A geometrical ghost field and its cosmological implications

This paper studies the cosmic evolution in an extended theory of gravity obtained geometrically by transforming the normal-gauge Lyra displacement vector field \(\phi _{\mu }\) as a vectorial function depending on a dynamical scalar field \(\varphi\) with negative kinetic energy. By using the latest observational data, it is revealed that for \(\omega ^{0} = -0.98\) the geometric fluid starts behaving as dark energy at the critical scale factor \(a_{de}=0.196844\) corresponding to a redshift \(z_{de}= 4.080165\) while the universe starts accelerating at the critical scale factor \(a_{ac} = 0.625436\) corresponding to a redshift of \(z_{ac}= 0.598885\), and the age of the universe is \(t_{0}= 13.6423\) Gyr.