Born-Infeld-type gravity

Generalizations of gravitational Born-Infeld type Lagrangians are investigated. Phenomenological constraints (reduction to Einstein-Hilbert action for small curvature, spin-two ghost freedom, and absence of Coulomb-like Schwarschild singularity) select one effective Lagrangian whose dynamics is dictated by the tensors $g_{\mu \nu }$ and ${\mathcal{R}}_{\mu \nu \rho \sigma }$ (not $R_{\mu \nu }$ or the scalar $R$).

Figure 1

Here we show the possible saturation patterns for the case $n=2$. In (a) we saturate with four 2-index symmetric tensors; in (b) we saturate with two 2-index tensors and one 4-index tensor; In (c) we saturate with two 4-index tensors. The black points indicate the four indices for each $e^{{\mu }_i{\nu }_i{\rho }_i{\sigma }_i}$ pseudotensor ($i=1$, 2).

Figure 2

The black points represent the indices of the four $e^{{\mu }_i{\nu }_i{\rho }_i{\lambda }_i}$ pseudotensors ($i=1$, 2, 3, 4) while the colored dashed curves are the way each ${\mathcal{G}}_{{\mu }_i{\nu }_i{\rho }_i{\lambda }_i}$ tensor saturates the respective $e$-tensors. The first case (a) is describing Eq. (29) while the case (b) is for Eq. (30).

Figure 3

$\alpha -\beta$ parameter space for $m_0$ (straight line) and $\Lambda$ (dotted line) zero values, in the case with $R_0\ne 0$.