$f(R)$ gravity with torsion and the Immirzi field: Signature for gravitational wave detection

We propose a Nieh-Yan extension of $f(R)$ models in the presence of Immirzi field and the resulting theory is studied in the context of first-order formalism. We claim in our model that the ambiguities related to the Palatini approach are solved, allowing us to fully solve the theory in terms of the Immirzi field. In particular, we analyze within such a theoretical framework the propagation of gravitational waves in vacuum, and we outline that a dynamical Immirzi field could be regarded as a propagating torsion field with nontrivial and detectable effects on standard gravitational polarizations.

Figure 1

The lines of the tangential forces related to the $\beta$-mode for $\sin \omega t>0$ (the direction of arrows reverses for $\sin \omega t<0$). With the black solid lines are shown the standard polarizations ($\epsilon =0$).

Figure 2

The lines of force related to the case $0<\epsilon <1$ for $\sin \omega t>0$ (the direction of arrows reverses for $\sin \omega t<0$). With the black solid lines are shown the standard polarizations ($\epsilon =0$), whereas with the red solid lines the effective cross mode.

Figure 3

The lines of force related to the case $\epsilon >1$ for $\sin \omega t>0$ (the direction of arrows reverses for $\sin \omega t<0$). With the black solid lines the standard polarizations are shown.

Figure 4

The lines of force related to the case $\epsilon =1$ for $\sin \omega t>0$ (the direction of arrows reverses for $\sin \omega t<0$). With the black solid lines the standard polarizations are shown, whereas the colored solid lines represent the strain stresses.