Genericness of Inflation in Isotropic Loop Quantum Cosmology

Nonperturbative corrections from loop quantum cosmology (LQC) to the scalar matter sector are already known to imply inflation. We prove that the LQC modified scalar field generates exponential inflation in the small scale factor regime, for all positive definite potentials, independent of initial conditions and independent of ambiguity parameters. For positive semidefinite potentials it is always possible to choose, without fine-tuning, a value of one of the ambiguity parameters such that exponential inflation results, provided zeros of the potential are approached at most as a power law in the scale factor. In conjunction with the generic occurrence of bounce at small volumes, particle horizon is absent, thus eliminating the horizon problem of the standard big bang model.

Figure 1

Plot of ${\omega }^{\mathrm{e}\mathrm{f}\mathrm{f}}$ as a function of $a^2$ and $\omega$ for different constant values $\omega =0.9,0.33,0.0001$. The ambiguity parameters are $j=5,l=0.5$ and $a^2$ is in units of $\frac{1}{6}\gamma {\mu }_0{\ell }_{\mathrm{P}}^2$. For the small scale factor, ${\omega }^{\mathrm{e}\mathrm{f}\mathrm{f}}$ always approaches $-1$ from below while for larger values it approaches $\omega$.