Constraints on the anisotropy of dark energy

Abstract

If the equation of state of dark energy is anisotropic there will be additional quadrupole anisotropy in the cosmic microwave background induced by the time dependent anisotropic stress quantified in terms of $\Delta w$. Assuming that the entire amplitude of the observed quadrupole is due to this anisotropy, we conservatively impose a limit of $|\Delta w|<2.1\times 10^{-4}$ for any value of $w\ge -1$ assuming that ${\Omega }_{\mathrm{m}}<0.5$. This is considerably tighter than that which comes from SNe. Stronger limits, upto a factor of 10, are possible for specific values of ${\Omega }_{\mathrm{m}}$ and $w$. Since we assume this component is uncorrelated with the stochastic component from inflation, we find that both the expectation value and the sample variance are increased. There no improvement in the likelihood of an anomalously low quadrupole as suggested by previous work on an elliptical universe.

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