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With the goal of studying the cosmological constant (CC) problem, we presentan exhaustive analysis of unimodular gravity as a possible candidate to resolvethe CC origin and with this, the current Universe acceleration. In this theory,a correction constant (CC-like) in the field equations sources the late cosmicacceleration. This constant is related to a new parameter, $z_{ini}$, which isinterpreted as the redshift of CC-like emergence. By comparing with the CCvalue obtained from Planck and Supernovaes measurements, it is possible toestimate $z_{ini}=11.15^{+0.01}_{-0.02}$ and $z_{ini}=11.43^{+0.03}_{-0.06}$respectively, which is close to the reionization epoch. Moreover, we use theobservational Hubble data (OHD), Type Ia Supernovae (SnIa), Baryon AcousticOscillations (BAO) and the Cosmic Microwave Background Radiation (CMB) distancedata to constrain the UG cosmological parameters. A Joint analysis(OHD+SnIa+BAO+CMB), results in $z_{ini}=11.47^{+0.074}_{-0.073}$ within$1\sigma$ confidence level consistent with our estimation from Planck andSupernovae measurements. We also include linear perturbations, starting withscalar and tensor perturbations and complementing with the perturbed Boltzmannequation for photons. We show that the $00$ term in the UG field equations andthe Boltzmann equation for photons contains corrections, meanwhile the otherequations are similar as those obtained in standard cosmology.

The Universe acceleration from the Unimodular gravity view point: Background and linear perturbations