It is well known that a closed universe with a minimally coupled massive scalar field always collapses to a singularity unless the initial conditions are extremely fine-tuned. We show that the corrections to the equations of motion for the massive scalar field, given by loop quantum gravity in the high curvature regime, always lead to a bounce independently of the initial conditions. In contrast with the previous works in loop quantum cosmology, we note that the singularity can be avoided even at the semiclassical level of effective dynamical equations with nonperturbative quantum gravity modifications, without using a discrete quantum evolution.

We investigate the cosmological dynamics in teleparallel gravity with nonminimal coupling. We analytically extract several asymptotic solutions, and we numerically study the exact phase-space behavior. Comparing the obtained results with the corresponding behavior of nonminimal scalar-curvature theory, we find significant differences, such as the rare stability and the frequent presence of oscillatory behavior.

We investigate inflationary dynamics in the framework of the Einstein-Gauss-Bonnet gravity. In the model under consideration, the inflaton field is nonminimally coupled to the Gauss-Bonnet curvature invariant, so that the latter appears to be dynamically important. We consider a quartic potential for the inflaton field, in particular, the one asymptotically connected to the Higgs inflation, and a wider class of coupling functions not considered in the earlier work. Keeping in mind the observational bounds on the parameters—the amplitude of scalar perturbations $A_s$, spectral index $n_s$ and tensor-to-scalar ratio $r$, we demonstrate that the model a quartic potential and the proposed coupling function is in agreement with observations.

We examine the class of initial conditions that give rise to inflation. Our analysis is carried out for several popular models including Higgs inflation, Starobinsky inflation, chaotic inflation, axion-monodromy inflation, and noncanonical inflation. In each case we determine the set of initial conditions that give rise to sufficient inflation, with at least 60 $e$-foldings. A phase-space analysis is performed for each of these models and the effect of the initial inflationary energy scale on inflation is studied numerically. This paper discusses two scenarios of Higgs inflation: (i) the Higgs is coupled to the scalar curvature, and (ii) the Higgs Lagrangian contains a noncanonical kinetic term. In both cases we find Higgs inflation to be very robust since it can arise for a large class of initial conditions. One of the central results of our analysis is that, for plateau-like potentials associated with the Higgs and Starobinsky models, inflation can be realized even for initial scalar field values that lie close to the minimum of the potential. This dispels a misconception related to plateau potentials prevailing in the literature. We also find that inflation in all models is more robust for larger values of the initial energy scale.

We study flat Friedmann-Lemaître-Robertson-Walker cosmological models for a scalar field coupled nonminimally to teleparallel gravity with generic coupling and potential functions. The goal in this paper is to determine the conditions under which cosmological evolution tends to the limit where the variation of the gravitational “constant” ceases and the system evolves close to general relativity (GR). These conditions can be read off from the approximate analytical solutions describing the process in matter and potential domination eras. Only those models where the GR limit exists and is an attractor can be considered viable. We expect the results to hold in the original “pure tetrad” formulation as well as in the recently suggested covariant formulation of the teleparallel theory. In the former case the GR attractor simultaneously provides a mechanism for how cosmological evolution suppresses the problematic degrees of freedom stemming from the lack of local Lorentz invariance.

We investigate the scalar field dynamics of models with nonminimally coupled scalar fields in the presence of the Gauss-Bonnet term and derive the structure of the effective potential and conditions for stable de Sitter solutions in general. Specializing to specific couplings, we explore the possibility of realizing the stable de Sitter configurations which may have implications for both the early Universe and late time evolution.