Dark Energy From Dynamical Projective Connections

Abstract

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.

arXiv comment49 pages. Made revisions required for acceptance to the journal Classical and Quantum Gravity

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Cited by in corpus (6)

• General structure of Thomas$-$Whitehead gravity
• Inflation from Dynamical Projective Connections
• Covariant and Manifestly Projective Invariant Formulation of Thomas-Whitehead Gravity
• Nöther Currents, Black Hole Entropy Universality and CFT Duality in Conformal Weyl Gravity
• The modified Newton attraction law and its connection with cosmological $\Lambda$--term
• Constraint Analysis and Quantization of Anomalous 2-D Thomas-Whitehead Gravity