Theory (In-)Equivalence and conventionalism in f(R) gravity

Area of Science:

• Cosmology and Astrophysics
• Theoretical Physics
• Philosophy of Science

Background:

• f(R) Gravity offers a potential unified treatment of cosmic expansion.
• It is considered a natural extension of General Relativity within Riemannian Geometry.
• Recent attention in astrophysics and cosmology highlights its significance.

Purpose of the Study:

• Critically examine three inter-related claims in the f(R) Gravity literature.
• Assess the equivalence of f(R) Gravity to Brans-Dicke Theory.
• Evaluate claims regarding conventional elements in f(R) Gravity's spacetime geometry and the matter-spacetime distinction.

Main Methods:

• Philosophical and theoretical analysis of f(R) Gravity.
• Comparison with Brans-Dicke Theory.
• Examination of conventionalist arguments in spacetime geometry.

Main Results:

• The claim of f(R) Gravity's equivalence to a specific Brans-Dicke Theory is vindicated.
• Claims that f(R) Gravity's spacetime geometry has substantial conventional elements are largely unwarranted.
• The argument for conventionalism about spacetime geometry in f(R) Gravity is strengthened on different grounds.

Conclusions:

• f(R) Gravity's mathematical equivalence to a Brans-Dicke Theory is established.
• The conventionalist interpretation of spacetime geometry in f(R) Gravity requires further, distinct justification.
• A stronger case for conventionalism in f(R) Gravity and General Relativity exists beyond the examined claims.