Emergent Universe Model from Modified Heisenberg Algebra

We provide an Emergent Universe picture in which the fine-tuning on the initial conditions is replaced by cut-off physics, implemented on a semiclassical level when referred to the Universe dynamics and on a purely quantum level for the quantum fluctuations of the inflaton field. The adopted cut-off physics is inspired by Polymer Quantum Mechanics but expanded in the limit of a small lattice step. On a quasi-classical level, this results in modified Poisson Brackets for the Hamiltonian Universe dynamics similar to a Generalized Uncertainty Principle algebra. The resulting Universe is indeed asymptotically Einstein-static, emerging from a finite volume configuration in the distant past and then properly reconnecting with the most relevant Universe phases. The calculation of the modifications of the primordial inflaton spectrum is then performed by treating new physics as a small correction on the standard Hamiltonian of each Fourier mode of the field. The merit of this study is to provide a new paradigm for a non-singular Emergent Universe, which is associated with a precise fingerprint on the temperature distribution of the microwave background, in principle observable by future experiments.