A B S T R A C TAdams et al. have noted that according to our current understanding of the unification of fundamental interactions, there should have been phase transitions associated with spontaneous symmetry breaking during the inflationary era. This may have resulted in the breaking of scale-invariance of the primordial density perturbation for brief periods. A possible such feature was identified in the power spectrum of galaxy clustering in the automated plate measurement (APM) survey at the scale k , 0:1 h Mpc 2 1 and it was shown that the secondary acoustic peaks in the power spectrum of the cosmic microwave background (CMB) anisotropy should consequently be suppressed. We demonstrate that this prediction is confirmed by the recent Boomerang and Maxima observations, which favour a step-like spectral feature in the range k , ð0:06-0:6Þ h Mpc 2 1 , independently of the similar previous indication from the APM data. Such a spectral break enables an excellent fit to both APM and CMB data with a baryon density consistent with the big bang nucleosynthesis (BBN) value. It also allows the possibility of a matter-dominated universe with zero cosmological constant, which we show can now account for even the evolution of the abundance of rich clusters.

This paper presents a comparison of the predictions for the two‐ and three‐point correlation functions of density fluctuations, ξ and ζ, in gravitational perturbation theory (PT) against large cold dark matter (CDM) simulations. This comparison is made possible for the first time on large weakly non‐linear scales (>10 h−1 Mpc) thanks to the development of a new algorithm for estimating correlation functions for millions of points in only a few minutes. Previous studies in the literature comparing the PT predictions of the three‐point statistics with simulations have focused mostly on Fourier space, angular space or smoothed fields. Results in configuration space, such as those presented here, were limited to small scales where leading‐order PT gives a poor approximation. Here we also propose and apply a method for separating the first‐order and subsequent contributions to PT by combining different output times from the evolved simulations. We find that in all cases there is a regime where simulations do reproduce the leading‐order (tree‐level) predictions of PT for the reduced three‐point function Q3∼ζ/ξ2. For steeply decreasing correlations (such as the standard CDM model) deviations from the tree‐level results are important even at relatively large scales, ≃20 Mpc h−1. On larger scales ξ goes to zero and the results are dominated by sampling errors. In more realistic models (such as the ΛCDM cosmology) deviations from the leading‐order PT become important at smaller scales r≃10 Mpc h‐1, although this depends on the particular three‐point configuration. We characterize the range of validity of this agreement and show the behaviour of the next‐order (one‐loop) corrections.

We address the problem of encoding and compressing data dominated by noise. Information is decomposed into ‘reference’ sequences plus arrays containing noisy differences susceptible to being described by a known probability distribution. One can then give reliable estimates of the optimal compression rates by estimating the corresponding Shannon entropy. As a working example, this idea is applied to an idealized model of the cosmic microwave background (CMB) data on board the Planck satellite. Data reduction is a critical issue in space missions because the total information that can be downloaded to Earth is sometimes limited by telemetry allocation. Similar limitations might arise in remotely operated ground based telescopes. This download‐rate limitation could reduce the amount of diagnostics sent on the stability of the instruments and, as a consequence, curb the final sensitivity of the scientific signal. Our proposal for Planck consists of taking differences of consecutive circles at a given sky pointing. To a good approximation, these differences could be made independent of the external signal, so that they are dominated by thermal (white) instrumental noise, which is simpler to model than the sky signal. Similar approaches can be found in other individual applications. Generic simulations and analytical predictions show that high compression rates, can be obtained with minor or zero loss of sensitivity. Possible effects of digital distortion are also analysed. The proposed scheme is flexible and reliable enough to be optimized in relation to other critical aspects of the corresponding application. For Planck, this study constitutes an important step towards a more realistic modelling of the final sensitivity of the CMB temperature anisotropy maps.