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Swampland criteria for rescaled Einstein-Hilbert gravity with string corrections

In this work we examine the Swampland criteria for a specific class of rescaled $f(R)$ gravitational models, that are capable of unifying the primordial era of the Universe with the late-time era with the inclusion of string corrections. In particular, we develop separately the theoretical framework of Gauss-Bonnet and Chern-Simons theories considering that, the rescale parameter is constrained to reside in the area $0<α<1$. As showcased, in the context of the aforementioned theories, a viable inflationary phenomenology consistent with the latest Planck data can be obtained for both cases for a wide variety of values. The Swampland criteria which where examined are satisfied, not necessarily simultaneously, for small values of the rescale parameter, which is in agreement with the case of a canonical scalar field with absent string corrective terms. The Gauss-Bonnet model is also further constrained, in order to obtain a propagation velocity of tensor perturbations which coincides with that of light, according to the recent observations from the GW170817. As a result of this assumption the degrees of freedom of the theory are reduced. An interesting feature which arises from the overall phenomenology is that, due to the inclusion of string corrections the tensor spectral index of primordial perturbations is now capable of obtaining a positive value which is not possible in the case of the canonical scalar field. Last but not least, the power-law model which is known to be incompatible with observations is now rendered viable by including a parity violating term and as showcased, it satisfies the Swampland criteria as well.