On Energy Conditions and Stability in Effective Loop Quantum Cosmology

In isotropic loop quantum cosmology, non-perturbatively modified dynamics of a minimally coupled scalar field violates weak, strong and dominant energy conditions when they are stated in terms of equation of state parameter. The violation of strong energy condition helps to have non-singular evolution by evading singularity theorems thus leading to a generic inflationary phase. However, the violation of weak and dominant energy conditions raises concern, as in general relativity these conditions ensure causality of the system and stability of vacuum via Hawking-Ellis conservation theorem. It is shown here that the non-perturbatively modified kinetic term contributes negative pressure but positive energy density. This crucial feature leads to violation of energy conditions but ensures positivity of energy density, as scalar matter Hamiltonian remains bounded from below. It is also shown that the modified dynamics restricts group velocity for inhomogeneous modes to remain sub-luminal thus ensuring causal propagation across spatial distances.Comment: 29 pages, revtex4; few clarifications, references added, to appear in CQ

Universe from vacuum in loop-string cosmology

In this paper we study the description of the Universe based on the low energy superstring theory modified by the Loop Quantum Gravity effects.This approach was proposed by De Risi et al. in the Phys. Rev. D {\bf 76} (2007) 103531. We show that in the contrast with the string motivated pre-Big Bang scenario, the cosmological realisation of the $t$-duality transformation is not necessary to avoid an initial singularity. In the model considered the universe starts its evolution in the vacuum phase at time $t\to - \infty$. In this phase the scale factor $a\to 0$, energy density $\rho \to 0$ and coupling of the interactions $g^2_s \to 0$. After this stage the universe evolves to the non-singular hot Big Bang phase $\rho \to \rho_{\text{max}} < \infty$. Then the standard classical universe emerges. During the whole evolution the scale factor increases monotonically. We solve this model analytically. We also propose and solve numerically the model with an additional dilaton potential in which the universe starts the evolution from the asymptotically free vacuum phase $g^2_s \to 0$ and then evolves non-singularly to the emerging dark energy dominated phase with the saturated coupling constant $g^2_s \to \text{const}$.Comment: JHEP3 LaTeX class, 19 pages, 9 figures, v2: added some comments and references, v3: new numerical result added, new figure

Effective State Metamorphosis in Semi-Classical Loop Quantum Cosmology

Modification to the behavior of geometrical density at short scales is a key result of loop quantum cosmology, responsible for an interesting phenomenology in the very early universe. We demonstrate the way matter with arbitrary scale factor dependence in Hamiltonian incorporates this change in its effective dynamics in the loop modified phase. For generic matter, the equation of state starts varying near a critical scale factor, becomes negative below it and violates strong energy condition. This opens a new avenue to generalize various phenomenological applications in loop quantum cosmology. We show that different ways to define energy density may yield radically different results, especially for the case corresponding to classical dust. We also discuss implications for frequency dispersion induced by modification to geometric density at small scales.Comment: Revised version; includes expanded discussion of natural trans-Planckian modifications to frequency dispersion and robustness to quantization ambiguities. To appear in Class. Quant. Gra

Classical Setting and Effective Dynamics for Spinfoam Cosmology

We explore how to extract effective dynamics from loop quantum gravity and spinfoams truncated to a finite fixed graph, with the hope of modeling symmetry-reduced gravitational systems. We particularize our study to the 2-vertex graph with N links. We describe the canonical data using the recent formulation of the phase space in terms of spinors, and implement a symmetry-reduction to the homogeneous and isotropic sector. From the canonical point of view, we construct a consistent Hamiltonian for the model and discuss its relation with Friedmann-Robertson-Walker cosmologies. Then, we analyze the dynamics from the spinfoam approach. We compute exactly the transition amplitude between initial and final coherent spin networks states with support on the 2-vertex graph, for the choice of the simplest two-complex (with a single space-time vertex). The transition amplitude verifies an exact differential equation that agrees with the Hamiltonian constructed previously. Thus, in our simple setting we clarify the link between the canonical and the covariant formalisms.Comment: 38 pages, v2: Link with discretized loop quantum gravity made explicit and emphasize

Hints of (trans-Planckian) asymptotic freedom in semiclassical cosmology

We employ the semiclassical approximation to the Wheeler-DeWitt equation in the spatially flat de Sitter Universe to investigate the dynamics of a minimally coupled scalar field near the Planck scale. We find that, contrary to naive intuition, the effects of quantum gravitational fluctuations become negligible and the scalar field states asymptotically approach plane-waves at very early times. These states can then be used as initial conditions for the quantum states of matter to show that each mode essentially originated in the minimum energy vacuum. Although the full quantum dynamics cannot be solved exactly for the case at hand, our results can be considered as supporting the general idea of asymptotic safety in quantum gravity.Comment: 11 pages, 2 figures; replaced to match content of published versio

Early Universe Dynamics in Semi-Classical Loop Quantum Cosmology

Within the framework of loop quantum cosmology, there exists a semi-classical regime where spacetime may be approximated in terms of a continuous manifold, but where the standard Friedmann equations of classical Einstein gravity receive non-perturbative quantum corrections. An approximate, analytical approach to studying cosmic dynamics in this regime is developed for both spatially flat and positively-curved isotropic universes sourced by a self-interacting scalar field. In the former case, a direct correspondence between the classical and semi-classical field equations can be established together with a scale factor duality that directly relates different expanding and contracting universes. Some examples of non-singular, bouncing cosmologies are presented together with a scaling, power-law solution.Comment: 14 pages, In Press, JCA