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We consider a k-essence model in which a single scalar field can beresponsible for both primordial inflation and the present observed accelerationof the cosmological background geometry, while also admitting a nonsingular deSitter beginning of the Universe (it arises from de Sitter and ends in deSitter). The early one is driven by a slow-roll potential, and the late one isdriven by a dynamical dimensional reduction process which freezes the scalarfield in a degenerate surface, turning it into a cosmological constant. This isdone by proposing a realizable stable cosmic time crystal, although giving adifferent interpretation to the ''moving ground stat'', in which there is nomotion because the system loses degrees of freedom. Furthermore, the model isfree of pathologies such as propagating superluminal perturbations, negativeenergies, and perturbation instabilities.

Inflation and late-time accelerated expansion driven by $k$-essence degenerate dynamics