Dissipative quintessence and its cosmological implications

Abstract

We consider a generalization of the quintessence type scalar field cosmological models, by adding a multiplicative dissipative term in the scalar field Lagrangian, which generally is represented in an exponential form. The generalized dissipative Klein-Gordon equation is obtained in a general covariant form in Riemann geometry, from the variational principle with the help of the Euler-Lagrange equations. The energy-momentum tensor of the dissipative scalar field is also obtained from the dissipative Lagrangian, and its properties are discussed in detail. Several applications of the general formalism are presented for the case of the cosmological Friedmann-Lema\^{\i}tre-Robertson-Walker metric. The generalized Friedmann equations in the presence of the dissipative scalar field are obtained for a specific form of dissipation, with the dissipation exponent represented as the time integral of the product of the Hubble function, and of a function describing the dissipative properties of the scalar field. For this case the Friedmann equations reduce to a system of differential-integral equations, which, by means of some appropriate transformation, can be represented in the redshift space as a first order dynamical system. Several cosmological models, corresponding to different choices of the dissipation function, and of the scalar field potential, are considered in detail. For the different values of the model parameters the evolution of the cosmological parameters (scale factor, Hubble function, deceleration parameter, the effective density and pressure of the scalar field, and the parameter of the dark energy equation of state, respectively) is considered in detail by using both analytical and numerical techniques. A comparison with the observational data for the Hubble function and with the predictions of the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ paradigm is presented for each dissipative scalar field model. In the large time limit the model describes an accelerating universe, with the effective negative pressure induced by the dissipative effects associated with the scalar field. Accelerated expansion in the absence of the scalar field potential is also possible, with the kinetic term dominating the expansionary evolution. The dissipative scalar field models describe well the data, with the model free parameters obtained by a trial and error method. The obtained results show the dissipative scalar field model offers an effective dynamical possibility for replacing the cosmological constant and for explaining the recent cosmological observational data.