Cosmological signature change in Cartan gravity with dynamical symmetry breaking
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Accepted version
Author(s)
Magueijo, Joao
Rodriguez-Vazquez, Matias
Westman, Hans
Zlosnik, Tom
Type
Journal Article
Abstract
We investigate the possibility for classical metric signature change in a straightforward generalization of the first-order formulation of gravity, dubbed “Cartan gravity.” The mathematical structure of this theory mimics the electroweak theory in that the basic ingredients are an
S
O
(
1
,
4
)
Yang-Mills gauge field
A
a
b
μ
and a symmetry breaking Higgs field
V
a
, with no metric or affine structure of spacetime presupposed. However, these structures can be recovered, with the predictions of general relativity exactly reproduced, whenever the Higgs field breaking the symmetry to
S
O
(
1
,
3
)
is forced to have a constant (positive) norm
V
a
V
a
. This restriction is usually imposed “by hand,” but in analogy with the electroweak theory we promote the gravitational Higgs field
V
a
to a genuine dynamical field, subject to nontrivial equations of motion. Even though we limit ourselves to actions polynomial in these variables, we discover a rich phenomenology. Most notably we derive classical cosmological solutions exhibiting a smooth transition between Euclidean and Lorentzian signature in the four-metric. These solutions are nonsingular and arise whenever the
S
O
(
1
,
4
)
norm of the Higgs field changes sign; i.e. the signature of the metric of spacetime is determined dynamically by the gravitational Higgs field. It is possible to find a plethora of such solutions and in some of them this dramatic behavior is confined to the early Universe, with the theory asymptotically tending to Einstein gravity at late times. Curiously the theory can also naturally embody a well-known dark energy model: Peebles-Ratra quintessence.
S
O
(
1
,
4
)
Yang-Mills gauge field
A
a
b
μ
and a symmetry breaking Higgs field
V
a
, with no metric or affine structure of spacetime presupposed. However, these structures can be recovered, with the predictions of general relativity exactly reproduced, whenever the Higgs field breaking the symmetry to
S
O
(
1
,
3
)
is forced to have a constant (positive) norm
V
a
V
a
. This restriction is usually imposed “by hand,” but in analogy with the electroweak theory we promote the gravitational Higgs field
V
a
to a genuine dynamical field, subject to nontrivial equations of motion. Even though we limit ourselves to actions polynomial in these variables, we discover a rich phenomenology. Most notably we derive classical cosmological solutions exhibiting a smooth transition between Euclidean and Lorentzian signature in the four-metric. These solutions are nonsingular and arise whenever the
S
O
(
1
,
4
)
norm of the Higgs field changes sign; i.e. the signature of the metric of spacetime is determined dynamically by the gravitational Higgs field. It is possible to find a plethora of such solutions and in some of them this dramatic behavior is confined to the early Universe, with the theory asymptotically tending to Einstein gravity at late times. Curiously the theory can also naturally embody a well-known dark energy model: Peebles-Ratra quintessence.
Date Issued
2014-03-31
Date Acceptance
2014-03-01
Citation
Physical Review D: Particles, Fields, Gravitation and Cosmology, 2014, 89 (6), pp.063542-1-063542-18
ISSN
1550-2368
Publisher
American Physical Society
Start Page
063542-1
End Page
063542-18
Journal / Book Title
Physical Review D: Particles, Fields, Gravitation and Cosmology
Volume
89
Issue
6
Copyright Statement
© 2014 American Physical Society
Sponsor
Science and Technology Facilities Council (STFC)
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000334311300006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
ST/J000353/1
Subjects
Science & Technology
Physical Sciences
Astronomy & Astrophysics
Physics, Particles & Fields
Physics
POINCARE GAUGE-THEORY
SUPERGRAVITY
RELATIVITY
INVARIANCE
EQUATIONS
CONSTANT
FIELDS
MATTER
Publication Status
Published
Article Number
ARTN 063542
Date Publish Online
2014-03-31