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Register a new userA quantitative criteria for the coincidence problem
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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.
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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.
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.
In this paper we study a model of interacting dark energy - dark matter where the ratio between these components is not constant, changing from early to late times in such a way that the model can solve or alleviate the cosmic coincidence problem (CP). The interaction arises from an assumed relation of the form $rho_xproptorho_d^alpha$, where $rho_x$ and $rho_d$ are the energy densities of dark energy and dark matter components, respectively, and $alpha$ is a free parameter. For a dark energy equation of state parameter $w=-1$ we found that, if $alpha=0$, the standard $Lambda$CDM model is recovered, where the coincidence problem is unsolved. For $0<alpha<1$, the CP would be alleviated and for $alphasim 1$, the CP would be solved. The dark energy component is analyzed with both $w=-1$ and $w eq -1$. Using Supernovae type Ia and Hubble parameter data constraints, in the case $w=-1$ we find $alpha=0.109^{+0.062}_{-0.072}$ at 68% C.L., and the CP is alleviated. This model is also slightly favoured against nonflat $Lambda$CDM model by using a Bayesian Information Criterion (BIC) analysis. For $w eq-1$, a degeneracy arises on the $w$ - $alpha$ plane. In order to break such degeneracy we add cosmic microwave background distance priors and baryonic acoustic oscillations data to the constraints, yielding $alpha=-0.075pm 0.046$ at 68% C.L.. In this case we find that the CP is not alleviated even for 2$sigma$ interval for $alpha$. Furthermore, this last model is discarded against nonflat $Lambda$CDM according to BIC analysis.
In the framework of a phenomenological cosmological model with the assumption of $rho_{X} propto rho_{m} a^{xi}$ ($rho_{X}$ and $rho_{m} $ are the energy densities of dark energy and matter, respectively.), we intend to diagnose the cosmic coincidence problem by using the recent samples of Type Ia supernovae (SNe Ia), baryon acoustic oscillation (BAO) and cosmic microwave background (CMB). $xi$ is a key parameter to characterize the severity of the coincidence problem, wherein $xi=3$ and $0$ correspond to the $Lambda$CDM scenario and the self-similar solution without the coincidence problem, respectively. The case of $xi = Constant$ has been investigated in the previous studies, while we further consider the case of $xi(z) = xi_{0} + xi_{z}*frac{z}{1+z}$ to explore the possible evolution. A joint analysis of the Pantheon SNe Ia sample with the recent BAO and CMB data figures out that $xi=3.75_{-0.21}^{+0.13}$ in the case of $xi = Constant$ at $68%$ confidence level (CL), in addition, $xi_{0} = 2.78_{-1.01}^{+0.28}$ and $xi_{z} = 0.93_{-0.91}^{+1.56}$ in the case of $xi(z) = xi_{0} + xi_{z}*frac{z}{1+z}$ at $68%$ CL . It implies that the temporal evolution of the scaling parameter $xi$ is supported by the joint sample at $68%$ CL; moreover, the $Lambda$CDM model is excluded by the joint sample at $68%$ CL in both cases, and the coincidence problem still exists. In addition, according to the model selection techniques, the $Lambda$CDM model is the favorite one in terms of the AIC and BIC techniques, however, the scenario of $xi(z)$ is most supported in term of the DIC technique.
It is a mystery why the density of matter and the density of vacuum energy are nearly equal today when they scale so differently during the expansion of the Universe. We suggest a paradigm that might allow for a non-anthropic solution to this cosmic coincidence problem. The fact that the half life of Uranium 238 is very near to the age of the solar system is not considered a coincidence since there are many nuclides with half lives ranging over a huge range of time scales implying that there is likely to be some nuclide with a half life near to any given time scale. Likewise it may be that the vacuum field energy causing the universal acceleration today is just one of a large ensemble of scalar field energies, which have dominated the Universe in the past and then faded away. Given that in standard cosmology and particle physics there are already several scalar fields that probably contribute to universal vacuum energy (the Higgs field, the inflaton, and whatever quintessence/dark energy field causes the current acceleration), the idea of a large ensemble of fields does not seem far fetched. Predictions of the idea include: 1) The current vacuum energy driving the acceleration is not constant and will eventually fade away, 2) The ratio w of scalar field pressure to density is currently changing and is not precisely negative one, 3) There were likely periods of vacuum dominance and acceleration in the past, 4) the current phase of acceleration will end but there may be additional periods of acceleration in the future, 5) the ultimate fate of the Universe cannot be decided until the nature of these fields is known, but the eventual sum of densities from all scalar fields could be zero, as was usually assumed before the discovery of the current universal acceleration.
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