Built on

Desgrange C, Heinesen A and Buchert T 2019 Dynamical spatial curvature as a fit to type Ia supernovae Int. J. of Mod. Phys. D 28
Original
1902
Earlier work this paper cites.
Gregoris D, Ong Y C and Wang B 2019 Curvature invariants and lower dimensional black hole horizons Eur. Phys. J. C 79
Original
1902
Earlier work this paper cites.
Roukema B F and Ostrowski J J 2019 Does spatial flatness forbid the turnaround epoch of collapsing structures? J. Cosmol. Astropart. Phys. 12
Original
1902
Earlier work this paper cites.
Vigneron Q and Buchert T 2019 Dark matter from backreaction? Collapse models on galaxy cluster scales Class. Quantum Grav. 36
Original
1902
Earlier work this paper cites.
Le Delliou M and Lorca Espiro J 2020 Is the cosmological constant of topological origin? Physics of the Dark Universe 29
Original
1906
Earlier work this paper cites.
Fennen M and Giulini D 2020 Lie sphere geometry in lattice cosmology Class. Quantum Grav. 37
Original
1909
Earlier work this paper cites.
Lorca Espiro J and Le Delliou M 2020 Dark energy from topology J. Cosmol. Astropart. Phys. 03
Original
1910
Earlier work this paper cites.
Buchert T, Mourier P and Roy X 2020 On average properties of inhomogeneous fluids in general relativity III: general fluid cosmologies Gen. Relativ. Grav. 52
Original
1912
Earlier work this paper cites.
Lanczos C 1938 A remarkable property of the Riemann-Christoffel tensor in four dimensions Annals of Mathematics 39
1938
Earlier work this paper cites.
Chern S 1944 A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds Ann. Math. 45
1944
Earlier work this paper cites.
Huber A 1957 On subharmonic functions and differential geometry in the large Comment. Math. Helv. 32
1957
Earlier work this paper cites.
Sussman R A 2013 Weighed scalar averaging in LTB dust models, part I: statistical fluctuations and gravitational entropy Class. Quantum Grav. 30
Original
1962
Earlier work this paper cites.
Chern S 1963 Pseudo-Riemannian geometry and the Gauss-Bonnet formula An. Acad. Brasil. Ci. 35
1963
Earlier work this paper cites.
Richards I 1963 On the classification of noncompact surfaces Trans. Amer. Math. Soc. 106
1963
Earlier work this paper cites.
Geroch R 1970 Domain of Dependence J. of Math. Phys. 11
1970
Earlier work this paper cites.
Hawking S W 1971 Black holes in general relativity Commun. Math. Phys. 25
1971
Earlier work this paper cites.
Yodzis P 1974 On the expansion of closed universes Proc. Royal Irish Acad. 74A
1974
Earlier work this paper cites.
Kazdan J L Warner F W 1975 Inventiones math. 28
1975
Earlier work this paper cites.
Szekeres P 1975 A class of inhomogeneous cosmological models Comm. Math. Phys. 41
1975
Earlier work this paper cites.
Bergery L B 1981 La courbure scalaire des variétés riemanniennes Séminaire N. Bourbaki 556
1981
Earlier work this paper cites.
Jackiw R 1985 Lower dimensional gravity Nucl. Phys. B 252
1985
Earlier work this paper cites.
Besse A L 1987 Einstein manifolds Ergebnisse der Mathematik und ihrer Grenzgebiete 10
1987
Earlier work this paper cites.
Hughston L P and Tod K P 1991 An Introduction to General Relativity , Cambridge Univ. Press
1991
Earlier work this paper cites.
Bañados M, Teitelboim C and Zanelli J 1992 Black hole in three-dimensional spacetime, Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
Hulin D, Troyanov M 1992 Prescribing curvature on open surfaces Math. Ann. 293
1992
Earlier work this paper cites.
Bredon G E 1993 Topology and Geometry Graduate Texts in Mathematics , Springer-Verlag, Berlin
1993
Earlier work this paper cites.
Galloway G J 1993 On the topology of black holes Commun. Math. Phys. 151
1993
Earlier work this paper cites.
Melrose R B 1993 The Atiyah-Patodi-Singer index theorem Research notes in mathematics A K Peters/CRC Press
1993
Earlier work this paper cites.
Lohkamp J 1994 Metrics of negative Ricci curvature Annals of Mathematics 140
1994
Earlier work this paper cites.
Alty L J 1995 The generalized Gauss-Bonnet-Chern theorem J. Math. Phys. 36
1995
Earlier work this paper cites.
Bruni M, Matarrese S and Pantano O 1995 Dynamics of silent universes Astrophys. J. 445
1995
Earlier work this paper cites.
Kobayashi S and Nomizu K 1996 Foundations of Differential Geometry Volume 1 John Wiley & Sons, New York
1996
Earlier work this paper cites.
Buchert T and Ehlers J 1997 Averaging inhomogeneous Newtonian cosmologies Astron. Astrophys. 320
1997
Earlier work this paper cites.
van Elst H, Uggla C, Lesame W M, Ellis G F R and Maartens R 1997 Integrability of irrotational silent cosmological models Class. Quantum Grav. 14
1997
Earlier work this paper cites.

Similar

Krasiński A. 1997 Inhomogeneous Cosmological Models Cambridge University Press U.K
1997
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Mutoh H, Hirai T and Maeda K 1997 Dynamics of quiet universes Phys. Rev. D 55
1997
Cited alongside, same era.
Andersson L, Galloway G J and Howard R 1998 The cosmological time function Class. Quantum Grav. 15
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Carlip S 1998 Quantum gravity in 2 + 1 2+1 dimensions Cambridge Monographs on Math. Phys
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Cited alongside, same era.
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Then

Sussman R A 2011 Back-reaction and effective acceleration in generic LTB dust models Class. Quantum Grav. 28
Original
2011
Later among the works it cites.
Wiltshire D L 2011 What is dust?—Physical foundations of the averaging problem in cosmology Class. Quantum Grav. 28
Original
2011
Later among the works it cites.
Buchert T and Ostermann M 2012 Lagrangian theory of structure formation in relativistic cosmology. I. Lagrangian framework and definition of a nonperturbative approximation Phys. Rev. D 86
Original
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Later among the works it cites.
Buchert T and Räsänen S 2012 Backreaction in Late-Time Cosmology Annu. Rev. Nucl. Part. Sci. 62
Original
2012
Later among the works it cites.
Li N, Buchert T, Hosoya A, Morita M and Schwarz D J 2012 Relative information entropy and Weyl curvature of the inhomogeneous Universe Phys. Rev. D 86

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2020

Gauss-Bonnet-Chern approach to the averaged Universe

Brunswic, Léo, Buchert, Thomas

Understand

The standard model of cosmology with postulated dark energy and dark matter sources may be considered as a fairly successful fitting model to observational data.

However, this model leaves the question of the physical origin of these dark components open.
Fully relativistic contributions that act like dark energy on large scales and like dark matter on smaller scales can be found through generalization of the standard model by spatially averaging the inhomogeneous Universe within general relativity.
The spatially averaged 3+1 Einstein equations are effective balance equations that need a closure condition.

Built on

Desgrange C, Heinesen A and Buchert T 2019 Dynamical spatial curvature as a fit to type Ia supernovae Int. J. of Mod. Phys. D 28
Original
1902
Earlier work this paper cites.
Gregoris D, Ong Y C and Wang B 2019 Curvature invariants and lower dimensional black hole horizons Eur. Phys. J. C 79
Original
1902
Earlier work this paper cites.
Roukema B F and Ostrowski J J 2019 Does spatial flatness forbid the turnaround epoch of collapsing structures? J. Cosmol. Astropart. Phys. 12
Original
1902
Earlier work this paper cites.
Vigneron Q and Buchert T 2019 Dark matter from backreaction? Collapse models on galaxy cluster scales Class. Quantum Grav. 36
Original
1902
Earlier work this paper cites.
Le Delliou M and Lorca Espiro J 2020 Is the cosmological constant of topological origin? Physics of the Dark Universe 29
Original
1906
Earlier work this paper cites.
Fennen M and Giulini D 2020 Lie sphere geometry in lattice cosmology Class. Quantum Grav. 37
Original
1909
Earlier work this paper cites.
Lorca Espiro J and Le Delliou M 2020 Dark energy from topology J. Cosmol. Astropart. Phys. 03
Original
1910
Earlier work this paper cites.
Buchert T, Mourier P and Roy X 2020 On average properties of inhomogeneous fluids in general relativity III: general fluid cosmologies Gen. Relativ. Grav. 52
Original
1912
Earlier work this paper cites.
Lanczos C 1938 A remarkable property of the Riemann-Christoffel tensor in four dimensions Annals of Mathematics 39
1938
Earlier work this paper cites.
Chern S 1944 A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds Ann. Math. 45
1944
Earlier work this paper cites.
Huber A 1957 On subharmonic functions and differential geometry in the large Comment. Math. Helv. 32
1957
Earlier work this paper cites.
Sussman R A 2013 Weighed scalar averaging in LTB dust models, part I: statistical fluctuations and gravitational entropy Class. Quantum Grav. 30
Original
1962
Earlier work this paper cites.
Chern S 1963 Pseudo-Riemannian geometry and the Gauss-Bonnet formula An. Acad. Brasil. Ci. 35
1963
Earlier work this paper cites.
Richards I 1963 On the classification of noncompact surfaces Trans. Amer. Math. Soc. 106
1963
Earlier work this paper cites.
Geroch R 1970 Domain of Dependence J. of Math. Phys. 11
1970
Earlier work this paper cites.
Hawking S W 1971 Black holes in general relativity Commun. Math. Phys. 25
1971
Earlier work this paper cites.
Yodzis P 1974 On the expansion of closed universes Proc. Royal Irish Acad. 74A
1974
Earlier work this paper cites.
Kazdan J L Warner F W 1975 Inventiones math. 28
1975
Earlier work this paper cites.
Szekeres P 1975 A class of inhomogeneous cosmological models Comm. Math. Phys. 41
1975
Earlier work this paper cites.
Bergery L B 1981 La courbure scalaire des variétés riemanniennes Séminaire N. Bourbaki 556
1981
Earlier work this paper cites.
Jackiw R 1985 Lower dimensional gravity Nucl. Phys. B 252
1985
Earlier work this paper cites.
Besse A L 1987 Einstein manifolds Ergebnisse der Mathematik und ihrer Grenzgebiete 10
1987
Earlier work this paper cites.
Hughston L P and Tod K P 1991 An Introduction to General Relativity , Cambridge Univ. Press
1991
Earlier work this paper cites.
Bañados M, Teitelboim C and Zanelli J 1992 Black hole in three-dimensional spacetime, Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
Hulin D, Troyanov M 1992 Prescribing curvature on open surfaces Math. Ann. 293
1992
Earlier work this paper cites.
Bredon G E 1993 Topology and Geometry Graduate Texts in Mathematics , Springer-Verlag, Berlin
1993
Earlier work this paper cites.
Galloway G J 1993 On the topology of black holes Commun. Math. Phys. 151
1993
Earlier work this paper cites.
Melrose R B 1993 The Atiyah-Patodi-Singer index theorem Research notes in mathematics A K Peters/CRC Press
1993
Earlier work this paper cites.
Lohkamp J 1994 Metrics of negative Ricci curvature Annals of Mathematics 140
1994
Earlier work this paper cites.
Alty L J 1995 The generalized Gauss-Bonnet-Chern theorem J. Math. Phys. 36
1995
Earlier work this paper cites.
Bruni M, Matarrese S and Pantano O 1995 Dynamics of silent universes Astrophys. J. 445
1995
Earlier work this paper cites.
Kobayashi S and Nomizu K 1996 Foundations of Differential Geometry Volume 1 John Wiley & Sons, New York
1996
Earlier work this paper cites.
Buchert T and Ehlers J 1997 Averaging inhomogeneous Newtonian cosmologies Astron. Astrophys. 320
1997
Earlier work this paper cites.
van Elst H, Uggla C, Lesame W M, Ellis G F R and Maartens R 1997 Integrability of irrotational silent cosmological models Class. Quantum Grav. 14
1997
Earlier work this paper cites.

Similar

Krasiński A. 1997 Inhomogeneous Cosmological Models Cambridge University Press U.K
1997
Cited alongside, same era.
Mutoh H, Hirai T and Maeda K 1997 Dynamics of quiet universes Phys. Rev. D 55
1997
Cited alongside, same era.
Andersson L, Galloway G J and Howard R 1998 The cosmological time function Class. Quantum Grav. 15
1998
Cited alongside, same era.
Carlip S 1998 Quantum gravity in 2 + 1 2+1 dimensions Cambridge Monographs on Math. Phys
1998
Cited alongside, same era.
Buchert T 2000 On average properties of inhomogeneous cosmologies, In: 9th JGRG Meeting, Hiroshima 1999, Y. Eriguchi et al. (eds.), J.G.R.G. 9
1999
Cited alongside, same era.
Buchert T 2000 On average properties of inhomogeneous fluids in general relativity I: Dust cosmologies Gen. Relativ. Grav. 32

Then

Sussman R A 2011 Back-reaction and effective acceleration in generic LTB dust models Class. Quantum Grav. 28
Original
2011
Later among the works it cites.
Wiltshire D L 2011 What is dust?—Physical foundations of the averaging problem in cosmology Class. Quantum Grav. 28
Original
2011
Later among the works it cites.
Buchert T and Ostermann M 2012 Lagrangian theory of structure formation in relativistic cosmology. I. Lagrangian framework and definition of a nonperturbative approximation Phys. Rev. D 86
Original
2012
Later among the works it cites.
Buchert T and Räsänen S 2012 Backreaction in Late-Time Cosmology Annu. Rev. Nucl. Part. Sci. 62
Original
2012
Later among the works it cites.
Li N, Buchert T, Hosoya A, Morita M and Schwarz D J 2012 Relative information entropy and Weyl curvature of the inhomogeneous Universe Phys. Rev. D 86

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2000

Cited alongside, same era.

Buchert T 2001 On average properties of inhomogeneous fluids in general relativity II: Perfect fluid cosmologies Gen. Relativ. Grav. 33

2001

Cited alongside, same era.

Buchert T and Carfora M 2002 Regional averaging and scaling in relativistic cosmology Class. Quantum Grav. 19

2002

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Heinesen A and Buchert T 2020 Solving the curvature and Hubble parameter inconsistencies through structure formation-induced curvature Class. Quantum Grav. 37

Original

2002

Cited alongside, same era.

Nicolaescu L I 2003 The Reidemeister Torsion of 3–Manifolds De Gruyter Studies in Mathematics

2003

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Barbot T 2005 Globally hyperbolic flat spacetimes J. Geom. Phys. 53

2005

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Bonsante F 2005 Flat spacetimes with compact hyperbolic Cauchy surfaces J. Diff. Geom. 69

2005

Cited alongside, same era.

Original

2012