We show how to use multiple tracers of large-scale density with different biases to measure the redshift-space distortion parameter \beta \equiv b ^ { -1 } f \equiv b ^ { -1 } d \ln D / d \ln a ( where D is the growth rate and a the expansion factor ) , to a much better precision than one could achieve with a single tracer , to an arbitrary precision in the low noise limit .
In combination with the power spectrum of the tracers this allows a much more precise measurement of the bias-free velocity divergence power spectrum , f ^ { 2 } P _ { m } – in fact , in the low noise limit f ^ { 2 } P _ { m } can be measured as well as would be possible if velocity divergence was observed directly , with rms improvement factor \sim \left [ 5.2 \left ( \beta ^ { 2 } +2 \beta + 2 \right ) / \beta ^ { 2 } \right ] ^ { 1 / 2 } ( e.g. , \simeq 10 times better than a single tracer for \beta = 0.4 ) .
This would allow a high precision determination of fD as a function of redshift with an error as low as 0.1 % .
We find up to two orders of magnitude improvement in Figure of Merit for the Dark Energy equation of state relative to Stage II , a factor of several better than other proposed Stage IV Dark Energy surveys .
The ratio b _ { 2 } / b _ { 1 } will be determined with an even greater precision than \beta , producing , when measured as a function of scale , an exquisitely sensitive probe of the onset of non-linear bias .
We also extend in more detail previous work on the use of the same technique to measure non-Gaussianity .
Currently planned redshift surveys are typically designed with signal to noise of unity on scales of interest , and are not optimized for this technique .
Our results suggest that this strategy may need to be revisited as there are large gains to be achieved from surveys with higher number densities of galaxies .