Bulk viscous cosmological models with a cosmological constant: Observational constraints

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Table 1.

Free parameters and priors used in the MCMC analysis.

Model		Parameter space	Prior
m = 0	ΛvCDM	$Θ = {H_{0}, Ω_{b 0} h^{2}, Ω_{vc 0} h^{2}, M, {\tilde{ζ}}_{0}}$ $Mathematical equation: $ \Theta = \{H_0, \Omega_{\mathrm{b0}}h^2, \Omega_{\mathrm{vc0}}h^2, M, \tilde{\zeta}_{0}\} $$	π(Ω_vc0h²); π(Ω_dm0h²): 𝒩(0.12, 0.01)
m = 0	ΛvCDM + Ω_K	$Θ = {H_{0}, Ω_{K 0}, Ω_{b 0} h^{2}, Ω_{vc 0} h^{2}, M, {\tilde{ζ}}_{0}}$ $Mathematical equation: $ \Theta = \{H_0, \Omega_{\mathrm{K0}}, \Omega_{\mathrm{b0}}h^2, \Omega_{\mathrm{vc0}}h^2, M, \tilde{\zeta}_{0}\} $$	π(Ω_b0h²): 𝒩(0.022, 0.01)

m free	ΛvCDM	$Θ = {H_{0}, Ω_{b 0} h^{2}, Ω_{vc 0} h^{2}, M, m, {\tilde{ζ}}_{0}}$ $Mathematical equation: $ \Theta = \{H_0, \Omega_{\mathrm{b0}}h^2, \Omega_{\mathrm{vc0}}h^2, M, m, \tilde{\zeta}_{0}\} $$	$π ({\tilde{ζ}}_{0})$ $Mathematical equation: $ \pi(\tilde{\zeta}_{0}) $$ : 𝒰(0, 1)
m free	ΛvCDM + Ω_K	$Θ = {H_{0}, Ω_{K 0}, Ω_{b 0} h^{2}, Ω_{vc 0} h^{2}, M, m, {\tilde{ζ}}_{0}}$ $Mathematical equation: $ \Theta = \{H_0, \Omega_{\mathrm{K0}}, \Omega_{\mathrm{b0}}h^2, \Omega_{\mathrm{vc0}}h^2, M, m, \tilde{\zeta}_{0}\} $$	π(m): 𝒰(−2, 2)

${\tilde{ζ}}_{0} = 0$ $Mathematical equation: $ \tilde{\zeta}_0=0 $$	ΛCDM	Θ = {H₀, Ω_b0h², Ω_dm0h², M}	π(H₀): 𝒰(30, 99)
	ΛCDM + Ω_K	Θ = {H₀, Ω_K0, Ω_b0h², Ω_dm0h², M}	π(Ω_K0): 𝒰(−0.4, 0.4); π(M): 𝒰(−30, −5)

Notes. We list the prior ranges, using 𝒩(μ, σ) to denote a Gaussian and 𝒰(a, b) to denote a uniform prior.

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