Quantum cosmology of a dynamical Lambda
File(s)
Published version
Author(s)
Magueijo, João
Zlosnik, Tom
Speziale, Simone
Type
Journal Article
Abstract
By allowing torsion into the gravitational dynamics one can promote the cosmological constant
Λ
to a dynamical variable in a class of quasitopological theories. In this paper we perform a minisuperspace quantization of these theories in the connection representation. If
Λ
is kept fixed, the solution is a delta-normalizable version of the Chern-Simons (CS) state, which is the dual of the Hartle and Hawking and Vilenkin wave functions. We find that the CS state solves the Wheeler–De Witt equation also if
Λ
is rendered dynamical by an Euler quasitopological invariant, in the parity-even branch of the theory. In the absence of an infrared (IR) cutoff, the CS state suggests the marginal probability
P
(
Λ
)
=
δ
(
Λ
)
. Should there be an IR cutoff (for whatever reason), the probability is sharply peaked at the cut off. In the parity-odd branch, however, we can still find the CS state as a particular (but not most general) solution, but further work is needed to sharpen the predictions. For the theory based on the Pontryagin invariant (which only has a parity-odd branch) the CS wave function no longer is a solution to the constraints. We find the most general solution in this case, which again leaves room for a range of predictions for
Λ
.
Λ
to a dynamical variable in a class of quasitopological theories. In this paper we perform a minisuperspace quantization of these theories in the connection representation. If
Λ
is kept fixed, the solution is a delta-normalizable version of the Chern-Simons (CS) state, which is the dual of the Hartle and Hawking and Vilenkin wave functions. We find that the CS state solves the Wheeler–De Witt equation also if
Λ
is rendered dynamical by an Euler quasitopological invariant, in the parity-even branch of the theory. In the absence of an infrared (IR) cutoff, the CS state suggests the marginal probability
P
(
Λ
)
=
δ
(
Λ
)
. Should there be an IR cutoff (for whatever reason), the probability is sharply peaked at the cut off. In the parity-odd branch, however, we can still find the CS state as a particular (but not most general) solution, but further work is needed to sharpen the predictions. For the theory based on the Pontryagin invariant (which only has a parity-odd branch) the CS wave function no longer is a solution to the constraints. We find the most general solution in this case, which again leaves room for a range of predictions for
Λ
.
Date Issued
2020-09-08
Date Acceptance
2020-09-01
Citation
Physical Review D: Particles, Fields, Gravitation and Cosmology, 2020, 102 (6), pp.064006 – 1-064006 – 14
ISSN
1550-2368
Publisher
American Physical Society
Start Page
064006 – 1
End Page
064006 – 14
Journal / Book Title
Physical Review D: Particles, Fields, Gravitation and Cosmology
Volume
102
Issue
6
Copyright Statement
© 2020 American Physical Society
Sponsor
Science and Technology Facilities Council (STFC)
Identifier
https://journals.aps.org/prd/abstract/10.1103/PhysRevD.102.064006
Grant Number
ST/P000762/1
Subjects
0201 Astronomical and Space Sciences
0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
0206 Quantum Physics
Nuclear & Particles Physics
Publication Status
Published
Article Number
064006
Date Publish Online
2020-09-08