We present new results for the 3-point correlation function , \zeta , measured as a function of scale , luminosity and colour from the final version of the two-degree field galaxy redshift survey ( 2dFGRS ) .
The reduced three point correlation function , Q _ { 3 } \sim \zeta / \xi ^ { 2 } , is estimated for different triangle shapes and sizes , employing a full covariance analysis .
The form of Q _ { 3 } is consistent with the expectations for the \Lambda -cold dark matter model , confirming that the primary influence shaping the distribution of galaxies is gravitational instability acting on Gaussian primordial fluctuations .
However , we find a clear offset in amplitude between Q _ { 3 } for galaxies and the predictions for the dark matter .
We are able to rule out the scenario in which galaxies are unbiased tracers of the mass at the 9- \sigma level .
On weakly non-linear scales , we can interpret our results in terms of galaxy bias parameters .
We find a linear bias term that is consistent with unity , b _ { 1 } = 0.93 ^ { +0.10 } _ { -0.08 } and a quadratic bias c _ { 2 } = b _ { 2 } / b _ { 1 } = -0.34 ^ { +0.11 } _ { -0.08 } .
This is the first significant detection of a non-zero quadratic bias , indicating a small but important non-gravitational contribution to the three point function .
Our estimate of the linear bias from the three point function is independent of the normalisation of underlying density fluctuations , so we can combine this with the measurement of the power spectrum of 2dFGRS galaxies to constrain the amplitude of matter fluctuations .
We find that the rms linear theory variance in spheres of radius 8 h ^ { -1 } Mpc is \sigma _ { 8 } = 0.88 ^ { +0.12 } _ { -0.10 } , providing an independent confirmation of values derived from other techniques .
On non-linear scales , where \xi > 1 , we find that Q _ { 3 } has a strong dependence on scale , colour and luminosity .