Recently a Born-Infeld action for dark energy and dark matter that uses additional affine connections was proposed. At the background level, it was shown that the new proposal can mimic the standard cosmological evolution. In Bianchi cosmologies, contrary to the scalar field approach (e.g., Chaplygin gas), the new approach leads to anisotropic pressure, raising the issues of stability of the isotropic solution under anisotropic perturbations and, being stable, how the anisotropies evolve. In this work, the Eddington-Born-Infeld proposal is extended to a Bianchi type I scenario and residual post-inflationary anisotropies are shown to decay in time. Moreover, it is shown that the shears decay following a damped oscillatory pattern, instead of the standard exponential-like decay. Allowing for some fine-tuning on the initial conditions, standard theoretical bounds on the shears can be avoided.

• Received 30 June 2008

DOI:https://doi.org/10.1103/PhysRevD.78.063013