The subject of this paper is the geometry and topology of cosmological spacetimes and vector bundles thereon, which are used to model physical fields propagating in the universe. Global hyperbolicity and factorization properties of the spacetime and the vector bundle that are usually independently assumed to hold are now derived from a minimal set of assumptions based on the recent progress in differential geometry and topology.
REFERENCES
1.
C.
Bär
, N.
Ginoux
, and F.
Pfäffle
, Wave Equations on Lorentzian Manifolds and Quantization
, ESI Lectures in Mathematics and Physics (AMS
, 2007
).2.
R.
Brunetti
, C.
Dappiaggi
, C.
Fredenhagen
, and J.
Yngvason
, Advances in Algebraic Quantum Field Theory
(Springer
, 2015
).3.
J.
Beem
, P.
Ehrlich
, and K.
Easley
, Global Lorentzian Geometry
, 2nd ed. (Marcel Dekker
, 1996
).4.
A.
Bernal
and M.
Sánchez
, “Smoothness of time functions and the metric splitting of globally hyperbolic spacetimes
,” Commun. Math. Phys.
257
, 43
(2005
).5.
J.
Berndt
, J. C.
Díaz-Ramos
, and M. J.
Vanaei
, “Cohomogeneity one actions on Minkowski spaces
,” Monatsh. Math.
184
, 185
(2017
).6.
E.
Bierstone
, “The equivariant covering homotopy property for differentiable G-fibre bundles
,” J. Differ. Geom.
8
, 615
(1973
).7.
D.
Burago
, Y.
Burago
, and S.
Ivanov
, A Course in Metric Geometry
, Graduate Series in Mathematics Vol. 33 (AMS
, 2001
).8.
A.
Burtscher
, “Length structures on manifolds with continuous Riemannian metrics
,” N. Y. J. Math.
21
, 273
(2015
).9.
Y.
Choquet-Bruhat
and S.
Cotsakis
, “Global hyperbolicity and completeness
,” J. Geom. Phys.
43
, 345
(2002
).10.
G.
Folland
, A Course in Abstract Harmonic Analysis
, 2nd ed. (CRC Press; Taylor&Francis
, 2015
).11.
S.
Hawking
and G. F.
Ellis
, The Large Scale Structure of Space-Time
, Cambridge Monographs on Mathematical Physics (Cambridge University Press
, 1973
).12.
13.
R. K.
Lashof
, “Equivariant bundles
,” Illinois J. Math.
26
, 257
(1982
).14.
W.
Lück
and B.
Uribe
, “Equivariant principal bundles and their classifying spaces
,” Algebraic Geom. Topol.
14
, 1925
(2014
).15.
K.
Nomizu
and H.
Ozeki
, “The existence of complete Riemannian metrics
,” Proc. Am. Math. Soc.
12
, 889
(1961
).16.
M.
Pflaum
, Analytic and Geometric Study of Stratified Spaces
, Lecture Notes in Mathematics (Springer-Verlag
, 2001
).17.
G.
Rudolph
and M.
Schmidt
, Differential Geometry and Mathematical Physics. Part I
(Springer
, 2013
).18.
H.
Stephani
, D.
Kramer
, M.
MacCallum
, C.
Hoenselaers
, and E.
Herlt
, Exact Solutions to Einstein’s Field Equations
, Cambridge Monographs in Mathematical Physics (Cambridge University Press
, 2003
).© 2021 Author(s).
2021
Author(s)
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