Bouncing loop quantum cosmology fromF(T)gravity

Abstract

The big bang singularity could be understood as a breakdown of Einstein's General Relativity at very high energies. Adopting this viewpoint, other theories, that implement Einstein Cosmology at high energies, might solve the problem of the primeval singularity. One of them is Loop Quantum Cosmology (LQC) with a small cosmological constant that models a universe moving along an ellipse, which prevents singularities like the big bang or the big rip, in the phase space (H, ρ), where H is the Hubble parameter and ρ the energy density of the universe. Using LQC when one considers a model of universe filled by radiation and matter where, due to the cosmological constant, there are a de Sitter and an anti de Sitter solution. This means that one obtains a bouncing non-singular universe which is in the contracting phase at early times. After leaving this phase, i.e., after bouncing, it passes trough a radiation and matter dominated phase and finally at late times it expands in an accelerated way (current cosmic acceleration). This model does not suffer from the horizon and flatness problems as in big bang cosmology, where a period of inflation that increases the size of our universe in more than 60 e-folds is needed in order to solve both problems. The model has two mechanisms to avoid these problems: The evolution of the universe through a contracting phase and a period of super-inflation (Ḣ > 0).

Note on the super-inflation in loop quantum cosmology

“…And Ref. [18] showed that super-inflation can support enough e-folding number while the Universe contains matter and a small cosmology constant Λ. Also, If one considers the Universe contains a scalar field or multiple scalar field with exponential potentials, the super-inflation is also possible to yield enough e-folding number [16].…”

“…To solve the horizon problem, we require that aH grows sufficiently during an early stage of the Universe's evolution. In fact, we needN ≡ ln a(t f )H(t f ) a(ti)H(ti) ∼ 60 at least [18]. In the standard inflation theory, the Hubble parameter H is nearly a constant, so the e-folding number is depending on the change of the scale factor, i.e.,N = N ≡ ln a f ai .…”

“…To show the super-inflation stage can solve the horizon problem, we will follow the method of [18] to calculate the particle horizon in LQC. For simplify, we choose the Case I.…”

“…Some papers found that the scale factor changes too small to solve the flatness and horizon problem during super-inflation stage [14], whereas the Hubble parameter H is visibly growing during this stage, then some papers argued that the horizon problem can be solved at the super-inflation area [15,18]. Also, the duration of super-inflation, or the change of scale factor depends on the initial value of the scalar field [19], or the parameter of the potential of the scalar field [16].…”

“…The super-inflation, which is caused by the quantum geometry effect in LQC [14], has been studied by many papers [15][16][17][18]. Some papers found that the scale factor changes too small to solve the flatness and horizon problem during super-inflation stage [14], whereas the Hubble parameter H is visibly growing during this stage, then some papers argued that the horizon problem can be solved at the super-inflation area [15,18].…”