Abstract
It is shown that the inflationary paradigm admits quantum complete extensions of space-time. The extended inflationary spacetimes still have geodesic borders, but quantum fields are prohibited from migrating across these borders by their evolution semigroups. The geodesic singularities lurking across the borders lack a physical description because the evolution semigroups give vanishing probabilistic support to quantum fields for populating regions bordering on these singularities. As an example, anisotropic Bianchi type-I cosmologies are shown to be quantum complete preludes to inflation. They admit Kasner-like geometries close to their geodesic borders. Quantum fields enjoy a contractive evolution in these asymptotic regions and ultimately become free. As a consequence, quantum probes cannot migrate across the geodesic border of Bianchi type-I cosmologies.
Highlights
A proper inflationary epoch in the primordial expansion history allows us to relate the variety of cosmic structures to quantum fluctuations of the dominant source during this stage [1,2,3]
The extended inflationary spacetimes still have geodesic borders, but quantum fields are prohibited from migrating across these borders by their evolution semigroups
The geodesic singularities lurking across the borders lack a physical description because the evolution semigroups give vanishing probabilistic support to quantum fields for populating regions bordering on these singularities
Summary
A proper inflationary epoch in the primordial expansion history allows us to relate the variety of cosmic structures to quantum fluctuations of the dominant source during this stage [1,2,3]. The ground state of the examined field configurations is time-dependent in dynamical spacetimes This time dependence is not given by a phase factor, i.e., the evolution of quantum states is not given by a unitary group. We show that generic quantum inflaton fields cannot migrate across the geodesic boundary of Bianchi type-I cosmologies This is guaranteed by a contractive evolution semigroup that assigns a vanishing probability for inflaton fields to populate the geodesic border. The result is universal in the sense that it holds for any inflaton potential This universality can be interpreted as a consequence of the Belinskii-Khalatnikhov-Lifshitz conjecture [11,12] which is operative at the geodesic border and guarantees that the dynamics at any spatial point is pefectly captured by an ordinary differential equation [13]
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