Fundamentos del Modelo Cosmológico FLRW: Derivación Completa desde Relatividad General

We present a systematic and complete derivation of the Friedmann-Lemaˆıtre-Robertson- Walker (FLRW) cosmological model from first principles of general relativity. Starting from the cosmological principle of homogeneity and isotropy, we deduce the FLRW metric, calculate the corresponding curvature tensors, and apply Einstein’s field equations to obtain the Friedmann equations that govern the evolution of the universe. Solutions for different cosmological epochs are included, along with analysis of the evolution of density parameters and discussion of the observational implications of the model. This derivation provides the complete theoretical foundations of the standard ΛCDM cosmological model, connecting differential geometry with the observable physics of the cosmos.Keywords: Cosmology, FLRW metric, Friedmann equations, general relativity, cosmological principle.