![]() Furthermore, the critical points are classified into three families. The absence of the matter in the action integral implies that the dimension of the dynamical system can be either one or two, while adding a pressureless fluid raises the dimension of the system to two or three. The dimensionless dynamical analysis and the corresponding critical points are presented in Sect. 2 we present the model to be studied, which is an Einstein–Aether scalar field cosmology with spatially flat FLRW spacetime, where the scalar field lagrangian has been modified so that the scalar field potential is non-minimally coupled to the aether field, as proposed in. For other dynamical studies in the context of the Einstein–Aether scenario we refer the reader the articles of. Results of this type have also been found elsewhere. There, it was found that the existence or the non-existence of the solutions to the reduced equations depends on the values of combinations of the initial parameters that enter the action integral. One such work, investigating the dynamical equations of the Einstein–Aether theory for the cases of FLRW as well as in an locally rotationally symmetric Bianchi Type III geometry. In all cases there is a period of slow-roll inflation at intermediate times and, in some cases, accelerated expansion at late times.Īpart from the FLRW background scenario, there have been more wideranging studies. Similar dynamical analysis can by found in, where it was shown that for isotropic expansion the dynamics are independent of the aether parameters, but this is not the case for anisotropic expansion. There has been further study of the dynamical evolution and stability of those inflationary solutions in homogeneous and isotropic Einstein–Aether cosmologies containing a self interacting scalar field which interacts with the aether. įor Einstein–Aether cosmologies provided exact solutions for specific forms of the scalar field potential in the framework of Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. For the Einstein–Aether cosmologies there have been several such studies. One of the ways to study a cosmological model is to perform a dynamical analysis by studying its critical points in order to connect them to the different observed eras, with their respective dynamical behaviours and characteristics. It is important to mention here that the Einstein–Aether approach also describes the classical limit of Hořava gravity. The Einstein–Aether theory can describe various cosmological phases, including those of early inflationary expansion and late dark-energy domination. At this point we recall that the unitarity of the timelike vector field is guaranteed by introducing a lagrange multiplier. The gravitational field equations are of second-order and correspond to variations of the action with respect to the metric tensor and the æther field. The introduction of the timelike vector field in the action integral is also a specific selection of preferred frame at each point in the spacetime, and so this modification spontaneously breaks the Lorentz symmetry. Einstein–Aether theory is a Lorentz-violating theory in which a unitary timelike vector field, called the æther, is introduced into the Einstein–Hilbert action.
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