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Register a new userAspects of the cosmological coincidence problem
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The observational fact that the present values of the densities of dark energy and dark matter are of the same order of magnitude, $rho_{de0}/rho_{dm0} sim mathcal{O}(1)$, seems to indicate that we are currently living in a very special period of the cosmic history. Within the standard model, a density ratio of the order of one just at the present epoch can be seen as coincidental since it requires very special initial conditions in the early Universe. The corresponding why now question constitutes the cosmological coincidence problem. According to the standard model the equality $rho_{de} = rho_{dm}$ took place recently at a redshift $z approx 0.55$. The meaning of recently is, however, parameter dependent. In terms of the cosmic time the situation looks different. We discuss several aspects of the coincidence problem, also in its relation to the cosmological constant problem, to issues of structure formation and to cosmic age considerations.
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In this paper we investigate possible solutions to the coincidence problem in flat phantom dark energy models with a constant dark energy equation of state and quintessence models with a linear scalar field potential. These models are representative of a broader class of cosmological scenarios in which the universe has a finite lifetime. We show that, in the absence of anthropic constraints, including a prior probability for the models inversely proportional to the total lifetime of the universe excludes models very close to the $Lambda {rm CDM}$ model. This relates a cosmological solution to the coincidence problem with a dynamical dark energy component having an equation of state parameter not too close to -1 at the present time. We further show, that anthropic constraints, if they are sufficiently stringent, may solve the coincidence problem without the need for dynamical dark energy.
The cosmic coincidence problem is a serious challenge to dark energy model. We suggest a quantitative criteria for judging the severity of the coincidence problem. Applying this criteria to three different interacting models, including the interacting quintessence, interacting phantom, and interacting Chaplygin gas models, we find that the interacting Chaplygin gas model has a better chance to solve the coincidence problem. Quantitatively, we find that the coincidence index C for the interacting Chaplygin gas model is smaller than that for the interacting quintessence and phantom models by six orders of magnitude.
We investigate the cosmology of massive spinor electrodynamics when torsion is non-vanishing. A non-minimal interaction is introduced between the torsion and the vector field and the coupling constant between them plays an important role in subsequential cosmology. It is shown that the mass of the vector field and torsion conspire to generate dark energy and pressureless dark matter, and for generic values of the coupling constant, the theory effectively provides an interacting model between them with an additional energy density of the form $sim 1/a^6$. The evolution equations mimic $Lambda$CDM behavior up to $1/a^3$ term and the additional term represents a deviation from $Lambda$CDM. We show that the deviation is compatible with the observational data, if it is very small. We find that the non-minimal interaction is responsible for generating an effective cosmological constant which is directly proportional to the mass squared of the vector field and the mass of the photon within its current observational limit could be the source of the dark energy.
The field equations in FRW background for the so called C-theories are presented and investigated. In these theories the usual Ricci scalar is substituted with $f(mathcal{R})$ where $mathcal{R}$ is a Ricci scalar related to a conformally scaled metric $hat{g}_{mu u} = mathcal{C}(mathcal{R})g_{mu u}$, where the conformal factor itself depends on $mathcal{R}$. It is shown that homogeneous perturbations of this Ricci scalar around general relativity FRW background of a large class of these theories are either inconsistent or unstable.
We analyze the global behaviour of the growth index of cosmic inhomogeneities in an isotropic homogeneous universe filled by cold non-relativistic matter and dark energy (DE) with an arbitrary equation of state. Using a dynamical system approach, we find the critical points of the system. That unique trajectory for which the growth index $gamma$ is finite from the asymptotic past to the asymptotic future is identified as the so-called heteroclinic orbit connecting the critical points $(Omega_m=0,~gamma_{infty})$ in the future and $(Omega_m=1,~gamma_{-infty})$ in the past. The first is an attractor while the second is a saddle point, confirming our earlier results. Further, in the case when a fraction of matter (or DE tracking matter) $varepsilon Omega^{rm tot}_m$ remains unclustered, we find that the limit of the growth index in the past $gamma_{-infty}^{varepsilon}$ does not depend on the equation of state of DE, in sharp contrast with the case $varepsilon=0$ (for which $gamma_{-infty}$ is obtained). We show indeed that there is a mathematical discontinuity: one cannot obtain $gamma_{-infty}$ by taking $lim_{varepsilon to 0} gamma^{varepsilon}_{-infty}$ (i.e. the limits $varepsilonto 0$ and $Omega^{rm tot}_mto 1$ do not commute). We recover in our analysis that the value $gamma_{-infty}^{varepsilon}$ corresponds to tracking DE in the asymptotic past with constant $gamma=gamma_{-infty}^{varepsilon}$ found earlier.
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