The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.

"relative State" Formulation of Quantum Mechanics

A four-form gauge flux makes a variable contribution to the cosmological constant. This has often been assumed to take continuous values, but we argue that it has a generalized Dirac quantization condition. For a single flux the steps are much larger than the observational limit, but we show that with multiple fluxes the allowed values can form a sufficiently dense `discretuum'. Multiple fluxes generally arise in M-theory compactifications on manifolds with non-trivial three-cycles. In theories with large extra dimensions a few four-forms suffice; otherwise of order 100 are needed. Starting from generic initial conditions, the repeated nucleation of membranes dynamically generates regions with λ in the observational range. Entropy and density perturbations can be produced.

https://iopscience.iop.org/article/10.1088/1126-6708/2000/06/006/pdf

Quantization of four-form fluxes and dynamical neutralization of the cosmological constant

Chern-Simons Modified General Relativity

We study an inflationary model developed by Kaloper and Sorbo, in which the inflaton is an axion with a sub-Planckian decay constant, whose potential is generated by mixing with a topological 4-form field strength. This gives a 4d construction of ``axion monodromy inflation: the axion winds many times over the course of inflation and draws energy from the 4-form. The classical theory is equivalent to chaotic inflation with a quadratic inflaton potential. Such models can produce ``high scale inflation driven by energy densities of the order of (1016GeV)4, which produces primordial gravitational waves potentially accessible to CMB polarization experiments. We analyze the possible corrections to this scenario from the standpoint of 4d effective field theory, identifying the physics which potentially suppresses dangerous corrections to the slow-roll potential. This yields a constraint relation between the axion decay constant, the inflaton mass, and the 4-form charge. We show how these models can evade the fundamental constraints which typically make high-scale inflation difficult to realize. Specifically, the moduli coupling to the axion-four-form sector must have masses higher than the inflationary Hubble scale (1014GeV). There are also constraints from states that become light due to multiple windings of the axion, as happens in explicit string theory constructions of this scenario. Further, such models generally have a quantum-mechanical ``tunneling mode in which the axion jumps between windings, which must be suppressed. Finally, we outline possible observational signatures.

An ignoble approach to large field inflation

We study an inflationary model developed by Kaloper and Sorbo, in which the inflaton is an axion with a sub-Planckian decay constant, whose potential is generated by mixing with a topological 4-form field strength. This gives a 4d construction of "axion monodromy inflation": the axion winds many times over the course of inflation and draws energy from the 4-form. The classical theory is equivalent to chaotic inflation with a quadratic inflaton potential. Such models can produce "high scale" inflation driven by energy densities of the order of $(10^{16}\ GeV)^4$, which produces primordial gravitational waves potentially accessible to CMB polarization experiments. We analyze the possible corrections to this scenario from the standpoint of 4d effective field theory, identifying the physics which potentially suppresses dangerous corrections to the slow-roll potential. This yields a constraint relation between the axion decay constant, the inflaton mass, and the 4-form charge. We show how these models can evade the fundamental constraints which typically make high-scale inflation difficult to realize. Specifically, the moduli coupling to the axion-four-form sector must have masses higher than the inflationary Hubble scale ($\la\ 10^{14}\ GeV$). There are also constraints from states that become light due to multiple windings of the axion, as happens in explicit string theory constructions of this scenario. Further, such models generally have a quantum-mechanical "tunneling mode" in which the axion jumps between windings, which must be suppressed. Finally, we outline possible observational signatures.

An Ignoble Approach to Large Field Inflation

http://cds.cern.ch/record/210697/files/199009243.pdf

Gravitational dynamics with Lorentz Chern-Simons terms

http://cds.cern.ch/record/200602/files/198910207.pdf

Four Forms and the Vanishing of the Cosmological Constant

The quantum cosmology of an anisotropic universe

http://cds.cern.ch/record/196560/files/198905525.pdf

Malcolm J. Duncan

Papers

Gravitational dynamics with Lorentz Chern-Simons terms

Four Forms and the Vanishing of the Cosmological Constant

The quantum cosmology of an anisotropic universe

Is the universe euclidean

Topological stability in higher dimensional theories