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In this work we consider the realization of a variant emergent Universescenario in the context of $f(R)$ gravity. We use well-known reconstructiontechniques existing in the literature, and we find the approximate form of thevacuum $f(R)$ that reproduces the specific variant emergent Universe scalefactor in the large curvature approximation. As we show, in the variantemergent Universe scenario, the Hubble horizon shrinks primordially and theUniverse undergoes in an accelerated expansion era. In a perturbation theoryapproach, the scalar and tensor curvature perturbations can be expressed interms of the phenomenological indices $\epsilon_i , i=1,3,4$, usually used forinflationary phenomenology, and we extract the spectral indices for the scalarand tensor perturbations, along with the tensor-to-scalar ratio expressed interms of the perturbation indices. Using a powerful genetic algorithm weinvestigate in depth the parameter space of the model, quantified by severalfree parameters, in order to study the viability of the model when this iscompared with the Planck 2018 data. We also investigate the implications of thevacuum $f(R)$ gravity we found on the Big Bang nucleosynthesis.

Primordial Cosmology of an Emergent-like Universe from Modified Gravity: Reconstruction and Phenomenology Optimization with a Genetic Algorithm