the remaining singular points are transformed into scaling solutions enriching the phase space. It is shown that for $$\alpha \ne 0$$α ≠ 0 , a separatrix arises modifying prominently the structure of the phase space. This represents a novel feature no mentioned before in the literature.

In this paper, we investigate the asymptotic dynamics of inflationary cosmological models that are based in scalar-tensor theories of gravity. Our main aim is to explore the global structure of the phase space in the framework of single-field inflation models. For this purpose, we emphasize the adequate choice of the variables of the phase space. Our results indicate that, although single-field inflation is generic in the sense that the corresponding critical point in the phase space exists for a wide class of potentials, along given phase space orbits—representing potential cosmic histories—the occurrence of the inflationary stage is rather dependent on the initial conditions. We have been able to give quantitative estimates of the relative probability (RP) for initial conditions leading to slow-roll inflation. For the nonminimal-coupling model with the ${\varphi }^2$ potential, our rough estimates yield an almost vanishing relative probability: ${10}^{-13}\%\lesssim \mathrm{RP}\ll {10}^{-8}\%$. These bonds are greatly improved in the scalar-tensor models, including the Brans-Dicke theory, where the relative probability $1\%\lesssim \mathrm{RP}\le 100\%$. Hence, slow-roll inflation is indeed a natural stage of the cosmic expansion in Brans-Dicke models of inflation. It is confirmed as well that the dynamics of vacuum Brans-Dicke theories with arbitrary potentials are nonchaotic.

In this paper we investigate the asymptotic dynamics of inflationary cosmological models that are based in scalar-tensor theories of gravity. Our main aim is to explore the global structure of the phase space in the framework of single-field inflation models. For this purpose we make emphasis in the adequate choice of the variables of the phase space. Our results indicate that, although single-field inflation is generic in the sense that the corresponding critical point in the phase space exists for a wide class of potentials, along given phase space orbits -- representing potential cosmic histories -- the occurrence of the inflationary stage is rather dependent on the initial conditions. We have been able to give quantitative estimates of the relative probability (RP) for initial conditions leading to slow-roll inflation. For the non-minimal coupling model with the $\phi^2$-potential our rough estimates yield to an almost vanishing relative probability: $10^{-13}\,\%\lesssim RP\ll 10^{-8}\,\%$. These bonds are greatly improved in the scalar-tensor models, including the Brans-Dicke theory, where the relative probability $1\,\%\lesssim RP\leq 100\,\%$. Hence slow-roll inflation is indeed a natural stage of the cosmic expansion in Brans-Dicke models of inflation. It is confirmed as well that the dynamics of vacuum Brans-Dicke theories with arbitrary potentials are non-chaotic.

In this paper we generalize the dynamical systems analysis of the cubic galileon model previously investigated in \cite{rtgui} by including self-interaction potentials beyond the exponential one. It will be shown that, consistently with the results of \cite{rtgui}, the cubic self-interaction of the galileon vacuum appreciably modifies the late-time cosmic dynamics by the existence of a phantom-like attractor (among other super-accelerated solutions that are not of interest in the present investigation). In contrast, in the presence of background matter the late-time cosmic dynamics remains practically the same as in the standard quintessence scenario. This means that we can not recover the cubic galileon vacuum continuously from the more general cubic quintessence with background matter, by setting to zero the matter energy density (and the pressure). This happens to be a kind of cosmological vDVZ discontinuity that can be evaded by means of the cosmological version of the Vainshtein screening mechanism.