Dark Energy From Dynamical Projective Connections

We further develop the gravitational model, Thomas-Whitehead Gravity (TW Gravity), that arises when projective connections become dynamical fields. TW Gravity has its origins in geometric actions from string theory where the TW projective connection appears as a rank two tensor, \(\mathcal{D}_{ab}\), on the spacetime manifold. Using a Gauss-Bonnet (GB) action built from the \((\mathrm{d}+1)\)-dimensional TW connection, and applying the tensor decomposition \(\mathcal{D}_{ab} = D_{ab} + 4\Lambda /(\mathrm{d}(\mathrm{d}-1)) g_{ab}\), we arrive at a gravitational model made up of a \(\mathrm{d}\)-dimensional Einstein-Hilbert + GB action sourced by \(D_{ab}\) and with cosmological constant \(\Lambda\). The \(\mathrm{d}=4\) action is studied and we find that \(\Lambda \propto 1/J_0\), with \(J_0\) the coupling constant for \(D_{ab}\). For \(\Lambda\) equal to the current measured value, \(J_0\) is on the order of the measured angular momentum of the observable Universe. We view this as \(\Lambda\) controlling the scale of patches of the Universe that acquire angular momentum, with the net angular momentum of multiple patches vanishing, as required by the cosmological principle. We further find a universal axial scalar coupling to all fermions where the trace, \(\mathcal{D} = \mathcal{D}_{ab}g^{ab}\) acts as the scalar. This suggests that \(\mathcal{D}\) is also a dark matter portal for non-standard model fermions.