We present a new model based on General Relativity in where a subtle change of curvature at late times is able to produce the observed Universe acceleration and an oscillating behavior in the effective equation of state. This model aims to test the cosmological principle, by introducing a slight modification in the traditional FLRW metric, through a non-constant curvature parameter. This model is defined by a smooth step-like function with a slight transition between two curvature values, fulfilling the premise that the derivative of this curvature parameter is preserved as approximately zero, $\dotκ\approx0$. To test our model, we implemented a MCMC likelihood analysis using Cosmic Chronometers and Type Ia supernovae data in order to constrain the free parameters of the model and reconstruct $H(z)$, $q(z)$, $w_{eff}(z)$, also comparing the results with the $Λ$CDM model. The main result is that this model provides an alternative to the acceleration of the Universe without the need of a dark energy component. In particular, it gives an equivalent phase transition at $z \sim 0.5$, while obtaining the same fraction of matter density, similar to what is expected for the standard $Λ$CDM model. Remarkably, it also predicts a slight decelerated state at $z=0$ in agreement with diverse Dark Energy parameterizations. We conclude that the behavior of our proposed model points towards a new and intriguing way to investigate slight violations to the cosmological principle, in particular the case of inhomogenities during low phase transitions.
Hubble Parameter and Baryon Acoustic Oscillation Measurement Constraints on the Hubble Constant, the Deviation from the Spatially-Flat $Λ$cdm Model, The Deceleration-Acceleration Transition Redshift, and Spatial Curvature
