Nonsingular power-law and assisted inflation in loop quantum cosmology

Abstract

We investigate the dynamics of single and multiple scalar fields with exponential potentials, leading to power-law and assisted inflation, in loop quantum cosmology. Unlike in the classical theory, dynamical trajectories in loop quantum cosmology are generically nonsingular, with a big bounce replacing classical big bang in the Planck regime. Post bounce, after a phase of super-inflation, dynamical trajectories evolve towards the classical attractor in the inflationary scenarios. Depending on the initial conditions, bounce is shown to occur in kinetic as well as potential dominated regimes. We analyze the number of e-foldings resulting from the phase of super-inflation, and find the dependence of the maximum possible number of e-foldings on the equation of state at the bounce and on the steepness of the potential.We find that if the potential is not steep, this phase can lead to large number of e-foldings in power-law inflation. For the assisted inflation scenario, an increase in the number of fields can yield a significant increase in the number of e-foldings during super-inflation.

Note on the super-inflation in loop quantum cosmology

“…[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].…”

“…In the standard inflation theory, the scale factor a changes rapidly and the Hubble parameter H remains nearly constant. According to the truth that the e-folding number comes from the changing of the scale factor in standard inflation, someone concluded that the e-folding number created during super-inflation in LQC is not sufficient [14], but then it was found that the e-folding number during super-inflation depends on the initial conditions [19] or the parameter of the potential of the scalar field [16]. To show the change of the scale factor a during the super-inflation stage, we will discuss the Universe filled with the interacting field between massless scalar field and radiation at first, and, then give some numerical results in this section.…”

“…Thus, every LQC solution has a super-inflation phase from ρ = ρ c to ρ = 1 2 ρ c , which is staying in the quantum geometry dominated area. Lots of papers researched the characteristic of super-inflation [14][15][16][17][18]. some concluded that the suer inflation can not solve the horizon problem, while others argued it is possible.…”

“…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]. All those researches discussed the Universe contains a selfinteract or massless scalar field.…”

“…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].…”