Cosmological tracking solutions

Abstract

A substantial fraction of the energy density of the universe may consist of quintessence in the form of a slowly-rolling scalar field. Since the energy density of the scalar field generally decreases more slowly than the matter energy density, it appears that the ratio of the two densities must be set to a special, infinitesimal value in the early universe in order to have the two densities nearly coincide today. Recently, we introduced the notion of tracker fields to avoid this initial conditions problem. In the paper, we address the following questions: What is the general condition to have tracker fields? What is the relation between the matter energy density and the equation-of-state of the universe imposed by tracker solutions? And, can tracker solutions explain why quintessence is becoming important today rather than during the early universe?

Fine Tuning in Quintessence Models with Exponential Potentials

“…Natural initial conditions from equipartition of energy after inflation suggests that Ω Q,i 10 −3 [10]. From equation (4.2) one has thenQ i ≈ 0.05.…”

“…In this case, this is not a selftuning solution, but a tracking [10] one, where ω Q is also frozen with the different value [7] 6) being able to accelerate the universe today. Other regimes cannot explain BBN and/or the present acceleration of the universe, when one is using simple exponential potential.…”

“…No quintessence model has solved this problem until now, since, in order to explain this coincidence, in general one adjusts the potential energy density to make the selftuning (or the tracking) field to freeze in a energy density that is of the order of the critical density today. In [10], for instance, two examples are considered:…”

Ghosts, instabilities, and superluminal propagation in modified gravity models

“…In this context, many potentials have been introduced that yield late-time acceleration and tracking behaviour (see [15][16][17][18][19][20][21][22][23][24]). …”

Holographic Dark Energy Cosmological Model in Scalar Tensor Theory of Gravitation

“…20% dark matter and baryonic matter and radiations occupy about 4% of total energy of the universe. The nature of the dark energy and dark matter is unknown and many radically different models have been proposed such as at tiny positive cosmological constant, quintessence (Caldwell; et al [6],Liddle and Scherrer [7], Steinhardt et al [8], Dvali et al [9], Deffayet [10]); the nonlinear E(R) models (Capozziello et al [11], Carroll et al [12], Nojiri and Odintsov [13]) and dark energy in brine worlds. Einstein himself pointed out that general relativity does not account satisfactorily for inertial properties of matter, i.e.…”