Maxwell extension of f(R) gravity
Oktay Cebecioǧlu, Ahmet Saban, Salih Kibaroğlu
Abstract
Abstract Inspired by the Maxwell symmetry generalization of general relativity (Maxwell gravity), we have constructed the Maxwell extension of f ( R ) gravity. We found that the semi-simple extension of the Poincare symmetry allows us to introduce geometrically a cosmological constant term in four-dimensional f ( R ) gravity. This symmetry also allows the introduction of a non-vanishing torsion to the Maxwell f ( R ) theory. It is found that the antisymmetric gauge field $$B^{ab}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>B</mml:mi> <mml:mrow> <mml:mi>ab</mml:mi> </mml:mrow> </mml:msup> </mml:math> associated with Maxwell extension is considered as a source of the torsion. It is also found that the gravitational equation of motion acquires a new term in the form of an energy–momentum tensor for the background field. The importance of these new equations is briefly discussed.