Induced equation of state for the universe epochs constrained by the hubble parameter
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We present a five dimensional cosmological metric that reveals a four-dimensional energy-momentum tensor. We analyse three cases for the resulting field equations: null, positive and negative cosmological constant Λ. For the case with null cosmological constant, we obtain a solution able to describe the radiation-dominated era of the universe. The positive five-dimensional cosmological constant case yields a bounce cosmological model. In the negative Λ case, the scale factor for the line element is obtained as a(t)=c5sinh([Formula presented]|Λ|t), where c5 is a constant. This solution can remarkably describe not only the late-time cosmic acceleration but also the non-accelerated stages of the cosmic expansion, namely the radiation and matter dominated epochs in a continuous form. We obtain an analytical equation of state capable of describing the different epochs of the universe and it reads as p=ω(z)ρ with ω(z)=[Formula presented][1−[Formula presented]], with p being the pressure of the universe, ρ its density and z is the redshift. In our model the constant c5 is related to the Hubble constant as H0=[Formula presented]coth[arcsinh([Formula presented])2] and this satisfactorily fits the observational data for the low redshift sample of the experimental measurements of the Hubble parameter, which results in H0=72.2−5.5+5.3 km s−1 Mpc−1 and c5=0.600−0.058+0.061.