The effects of phase space deformations on standard scalar field cosmology are studied. The deformation is introduced by modifying the symplectic structure of the minisuperspace variables to have a deformed Poisson algebra among the coordinates and the canonical momenta. It is found that in the deformed minisuperspace model, an accelerating scale factor arises in the absence of a cosmological constant, and this acceleration is a consequence of the phase space deformation parameter $$\beta${}$.

In this work, first, we study a flat Friedmann–Robertson–Walker Universe with two scalar fields but only one potential term, which can be thought as a simple quintessence plus a K-essence model. Employing the Hamiltonian formalism we are able to obtain the classical and quantum solutions. The second model studied, is also a flat Friedmann–Robertson–Walker Universe with two scalar fields, with the difference that the two potentials are considered as well as the standard kinetic energy and the mixed term (chiral field approach). Regarding this second model, it is shown that setting to zero the coefficient accompanying the mixed momenta term, two possible cases can be studied: a quintom like case ( m + 12 ) and a quintessence like case ( m − 12 ). For both scenarios classical and quantum solutions are presented.

Phase space deformations on scalar field cosmology are studied. The deformation is introduced by modifying the symplectic structure of the minisuperspace variables. The effects of the deformation are studied in the “C-frame” and the “NC-frame.” In order to remove the ambiguities of working on different frames, a new principle is introduced. When we impose that both frames should be physically equivalent, we conclude that the only possibility for this model, is to have an effective cosmological constantΛeff≥0. Finally we bound the parameter space forθandβ.

In this paper, we present an analysis of a chiral cosmological scenario from the perspective of K-essence formalism. In this setup, several scalar fields interact within the kinetic and potential sectors. However, we only consider a flat Friedmann–Robertson–Lamaître–Walker universe coupled minimally to two quintom fields: one quintessence and one phantom. We examine a classical cosmological framework, where analytical solutions are obtained. Indeed, we present an explanation of the “big-bang” singularity by means of a “big-bounce”. Moreover, having a barotropic fluid description and for a particular set of parameters, the phantom line is in fact crossed. Additionally, for the quantum counterpart, the Wheeler–DeWitt equation is analytically solved for various instances, where the factor-ordering problem has been taken into account (measured by the factor Q). Hence, this approach allows us to compute the probability density of the previous two classical subcases. It turns out that its behavior is in effect damped as the scale factor and the scalar fields evolve. It also tends towards the phantom sector when the factor ordering constant $\mathrm{Q}\ll 0$.

We construct a noncommutative extension of the Loop Quantum Cosmology effective scheme for the flat FLRW model with a free scalar field via a theta deformation. Firstly, a deformation is implemented in the configuration sector, among the holonomy variable and the matter degree of freedom. We show that this type of noncommutativity retains, to some degree, key features of the Loop Quantum Cosmology paradigm for a free field. Secondly, a deformation is implemented in the momentum sector, among the momentum associated with the holonomy variable and the momentum associated with the matter field. We show that in this latter case the scalar field energy density is the same as the one in standard Loop Quantum Cosmology.

We construct and study a simple noncommutative scheme (theta-deformation) for the effective loop quantum cosmology of the flat Friedmann-Lemaître-Robertson-Walker model in the presence of a homogeneous scalar field $\varphi$ with a potential $\mathcal{V}(\varphi )=\frac{1}{2}{m}^2{\varphi }^2$. We first conduct a simple analysis from the corresponding Hamilton equations of motion considering a generic term $\mathcal{V}(\varphi )$. It is observed that the characteristic big bounce of loop quantum cosmology is preserved under such noncommutative extension. When specializing to the quadratic case, numerical solutions to the corresponding Hamilton equations exhibiting an early inflationary epoch with a sufficiently large number of $e$-foldings are found. It is concluded that, in this noncommutative setup, solutions exist which are in the overall compatible with the early universe predicted by standard (effective) Loop Quantum Cosmology (i.e., a bouncing and inflationary early universe). The issue of the genericness of a sufficiently long inflationary period on the space of solutions in this noncommutative construct remains to be addressed.