Journal ArticleDOI
The uniqueness of the einstein field equations in a four-dimensional space.
TLDR
In this article, the Euler-Lagrange equations corresponding to a Lagrange density which is a function of g ≥ 2 and its first two derivatives are investigated and necessary and sufficient conditions for these equations to be of second order are obtained and it is shown that in a four-dimensional space the Einstein field equations (with cosmological term) are the only permissible second order Euler Lagrange equations.Abstract:
The Euler-Lagrange equations corresponding to a Lagrange density which is a function of g
ij and its first two derivatives are investigated. In general these equations will be of fourth order in g
ij. Necessary and sufficient conditions for these Euler-Lagrange equations to be of second order are obtained and it is shown that in a four-dimensional space the Einstein field equations (with cosmological term) are the only permissible second order Euler-Lagrange equations. This result is false in a space of higher dimension. Furthermore, the only permissible third order equation in the four-dimensional case is exhibited.read more
Citations
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The Einstein Tensor and Its Generalizations
TL;DR: In this paper, the number of independent tensors of this type depends crucially on the dimension of the space, and, in the four dimensional case, the only tensors with these properties are the metric and the Einstein tensors.
Journal ArticleDOI
Second-order scalar-tensor field equations in a four-dimensional space
TL;DR: In this article, the second-order Euler-Lagrange tensors are derived from a Lagrangian which is at most of second order in the derivatives of the field functions.
Journal ArticleDOI
The four-dimensionality of space and the einstein tensor
Abstract: All tensors of contravariant valency two, which are divergence free on one index and which are concomitants of the metric tensor, together with its first two derivatives, are constructed in the four‐dimensional case. The Einstein and metric tensors are the only possibilities.
Journal ArticleDOI
Beyond ΛCDM: Problems, solutions, and the road ahead
Philip Bull,Yashar Akrami,Julian Adamek,Tessa Baker,Emilio Bellini,Jose Beltrán Jiménez,Eloisa Bentivegna,Stefano Camera,Sebastien Clesse,Jonathan H. Davis,Enea Di Dio,Jonas Enander,Alan Heavens,Lavinia Heisenberg,Bin Hu,Claudio Llinares,Roy Maartens,Edvard Mörtsell,Seshadri Nadathur,Johannes Noller,Roman Pasechnik,Marcel S. Pawlowski,Thiago S. Pereira,Miguel Quartin,A. Ricciardone,Signe Riemer-Sørensen,Massimiliano Rinaldi,Jeremy Sakstein,Ippocratis D. Saltas,Vincenzo Salzano,Ignacy Sawicki,Adam R. Solomon,Adam R. Solomon,Adam R. Solomon,Douglas Spolyar,Glenn D. Starkman,Daniele A. Steer,Ismael Tereno,L. Verde,Francisco Villaescusa-Navarro,Mikael von Strauss,Hans A. Winther +41 more
TL;DR: There is a persistent interest in extending cosmology beyond the standard model, ΛCDM, motivated by a range of apparently serious theoretical issues, involving such questions as the cosmological constant problem, the particle nature of dark matter, the validity of general relativity on large scales, the existence of anomalies in the CMB and on small scales, and the predictivity and testability of the inflationary paradigm as mentioned in this paper.
Journal ArticleDOI
Beyond $\Lambda$CDM: Problems, solutions, and the road ahead
Philip Bull,Yashar Akrami,Julian Adamek,Tessa Baker,Emilio Bellini,Jose Beltrán Jiménez,Eloisa Bentivegna,Stefano Camera,Sebastien Clesse,Jonathan H. Davis,Enea Di Dio,Jonas Enander,Alan Heavens,Lavinia Heisenberg,Bin Hu,Claudio Llinares,Roy Maartens,Edvard Mörtsell,Seshadri Nadathur,Johannes Noller,Roman Pasechnik,Marcel S. Pawlowski,Thiago S. Pereira,Miguel Quartin,Angelo Ricciardone,Signe Riemer-Sørensen,Massimiliano Rinaldi,Jeremy Sakstein,Ippocratis D. Saltas,Vincenzo Salzano,Ignacy Sawicki,Adam R. Solomon,Douglas Spolyar,Glenn D. Starkman,Daniele A. Steer,Ismael Tereno,Licia Verde,Francisco Villaescusa-Navarro,Mikael von Strauss,Hans A. Winther +39 more
TL;DR: There is a persistent interest in extending cosmology beyond the standard model, $\Lambda$CDM as discussed by the authors, motivated by a range of apparently serious theoretical issues, involving such questions as the cosmological constant problem, the particle nature of dark matter, the validity of general relativity on large scales, the existence of anomalies in the CMB and on small scales, and the predictivity and testability of the inflationary paradigm.
References
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A Remarkable property of the Riemann-Christoffel tensor in four dimensions
TL;DR: In this paper, it was shown that two invariants are inactive in the formation of field equations and thus may be omitted from the integrand of the action principle, i.e., I, = Ra, 6Ra# and 12 = R2.