Quantum Gravity and Inflation

Abstract

Using the Ashtekar-Sen variables of loop quantum gravity, a new class of exact solutions to the equations of quantum cosmology is found for gravity coupled to a scalar field, that corresponds to inflating universes. The scalar field, which has an arbitrary potential, is treated as a time variable, reducing the hamiltonian constraint to a time-dependent Schroedinger equation. When reduced to the homogeneous and isotropic case, this is solved exactly by a set of solutions that extend the Kodama state, taking into account the time dependence of the vacuum energy. Each quantum state corresponds to a classical solution of the Hamiltonian-Jacobi equation. The study of the latter shows evidence for an attractor, suggesting a universality in the phenomena of inflation. Finally, wavepackets can be constructed by superposing solutions with different ratios of kinetic to potential scalar field energy, resolving, at least in this case, the issue of normalizability of the Kodama state.

18 Pages, 2 Figures; major corrections to equations but prior results still hold, updated references

References in corpus (4)

• Spin Foam Models for Quantum Gravity
• Lectures on Loop Quantum Gravity
• Quantum gravity with a positive cosmological constant
• A Note On The Chern-Simons And Kodama Wavefunctions

Cited by in corpus (14)

• Quantum Nature of the Big Bang
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Loop Quantum Cosmology
• Falsifiable predictions from semiclassical quantum gravity
• A Quantum Gravitational Relaxation of The Cosmological Constant
• A Singular Conformal Spacetime
• Limiting curvature mimetic gravity for group field theory condensates
• An Inner Product for 4D Quantum Gravity and the Chern-Simons-Kodama State
• Scalar field as a time variable during gravitational evolution
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Inflationary Quantum Cosmology: General Framework and Exact Bianchi I Solution
• An Exact Fermionic Chern-Simons-Kodama State in Quantum Gravity
• Finite states in four dimensional quantum gravity. The isotropic minisuperspace Asktekar--Klein--Gordon model
• Scalar fields in a five-dimensional Lovelock black hole spacetime