Abstract
We explore the possibility of further gravitational wave modes in F(T) gravity, where T is the torsion scalar in teleparallelism. It is explicitly demonstrated that gravitational wave modes in F(T) gravity are equivalent to those in General Relativity. This result is achieved by calculating the Minkowskian limit for a class of analytic function of F(T). This consequence is also confirmed by the preservative analysis around the flat background in the weak field limit with the scalar–tensor representation of F(T) gravity.
Highlights
It has been suggested from recent precise cosmological observations [1,2,3,4,5] that if the current universe is considered to strictly be homogeneous, there exist dark matter and baryons and the so-called ”dark energy”, whose contribute provides a negative pressure able to accelerate the universe today
On the other hand, supposing that gravitational waves are directly detected, by analyzing gravitational wave modes in Extended Theories of Gravity [7], which can explain the current cosmic acceleration, and those in General Relativity and comparing those modes with the observations, it is possible to judge, in principle, whether the origin of dark energy is geometric or not, that is, gravitation is described by Extended Theories of Gravity
Apart from the fundamental physics reasons, Extended Theories of Gravity have taken hold in cosmology, thanks to the fact that they “naturally” exhibit inflationary behaviors and are able to overcome the shortcomings of Standard Cosmological Model [10, 11]
Summary
Where Γρ νμ ≡ hρA∂μhAν is the Weitzenbock connection. We construct the contorsion tensor Kμνρ ≡ − (1/2). Tρ μν using the torsion and contorsion tensors, we obtain the so-called superpotential Sρ μν ≡ (1/2). As a result, combining the torsion tensor and the superpotential leads to scalar
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