Will Quantum Cosmology Resurrect Chaotic Inflation Model?

Abstract

The single field chaotic inflation model with a monomial power greater than one seems to be ruled out by the recent Planck and WMAP CMB data while Starobinsky model with a higher curvature term seems to be a viable model. Higher curvature terms being originated from quantum fluctuations, we revisit the quantum cosmology of the WheelerDeWitt equation for the chaotic inflation model. The semiclassical cosmology emerges from quantum cosmology with fluctuations of spacetimes and matter when the wave function is peaked around the semiclassical trajectory with quantum corrections a la the de Broglie-Bohm pilot theory.

Classical and quantum cosmology of the little rip abrupt event

“…where U 1 and U 2 are integration constants. For large values of ϕ, we have 37) and the wave function vanishes asymptotically. It is worth notice that for small values of the argument (2π √ σ/3 ) ϕ 3 in Eq.…”

“…Notice that the scalar part solutions depend on the scale factor. Using the Symanzik scaling law [35][36][37], we have that Φ n x,φ = .…”

Quantum Gravity Effects in Cosmology

“…(7). We may apply either the WKP approximation or the Liouville-Green (LG) transformation method, to the WDW equation (1) or (2). The LG transformation method, however, reduces to the WKB approximation in the limit of large variable while it also applies to the turning point up to an additional constant term [3].…”

“…There have been proposed different approaches to quantum gravity (for a review, see [1]). In partciular, the geometrodynamical approach to quantum gravity and cosmology seems to be practically useful in that the transition from quantum gravity to semiclasical gravity and then to classical gravity including quantum corrections for the Einstein and the energy-stress tensors prescribes dynamical laws and correlations in terms of classical cosmology variables and parameters [2].…”

“…[3,4]. The Born-Oppenheimer interpretation of the WDW equation with respect to the Planck scale for gravity part and the energy scale for the inflaton separates the gravity part from the inflaton part and a further application of de Broglie-Bohm pilotwave theory results in the classical equation together with quantum corrections of gravitational and field fluctuations [5,6] (for references, see [2]). The quantum cosmology for an inflationary model with inhomogeneous fluctuations predicted the power spectrum with quantum corrections, which is suppressed at large scales and provides a weaker upper bound on the Hubble constant H than the tensor-to-scalar ratio [7].…”