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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