Conformal gravity and F(R) gravity

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Difference between Conformal gravity and F(R) gravity

Conformal gravity vs. F(R) gravity

Conformal gravity are gravity theories that are invariant under conformal transformations in the Riemannian geometry sense; more accurately, they are invariant under Weyl transformations g_\rightarrow\Omega^2(x)g_ where g_ is the metric tensor and \Omega(x) is a function on spacetime. f(R) gravity is a type of modified gravity theory which generalizes Einstein's general relativity.

Dark energy

In physical cosmology and astronomy, dark energy is an unknown form of energy which is hypothesized to permeate all of space, tending to accelerate the expansion of the universe.

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Dark matter

Dark matter is a theorized form of matter that is thought to account for approximately 80% of the matter in the universe, and about a quarter of its total energy density.

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Einstein–Hilbert action

The Einstein–Hilbert action (also referred to as Hilbert action) in general relativity is the action that yields the Einstein field equations through the principle of least action.

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General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

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Lagrangian (field theory)

Lagrangian field theory is a formalism in classical field theory.

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Metric tensor

In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors and at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.

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Ricci curvature

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, represents the amount by which the volume of a small wedge of a geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space.

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Scalar curvature

In Riemannian geometry, the scalar curvature (or the Ricci scalar) is the simplest curvature invariant of a Riemannian manifold.

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Weyl tensor

In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian manifold.

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