Constraining the Barbero-Immirzi parameter from the duration of inflation in loop quantum cosmology

We revisit the predictions for the duration of the inflationary phase after the bounce in loop quantum cosmology. We present our analysis for different classes of inflationary potentials that include the monomial power-law chaotic type of potentials, the Starobinsky and the Higgs-like symmetry breaking potential with different values for the vacuum expectation value. Our setup can easily be extended to other forms of primordial potentials than the ones we have considered. Independently on the details of the contracting phase, if the dynamics starts sufficiently in the far past, the kinetic energy will come to dominate at the bounce, uniquely determining the amplitude of the inflaton at this moment. This will be the initial condition for the further evolution that will provide us with results for the number of e-folds from the bounce to the beginning of the accelerated inflationary regime and the subsequent duration of inflation. We also discuss under which conditions each model considered could lead to observable signatures on the spectrum of the cosmic microwave background or else be excluded for not predicting a sufficient amount of accelerated expansion. A first analysis is performed considering the standard value for the Barbero-Immirzi parameter, gamma similar or equal to 0.2375, which is obtained from black hole entropy calculations. In a second analysis, we consider the possibility of varying the value of this parameter, which is motivated by the fact that the Barbero-Immirzi parameter can be considered a free parameter of the underlying quantum theory in the context of loop quantum gravity. From this analysis, we obtain a lower limit for this parameter by requiring the minimum amount of inflationary expansion that makes the model consistent with the cosmic microwave background observations. When constraining the Barbero-Immirzi parameter, we have made use of the results for the scalar of curvature perturbations derived in loop quantum cosmology assuming the dressed metric approach and considering the Bunch-Davies vacuum as the initial condition for the perturbations in the contracting phase. Such choice provides basically the same results as considering the fourth-order adiabatic vacuum state at the bounce as an initial condition in the context of the dressed metric approach.

Automated summary

This study revisits the predictions for the duration of inflationary phase in loop quantum cosmology after the bounce, analyzing different types of inflationary potentials and their effects on the evolution of the universe. The research also discusses the observability of the models on the spectrum of cosmic microwave background and the minimum requirements for inflationary expansion based on the Barbero-Immirzi parameter.