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The redshift of matter-dark energy equality is 0.4. Suppose we see a large-scale overdensity in the CMB last-scattering surface, with fractional density fluctuation amplitude of

The redshift of matter-dark energy equality is 0.4. Suppose we see a large-scale overdensity in the CMB last-scattering surface, with fractional density fluctuation amplitude of 2 *10^-5. What size would the fractional overdensity be today? (This region is too large to have collapsed into a halo by today.) Note: the CMB is at redshift of 1090; fluctuations stop growing after dark energy domination (you can assume the transition to be instantaneous at z = 0.4). (Science note: since this overdensity is 13 comoving Gpc away from us, it is too far away for us to see the larger density fluctuation that it grew into by today! But the cosmological principle tells us that the average numbers of such overdense regions should be the same in our local universe.) Give your answer in scientific notation to two significant figures (one decimal place)

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