We present an improved analysis of the final dataset from the QUaD experiment. Using an improved technique to remove ground contamination, we double the effective sky area and hence increase the precision of our CMB power spectrum measurements by ~30% versus that previously reported. In addition, we have improved our modeling of the instrument beams and have reduced our absolute calibration uncertainty from 5% to 3.5% in temperature. The robustness of our results is confirmed through extensive jackknife tests and by way of the agreement we find between our two fully independent analysis pipelines. For the standard 6-parameter LCDM model, the addition of QUaD data marginally improves the constraints on a number of cosmological parameters over those obtained from the WMAP experiment alone. The impact of QUaD data is significantly greater for a model extended to include either a running in the scalar spectral index, or a possible tensor component, or both. Adding both the QUaD data and the results from the ACBAR experiment, the uncertainty in the spectral index running is reduced by ~25% compared to WMAP alone, while the upper limit on the tensor-to-scalar ratio is reduced from r < 0.48 to r < 0.33 (95% c.l). This is the strongest limit on tensors to date from the CMB alone. We also use our polarization measurements to place constraints on parity violating interactions to the surface of last scattering, constraining the energy scale of Lorentz violating interactions to < 1.5 x 10^{-43} GeV (68% c.l.). Finally, we place a robust upper limit on the strength of the lensing B-mode signal. Assuming a single flat band power between l = 200 and l = 2000, we constrain the amplitude of B-modes to be < 0.57 micro-K^2 (95% c.l.).
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