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Register a new userDynamical Analysis of an Integrable Cubic Galileon Cosmological Model
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Andronikos Paliathanasis
Publication date
2017
fields
Physics
and research's language is
English
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Recently a cubic Galileon cosmological model was derived by the assumption that the field equations are invariant under the action of point transformations. The cubic Galileon model admits a second conservation law which means that the field equations form an integrable system. The analysis of the critical points for this integrable model is the main subject of this work. To perform the analysis, we work on dimensionless variables different from that of the Hubble normalization. New critical points are derived while the gravitational effects which follow from the cubic term are studied.
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Cubic Galileon massive gravity is a development of de Rham-Gabadadze-Tolly (dRGT) massive gravity theory is which the space of the Stueckelberg field is broken. We consider the cubic Galileon term as a scalar field coupled to the graviton filed. We present a detailed study of the cosmological aspects of this theory of gravity. We analyze self-accelerating solutions of the background equations of motion to explain the accelerated expansion of the Universe. Exploiting the latest Union2 Type Ia Supernovea (SNIa) dataset, which consists of 557 SNIa, we show that cubic Galileon massive gravity theory is consistent with the observations. We also examine the tensor perturbations within the framework of this model and find an expression for the dispersion relation of gravitational waves, and show that it is consistent with the observational results.
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.
The cosmological dynamics of a quintessence model based on real gas with general equation of state is presented within the framework of a three-dimensional dynamical system describing the time evolution of the number density, the Hubble parameter, and the temperature. Two global first integrals are found and examples for gas with virial expansion and van der Waals gas are presented. The van der Waals system is completely integrable. In addition to the unbounded trajectories, stemming from the presence of the conserved quantities, stable periodic solutions (closed orbits) also exist under certain conditions and these represent models of a cyclic Universe. The cyclic solutions exhibit regions characterised by inflation and deflation, while the open trajectories are characterised by inflation in a fly-by near an unstable critical point.
We show that several integrable (i.e., exactly solvable) scalar cosmologies considered by Fre, Sagnotti and Sorin (Nuclear Physics textbf{B 877}(3) (2013), 1028--1106) can be generalized to include cases where the spatial curvature is not zero and, besides a scalar field, matter or radiation are present with an equation of state $p^{(m)} = w, rho^{(m)}$; depending on the specific form of the self-interaction potential for the field, the constant $w$ can be arbitrary or must be fixed suitably.
In this paper we apply the tools of the dynamical systems theory in order to uncover the whole asymptotic structure of the vacuum interactions of a galileon model with a cubic derivative interaction term. It is shown that, contrary to what occurs in the presence of background matter, the galileon interactions of vacuum appreciably modify the late-time cosmic dynamics. In particular, a local late-time attractor representing phantom behavior arises which is inevitably associated with a big rip singularity. It seems that the gravitational interactions of the background matter with the galileon screen the effects of the gravitational self-interactions of the galileon, thus erasing any potential modification of the late-time dynamics by the galileon vacuum processes. Unlike other galileon models inspired in the DGP scenario, self-accelerating solutions do not arise in this model.
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