f(R) gravity
E287409
f(R) gravity is a class of modified theories of gravity in which the Einstein–Hilbert action is generalized by replacing the Ricci scalar R with a function f(R), leading to alternative explanations for cosmic acceleration and gravitational phenomena.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Hu–Sawicki f(R) model | 1 |
| Palatini f(R) gravity | 1 |
| f(R) gravity canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2683217 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: f(R) gravity Context triple: [Ricci scalar, usedIn, f(R) gravity]
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A.
Gravitation and Cosmology
Gravitation and Cosmology is a landmark graduate-level textbook by Steven Weinberg that presents a comprehensive, modern treatment of general relativity and its applications to cosmology and astrophysics.
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B.
FLRW cosmological models
FLRW cosmological models are a family of solutions to Einstein’s field equations that describe a homogeneous and isotropic expanding or contracting universe, forming the standard framework for modern cosmology.
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C.
general relativity
General relativity is Albert Einstein’s theory of gravitation that describes gravity as the curvature of spacetime caused by mass and energy, successfully explaining phenomena from planetary orbits to black holes and gravitational waves.
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D.
Einstein field equations
The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
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E.
Painlevé–Gullstrand coordinates
Painlevé–Gullstrand coordinates are a coordinate system for the Schwarzschild black hole that is regular at the event horizon and represents spacetime as seen by freely falling observers.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: f(R) gravity Target entity description: f(R) gravity is a class of modified theories of gravity in which the Einstein–Hilbert action is generalized by replacing the Ricci scalar R with a function f(R), leading to alternative explanations for cosmic acceleration and gravitational phenomena.
-
A.
Gravitation and Cosmology
Gravitation and Cosmology is a landmark graduate-level textbook by Steven Weinberg that presents a comprehensive, modern treatment of general relativity and its applications to cosmology and astrophysics.
-
B.
FLRW cosmological models
FLRW cosmological models are a family of solutions to Einstein’s field equations that describe a homogeneous and isotropic expanding or contracting universe, forming the standard framework for modern cosmology.
-
C.
general relativity
General relativity is Albert Einstein’s theory of gravitation that describes gravity as the curvature of spacetime caused by mass and energy, successfully explaining phenomena from planetary orbits to black holes and gravitational waves.
-
D.
Einstein field equations
The Einstein field equations are the core mathematical framework of general relativity, relating the curvature of spacetime to the distribution of matter and energy.
-
E.
Painlevé–Gullstrand coordinates
Painlevé–Gullstrand coordinates are a coordinate system for the Schwarzschild black hole that is regular at the event horizon and represents spacetime as seen by freely falling observers.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
gravitational theory
ⓘ
modified theory of gravity ⓘ |
| affects |
Einstein field equations
ⓘ
surface form:
Friedmann equations in cosmology
|
| aimsToExplain |
cosmic acceleration
ⓘ
dark energy phenomenology without explicit dark energy ⓘ late-time acceleration of the universe ⓘ |
| basedOn | generalization of Einstein–Hilbert action ⓘ |
| belongsTo | class of higher-order gravity theories ⓘ |
| canBeReformulatedAs | scalar–tensor theory ⓘ |
| constrains | functional form of f(R) by stability conditions ⓘ |
| definedIn | four-dimensional spacetime in standard cosmological applications ⓘ |
| developedIn | late 20th century and early 21st century theoretical physics ⓘ |
| fieldEquations | fourth-order differential equations in the metric formalism ⓘ |
| generalizes |
Einstein–Hilbert action
ⓘ
surface form:
Einstein–Hilbert Lagrangian density
|
| hasExample |
Appleby–Battye f(R) model
ⓘ
Carroll et al. 1/R model ⓘ f(R) gravity self-linksurface differs ⓘ
surface form:
Hu–Sawicki f(R) model
Starobinsky R^2 inflation model ⓘ
surface form:
Starobinsky R + R^2 inflationary model
|
| hasVariant |
f(R) gravity
self-linksurface differs
ⓘ
surface form:
Palatini f(R) gravity
metric f(R) gravity ⓘ metric-affine f(R) gravity ⓘ |
| introduces | extra scalar degree of freedom ⓘ |
| isConstrainedBy |
baryon acoustic oscillation data
ⓘ
binary pulsar timing ⓘ cosmic microwave background observations ⓘ galaxy clustering measurements ⓘ gravitational wave observations ⓘ local gravity experiments ⓘ type Ia supernova observations ⓘ weak lensing surveys ⓘ |
| modifies | general relativity ⓘ |
| mustSatisfy |
Dolgov–Kawasaki stability condition in viable models
ⓘ
positivity of effective gravitational coupling in viable models ⓘ |
| predicts |
modified gravitational lensing in some models
ⓘ
modified growth of cosmological perturbations ⓘ scale-dependent effective gravitational constant ⓘ |
| replaces | Ricci scalar R with function f(R) ⓘ |
| requires | chameleon or screening mechanisms to satisfy local gravity tests in many models ⓘ |
| studiedIn |
Palatini formalism
ⓘ
metric formalism ⓘ metric-affine formalism ⓘ |
| subjectOf |
cosmological parameter constraints
ⓘ
solar system tests of gravity ⓘ viability conditions such as stability and absence of ghosts ⓘ |
| usedIn |
cosmology
ⓘ
dark energy model building ⓘ inflationary model building ⓘ large-scale structure formation studies ⓘ |
| uses | function of Ricci scalar ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: f(R) gravity Description of subject: f(R) gravity is a class of modified theories of gravity in which the Einstein–Hilbert action is generalized by replacing the Ricci scalar R with a function f(R), leading to alternative explanations for cosmic acceleration and gravitational phenomena.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Palatini f(R) gravity
this entity surface form:
Hu–Sawicki f(R) model