Diagnosing the cosmic coincidence problem and its evolution with recent observations. (arXiv:2107.08916v2 [astro-ph.CO] UPDATED)

Diagnosing the cosmic coincidence problem and its evolution with recent observations. (arXiv:2107.08916v2 [astro-ph.CO] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Zheng_J/0/1/0/all/0/1">Jie Zheng</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Chen_Y/0/1/0/all/0/1">Yun Chen</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Zhu_Z/0/1/0/all/0/1">Zong-Hong Zhu</a>

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.

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.

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