Non-Commutativity and its Role in Constant-Roll Inflation Models with Non-Minimal Coupling Constrained by Swampland Conjectures

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Abstract In this paper, using Hamiltonian formalism, we obtain solutions for constant-roll inflation according to the non-commutativity and the non-minimal coupling field of Lagrangian. We consider three different types of couplings: power-law, exponential, and logarithmic. Then, by plotting some figures, we study the effects of these coupling in constant-roll inflation with non-commutative parameters. We identify and specify the permissible regions of each case about swampland conjecture and determine the best model. We find that the exponential coupling, logarithmic coupling, and power-law coupling with $\theta>0$ agree with the dS swampland conjecture. These couplings give us similar results in both cases, some of which are compatible and some incompatible with the dS swampland conjectures. Moreover, $\theta>0$ is more compatible than $\theta<0$ and the consistency value in the second boundary condition is much higher than in the first. The order of better compatibility of couplings with the Swampland Conjecture is ranked as follows: exponential non-minimal coupling, logarithmic non-minimal coupling, and power-law non-minimal coupling. For each type of coupling, we calculate the values of the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ for two different potentials and compare them with the observational data from Planck 2018. We also determine the range of the free parameters $(a,b,q)$ of the further refining de Sitter swampland conjecture (FRDSSC) that make the model consistent with the conjecture. We find that the model satisfies the FRDSSC for all types of couplings and both potentials, with some constraints on the parameters.