Bianchi type I expanding universe in Weyl-invariant massive gravity

We will study the cosmological evolutions of a Weyl-invariant de Rham, Gabadadze, and Tolley (dRGT) massive gravity theory with a general fiducial metric. In the unitary gauge, this model is equivalent to a massive gauge field coupled to the dRGT massive gravity model. The massive gravity terms will serve as an effective cosmological constant for all metric spaces if the fiducial metric is treated as an auxiliary field. A further discussion will also be addressed on the bimetric theory. In particular, we will discuss the role played by the Weyl vector boson in Bianchi type I expanding space.

Figure 1

(a) The dotted curve $L$ is described by the equation ${\dot{\alpha }}_{e}p+\kappa q=0$. The solid curves are the contour evolution of the numerical solutions to Eq. (8.65) with the constants and initial conditions chosen as $\kappa =1$, ${\mathrm{\Lambda }}_e=3$, $p(0)=q(0)=1$, $\alpha (0)=0,\dot{\alpha }(0)=1$, ${\sigma }_{+}(0)=0$, and ${\dot{\sigma }}_{+}(0)=-1$. (b) Thick red line is the same as the red line contour shown in (a). Blue and thin green lines are the contours with ${\dot{\sigma }}_{+}(0)=0$ and ${\dot{\sigma }}_{+}(0)=1$, respectively. The rest of the chosen constants and initial conditions are the same as the constants and initial conditions of the red line shown in (a).