The DOI matches its Crossref record; 29 of the 29 references it cites were found in a registry or an index.
A note on covariant conservation of energy–momentum in modified gravities
Open accessAbstract
An explicit proof of the vanishing of the covariant divergence of the energy–momentum tensor in modified theories of gravity is presented. The gravitational action is written in arbitrary dimensions and allowed to depend nonlinearly on the curvature scalar and its couplings with a scalar field. Also the case of a function of the curvature scalar multiplying a matter Lagrangian is considered. The proof is given both in the metric and in the first-order formalism, i.e. under the Palatini variational principle. It is found that the covariant conservation of energy–momentum is built in to the field equations. This crucial result, called the generalized Bianchi identity, can also be deduced directly from the covariance of the extended gravitational action. Furthermore, in all of these cases, the freely falling world lines are determined by the field equations alone and turn out to be the geodesics associated with the metric compatible connection. The independent connection in the Palatini formulation of these generalized theories does not have a similar direct physical interpretation. However, in the conformal Einstein frame a certain bi-metricity emerges into the structure of these theories.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
General relativity with spin and torsion: Foundations and prospects
Hehl, F. W., von der Heyde, P., Kerlick, G. D., & Nester, J. M. (1976) · Reviews of Modern Physics · doi:10.1103/revmodphys.48.393 · Cited by 2,709
Is cosmic speed-up due to new gravitational physics?
Carroll, S. M., Duvvuri, V., Trodden, M., & Turner, M. S. (2004) · Physical Review D · doi:10.1103/physrevd.70.043528 · Cited by 2,269
Nojiri, S., & Odintsov, S. D. (2003) · Physical Review D · doi:10.1103/physrevd.68.123512 · Cited by 2,183
Gravitation: an Introduction to current research
Witten, L. (1962) · CERN Document Server (European Organization for Nuclear Research) · Cited by 2,004
Mathematical Theory of Relativity
Eddington, A. S. (1923) · Virtual Defense Library (Ministerio de Defensa) · Cited by 879
Gravitation—An introduction to current research
Kilmister, C. W. (1963) · Planetary and Space Science · doi:10.1016/0032-0633(63)90130-2 · Cited by 729
Cosmology of generalized modified gravity models
Carroll, S. M., De Felice, A., Duvvuri, V., Easson, D. A., Trodden, M., & Turner, M. S. (2005) · Physical Review D · doi:10.1103/physrevd.71.063513 · Cited by 604
Magnano, G., & Sokołowski, L. M. (1994) · Physical Review D · doi:10.1103/physrevd.50.5039 · Cited by 426
Dark energy dominance and cosmic acceleration in first-order formalism
Allemandi, G., Borowiec, A., Francaviglia, M., & Odintsov, S. D. (2005) · Physical Review D · doi:10.1103/physrevd.72.063505 · Cited by 383
1/Rcurvature corrections as the source of the cosmological acceleration
Vollick, D. N. (2003) · Physical Review D · doi:10.1103/physrevd.68.063510 · Cited by 361
Cited by
Sotiriou, T. P., & Faraoni, V. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.451 · Cited by 4,519
Unified cosmic history in modified gravity: From F(R) theory to Lorentz non-invariant models
Nojiri, S., & Odintsov, S. D. (2011) · Physics Reports · doi:10.1016/j.physrep.2011.04.001 · Cited by 4,366
Harko, T., Lobo, F. S. N., Nojiri, S., & Odintsov, S. D. (2011) · Physical Review D · doi:10.1103/physrevd.84.024020 · Cited by 2,772
Extra force inf(R)modified theories of gravity
Bertolami, O., Böhmer, C. G., Harko, T., & Lobo, F. S. N. (2007) · Physical Review D · doi:10.1103/physrevd.75.104016 · Cited by 1,008
Nojiri, S., & Odintsov, S. D. (2006) · Physical Review D · doi:10.1103/physrevd.74.086005 · Cited by 940
Metadata
- Authors
- Koivisto, T.
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2006-06-05
- Volume
- 23
- Issue
- 12
- Pages
- 4289-4296
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2016201553
- Cited by
- 354
- References
- 29
- FWCI
- 10.61
- Type
- journal article
- Language
- en
- Open access
- bronze
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: A note on covariant conservation of energy–momentum in modified gravities. https://app.cochat.ai/papers/10.1088/0264-9381/23/12/n01
- The paper
- Koivisto, T. (2006). A note on covariant conservation of energy–momentum in modified gravities. Classical and Quantum Gravity. https://doi.org/10.1088/0264-9381/23/12/n01
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
