There are evidences that the cosmic microwave background (CMB) large-angle anomalies imply a departure from statistical isotropy and hence from the standard cosmological model. We propose a $\Lambda \mathrm{CDM}$ model extension whose dark energy component preserves its nondynamical character but wields anisotropic vacuum pressure. Exact solutions for the cosmological scale factors are presented, upper bounds for the deformation parameter are evaluated and its value is estimated considering the elliptical universe proposal to solve the quadrupole anomaly. This model can be constructed from a Bianchi I cosmology with a cosmological constant from two different ways: (i) a straightforward anisotropic modification of the vacuum pressure consistently with energy-momentum conservation; (ii) a Poisson structure deformation between canonical momenta such that the dynamics remain invariant under scale factors rescalings.

• Received 9 August 2007

DOI:https://doi.org/10.1103/PhysRevD.77.023534