How Isotropic is the Universe?

A fundamental assumption in the standard model of cosmology is that the Universe is isotropic on large scales. Breaking this assumption leads to a set of solutions to Einstein’s field equations, known as Bianchi cosmologies, only a subset of which have ever been tested against data. For the first time, we consider all degrees of freedom in these solutions to conduct a general test of isotropy using cosmic microwave background temperature and polarization data from Planck. For the vector mode (associated with vorticity), we obtain a limit on the anisotropic expansion of $({\sigma }_V/H{)}_0<4.7\times {10}^{-11}$ (95% C.L.), which is an order of magnitude tighter than previous Planck results that used cosmic microwave background temperature only. We also place upper limits on other modes of anisotropic expansion, with the weakest limit arising from the regular tensor mode, $({\sigma }_{T,\text{reg}}/H{)}_0<1.0\times {10}^{-6}$ (95% C.L.). Including all degrees of freedom simultaneously for the first time, anisotropic expansion of the Universe is strongly disfavored, with odds of 121 000:1 against.

Figure 1

The CMB sky in the near-isotropic limit is formed from the addition of a standard, stochastic background for the inhomogeneities to a pattern arising from small anisotropic expansion. In this work, for the first time, we constrain all modes of the anisotropic expansion (scalar, vector, regular tensor, irregular tensor). Here we have depicted anisotropic expansion that is large compared to our limits (though still small compared to the isotropic mean) for illustrative purposes; specifically, $({\sigma }_S/H{)}_0=4.2\times {10}^{-10}$, $({\sigma }_V/H{)}_0=3.2\times {10}^{-10}$, $({\sigma }_{T,\text{reg}}/H{)}_0=1.1\times {10}^{-6}$, $({\sigma }_{T,\text{irr}}/H{)}_0=1.8\times {10}^{-8}$, with Bianchi scale parameter $x=0.62$. Each map shows temperature (left), $E$-mode polarization (upper right), and $B$-mode polarization (lower right). The overall temperature color scale for the bottom, final map is $-0.25\mathrm{mK}<T<0.25\mathrm{mK}$, with polarization amplitudes exaggerated by a factor of 30 relative to this. Other panels have been rescaled as indicated, for clarity.