Non-Singular Bouncing Universes in Loop Quantum Cosmology

In classical Bianchi-I spacetimes, underlying conditions for what dictates the singularity structure - whether it is anisotropic shear or energy density, can be easily determined from the generalized Friedmann equation. However, in non-singular bouncing anisotropic models these insights are difficult to obtain in the quantum gravity regime where the singularity is resolved at a non-vanishing mean volume which can be large compared to the Planck volume, depending on the initia...

The main objective of this manuscript is to investigate the bouncing cosmology in the background of $f(\mathcal{Q})$ gravity, where $\mathcal{Q}$ defines the non-metricity. For this purpose, we use the reconstruction approach and consider a flat Friedmann-Robertson-Walker spacetime with perfect matter configuration. We examine how the first contracting phase gives the expansion by using a temporal derivative of the scale factor, i.e., $\dot{a}<0$, $\dot{a}=0$ and $\dot{a}>0$ ...

Loop quantum cosmology applies techniques derived for a background independent quantization of general relativity to cosmological situations and draws conclusions for the very early universe. Direct implications for the singularity problem as well as phenomenology in the context of inflation or bouncing universes result, which will be reviewed here. The discussion focuses on recent new results for structure formation and generalizations of the methods.

Qualitative dynamics of three different loop quantizations of spatially flat isotropic and homogeneous models is studied using effective spacetime description of the underlying quantum geometry. These include the standard loop quantum cosmology (LQC), its recently revived modification (referred to as mLQC-I), and another related modification of LQC (mLQC-II) whose dynamics is studied in detail for the first time. Various features of LQC, including quantum bounce and pre-infla...

We show that simple scalar field models can give rise to curvature singularities in the effective Friedmann dynamics of Loop Quantum Cosmology (LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker cosmologies with a canonical scalar field and a negative exponential potential, or with a phantom scalar field and a positive potential. While LQC avoids big bang or big rip type singularities, we find sudden singularities where the Hubble rate is bounded, ...

In this Letter, we study analytically the evolutions of the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) universe and its linear perturbations in the framework of {\em the dressed metric approach} in loop quantum cosmology (LQC). Assuming that the evolution of the background is dominated by the kinetic energy of the inflaton at the quantum bounce, we find that both evolutions of the background and its perturbations are independent of the inflationary potentials during the ...

We study the dynamics of states perturbatively expanded about a harmonic system of loop quantum cosmology, exhibiting a bounce. In particular, the evolution equations for the first and second order moments of the system are analyzed. These moments back-react on the trajectories of the expectation values of the state and hence alter the energy density at the bounce. This analysis is performed for isotropic loop quantum cosmology coupled to a scalar field with a small but non-z...

We extend the Loop Quantum Cosmology matter bounce scenario in order to include a dark energy era, which ends abruptly at a Rip singularity where the scale factor and the Hubble rate diverge. In the "deformed matter bounce scenario", the Universe is contracting from an initial non-causal matter dominated era until it reaches a minimal radius. After that it expands in a decelerating way, until at late times, where it expands in an accelerating way, thus the model is described ...

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 high curvature regime, always lead to a bounce independently of the initial conditions. In contrast to the previous works in loop quantum cosmology, we note that the singularity can be ...

Several examples are known where quantum gravity effects resolve the classical big bang singularity by a bounce. The most detailed analysis has probably occurred for loop quantum cosmology of isotropic models sourced by a free, massless scalar. Once a bounce has been realized under fairly general conditions, the central questions are how strongly quantum it behaves, what influence quantum effects can have on its appearance, and what quantum space-time beyond the bounce may lo...