Signature transitions in quantum cosmology

Abstract

The authors exhibit a family of Hilbert subspaces describing solutions to the Wheeler-DeWitt equation. Each subspace describes a distinct quantum theory in which the parameters of the potential are required to satisfy a particular 'quantization' condition. Tentative evidence suggests that within each Hilbert subspace there exist states that may be identified with nondispersive wave packets peaking in the vicinity of submanifolds in superspace corresponding to classical cosmological eras. These submanifolds admit parameterizations corresponding to metric solutions of Einstein's equations that admit a transition between a Euclidean and a Lorentzian signature.

Wave packets and initial conditions in quantum cosmology

“…The construction of wave packets resulting from the solutions of the WD equation has been a feature common to most of the recent research work in quantum cosmology [6,7,8]. In particular, in reference [6] the construction of wave packets in a Friedmann universe is presented in detail and appropriate boundary conditions are motivated.…”

“…The choice of the initial conditions, or equivalently the coefficients in the sum, varies considerably amongst various authors. In [7,8], the wave packets are constructed by summing over the first few terms with the coefficients being chosen arbitrarily to be equal. However, in [6] the initial state is chosen to be a Gaussian with the appropriate symmetry and the undetermined coefficients being set to zero.…”

The quantum state of the universe from deformation quantization and classical-quantum correlation

“…Table ( 2) shows the first several zeroes of dJ0(ξ) dξ . The modified Table 2: Zeroes of Bessel function, j n , for n = 1, 2, 3. n j n 1 0 2 3.8317... represents a universe filled with cosmic string and radiation fluids, where the density parameter of radiation is given by…”

“…There are infinite number of transformations that recast such equations into forms with different finite number of degree of freedom interpretations. Distinctly an appropriate transformation, state and quantization should be those that have some chance of yielding a classical limit not too far removed the original classical predictions [2].…”

Signature Change in Noncommutative FRW Cosmology

“…This is well known as the no boundary proposal. In this direction of thinking about quantum interpretation of the early universe, many works have also been accomplished on different cosmological models to study whether it is possible to realize a classical signature change as an interpretation of the no boundary proposal [2,3,4,5,6,11]. Recently, the issue of signature change is again becoming of particular importance in the study of current acceleration of the universe [7], recovering the notion of time [8], the challenge for quantum gravity [9], and the events in emergent spacetimes [10].…”