Detailed study of the scalar and tensor perturbation spectra can provide much information about the primordial fluctuation-generator , be it inflation or something else .
The tensor perturbation spectrum may be observable through its influence on CMB polarization , but only if the tensor-to-scalar ratio , r \equiv T / S , is greater than about 10 ^ { -5 } .
The tensor tilt can be measured with an error of \sigma ( n _ { T } ) that decreases with r from 0.1 at r = 0.001 to 0.02 at r = 0.1 .
Current CMB constraints on the scalar perturbation spectrum can be improved by higher–resolution CMB observations and/or by tomographic cosmic shear observations .
These can both shrink errors on the tilt ( n _ { S } ) and running ( n _ { S } ^ { \prime } \equiv dn _ { S } / d \ln k ) to the 10 ^ { -3 } level .
Stunning as these results would be , it may become very desirable to improve upon them an order of magnitude further in order to study the expected departures from n _ { S } ^ { \prime } = 0 .
Such improvements are likely to require observation of three–dimensional clustering over very large volumes .
Unfortunately , to get down to the 10 ^ { -4 } level will require a sparse spectroscopic redshift survey with about 10 ^ { 9 } galaxies spread over a volume less than but comparable to that of the observable Universe .