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In the context of gravity (general relativity), higher curvature corrections are modifications of the Einstein-Hilbert action that include not just the linear appearance of the scalar curvature $R$ but higher scalar powers of the Riemann curvature tensor.
When viewing Einstein-Hilbert gravity as an effective field theory valid at low energy/long wavelengths, then higher curvature corrections are precisely the terms that may appear at higher energy in pure gravity. Notably the effective field theories induced by string theory come with infinite towers of higher curvature corrections.
In the context of cosmology, higher curvature corrections are a candidate for the inflaton field, see at Starobinsky model of cosmic inflation.
A spacetime that extremizes the Einstein-Hilbert action for given cosmological constant and arbitrary higher curvature correction is called a universal spacetime.
A systematic analysis of the possible supersymmetric higher curvature corrections of D=11 supergravity makes the I8-characteristic 8-form
(a differential form built from the Riemann curvature, expressing a polynomial in the first and second Pontryagin classes, see at I8) appear as the higher curvature correction at order $\ell^6$, where $\ell$ is the Planck length in 11d (Souères-Tsimpis 17, Section 4).
At this order, the equation of motion for the supergravity C-field flux $G_4$ and its dual $G_7$ is (Souères-Tsimpis 17, (4.3))
where the flux forms themselves appear in their higher order corrected form as power series in the Planck length
Beware that this is not the lowest order higher curvature correction: there is already one at $\mathcal{O}(\ell^3)$, given by $\ell^3 G_4 \wedge \tfrac{1}{2}p_1(R)$ (Souères-Tsimpis 17, Section 3.2). Hence the full correction at $\mathcal{O}(\ell^3)$ should be the further modification of (2) to
Discussion of quadratic curvature currections includes (see also at Starobinsky model of cosmic inflation)
Discussion of causal locality in the presence of higher curvature corrections includes
Xian O. Camanho, Jose D. Edelstein, Juan Maldacena, Alexander Zhiboedov, Causality Constraints on Corrections to the Graviton Three-Point Coupling (arXiv:)
Giuseppe D’Appollonio, Paolo Di Vecchia, Rodolfo Russo, Gabriele Veneziano, Regge behavior saves String Theory from causality violations (arXiv:1502.01254)
Discussion in the context of corrections to black hole entropy include
Discussion of higher curvature corrections in cosmology and cosmic inflation (for more see at Starobinsky model of cosmic inflation):
Gustavo Arciniega, Jose D. Edelstein, Luisa G. Jaime, Towards purely geometric inflation and late time acceleration (arXiv:1810.08166)
Gustavo Arciniega, Pablo Bueno, Pablo A. Cano, Jose D. Edelstein, Robie A. Hennigar, Luisa G. Jaimem, Geometric Inflation (arXiv:1812.11187)
Discussion of higher curvature corrections to 11-dimensional supergravity includes
Arkady Tseytlin, $R^4$ terms in 11 dimensions and conformal anomaly of (2,0) theory, Nucl. Phys. B584: 233-250, 2000 (arXiv:hep-th/0005072)
Kasper Peeters, Pierre Vanhove, Anders Westerberg, Supersymmetric $R^4$ actions and quantum corrections to superspace torsion constraints (arXiv:hep-th/0010182)
H. Lu, Christopher Pope, Kellogg Stelle, Paul Townsend, Supersymmetric Deformations of $G_2$ Manifolds from Higher-Order Corrections to String and M-Theory, JHEP 0410:019, 2004 (arXiv:hep-th/0312002)
(specifically for M-theory on G2-manifolds)
H. Lu, Christopher Pope, Kellogg Stelle, Paul Townsend, String and M-theory Deformations of Manifolds with Special Holonomy, JHEP 0507:075, 2005 (arXiv:hep-th/0410176)
(specifically for M-theory on G2-manifolds)
Dimitrios Tsimpis, 11D supergravity at $\mathcal{O}(\ell^3)$, JHEP0410:046, 2004 (arXiv:hep-th/0407271)
Paul Howe, $R^4$ terms in supergravity and M-theory (arXiv:hep-th/0408177)
Martin Cederwall, Ulf Gran, Bengt Nilsson, Dimitrios Tsimpis, Supersymmetric Corrections to Eleven-Dimensional Supergravity, JHEP0505:052, 2005 (arXiv:hep-th/0409107)
Yoshifumi Hyakutake, Sachiko Ogushi, $R^4$ Corrections to Eleven Dimensional Supergravity via Supersymmetry, Phys.Rev. D74 (2006) 025022 (arXiv:hep-th/0508204)
Yoshifumi Hyakutake, Sachiko Ogushi, Higher Derivative Corrections to Eleven Dimensional Supergravity via Local Supersymmetry, JHEP0602:068, 2006 (arXiv:hep-th/0601092)
Anirban Basu, Constraining gravitational interactions in the M theory effective action, Classical and Quantum Gravity, Volume 31, Number 16, 2014 (arXiv:1308.2564)
Bertrand Souères, Dimitrios Tsimpis, The action principle and the supersymmetrisation of Chern-Simons terms in eleven-dimensional supergravity, Phys. Rev. D 95, 026013 (2017) (arXiv:1612.02021)
(discussion of I8 in Section 4)
and from the ABJM model:
Discussion in view of the Starobinsky model of cosmic inflation is in
Katrin Becker, Melanie Becker, Supersymmetry Breaking, M-Theory and Fluxes, JHEP 0107:038,2001 (arXiv:hep-th/0107044)
Kazuho Hiraga, Yoshifumi Hyakutake, Inflationary Cosmology via Quantum Corrections in M-theory (arXiv:1809.04724)
Kazuho Hiraga, Yoshifumi Hyakutake, Scalar Cosmological Perturbations in M-theory with Higher Derivative Corrections (arxiv:1910.12483)
and in view of de Sitter spacetime vacua:
Last revised on November 10, 2019 at 08:31:47. See the history of this page for a list of all contributions to it.