Measuring cosmological parameters

In this review, the status of measurements of the matter density (Ωm), the vacuum energy density or cosmological constant (ΩΛ), the Hubble constant (H0), and the ages of the oldest measured objects (t0) are summarized. Three independent types of methods for measuring the Hubble constant are considered: the measurement of time delays in multiply imaged quasars, the Sunyaev–Zel’dovich effect in clusters, and Cepheid-based extragalactic distances. Many recent independent dynamical measurements are yielding a low value for the matter density (Ωm ≈ 0.2–0.3). A wide range of Hubble constant measurements appear to be converging in the range of 60–80 km/sec per megaparsec. Areas where future improvements are likely to be made soon are highlighted—in particular, measurements of anisotropies in the cosmic microwave background. Particular attention is paid to sources of systematic error and the assumptions that underlie many of the measurement methods.

Cosmic microwave background theory

A long-standing goal of theorists has been to constrain cosmological parameters that define the structure formation theory from cosmic microwave background (CMB) anisotropy experiments and large-scale structure (LSS) observations. The status and future promise of this enterprise is described. Current band-powers in ℓ-space are consistent with a ΔT flat in frequency and broadly follow inflation-based expectations. That the levels are ∼(10−5)2 provides strong support for the gravitational instability theory, while the Far Infrared Absolute Spectrophotometer (FIRAS) constraints on energy injection rule out cosmic explosions as a dominant source of LSS. Band-powers at ℓ ≳ 100 suggest that the universe could not have re-ionized too early. To get the LSS of Cosmic Background Explorer (COBE)-normalized fluctuations right provides encouraging support that the initial fluctuation spectrum was not far off the scale invariant form that inflation models prefer: e.g., for tilted Λ cold dark matter sequences of fixed 13-Gyr age (with the Hubble constant H0 marginalized), ns = 1.17 ± 0.3 for Differential Microwave Radiometer (DMR) only; 1.15 ± 0.08 for DMR plus the SK95 experiment; 1.00 ± 0.04 for DMR plus all smaller angle experiments; 1.00 ± 0.05 when LSS constraints are included as well. The CMB alone currently gives weak constraints on Λ and moderate constraints on Ωtot, but theoretical forecasts of future long duration balloon and satellite experiments are shown which predict percent-level accuracy among a large fraction of the 10+ parameters characterizing the cosmic structure formation theory, at least if it is an inflation variant.

Scaling the universe: Gravitational lenses and the Hubble constant

Gravitational lenses, besides being interesting in their own right, have been demonstrated to be suitable as “gravitational standard rulers” for the measurement of the rate of expansion of the Universe (Ho), as well as to constrain the values of the cosmological parameters such as Ωo and Λo that control the evolution of the volume of the Universe with cosmic time.

Training and search methods for speech recognition.

Speech recognition involves three processes: extraction of acoustic indices from the speech signal, estimation of the probability that the observed index string was caused by a hypothesized utterance segment, and determination of the recognized utterance via a search among hypothesized alternatives. This paper is not concerned with the first process. Estimation of the probability of an index string involves a model of index production by any given utterance segment (e.g., a word). Hidden Markov models (HMMs) are used for this purpose [Makhoul, J. & Schwartz, R. (1995) Proc. Natl. Acad. Sci. USA 92, 9956-9963]. Their parameters are state transition probabilities and output probability distributions associated with the transitions. The Baum algorithm that obtains the values of these parameters from speech data via their successive reestimation will be described in this paper. The recognizer wishes to find the most probable utterance that could have caused the observed acoustic index string. That probability is the product of two factors: the probability that the utterance will produce the string and the probability that the speaker will wish to produce the utterance (the language model probability). Even if the vocabulary size is moderate, it is impossible to search for the utterance exhaustively. One practical algorithm is described [Viterbi, A. J. (1967) IEEE Trans. Inf. Theory IT-13, 260-267] that, given the index string, has a high likelihood of finding the most probable utterance.

The microwave background anisotropies: Observations

Most cosmologists now believe that we live in an evolving universe that has been expanding and cooling since its origin about 15 billion years ago. Strong evidence for this standard cosmological model comes from studies of the cosmic microwave background radiation (CMBR), the remnant heat from the initial fireball. The CMBR spectrum is blackbody, as predicted from the hot Big Bang model before the discovery of the remnant radiation in 1964. In 1992 the cosmic background explorer (COBE) satellite finally detected the anisotropy of the radiation—fingerprints left by tiny temperature fluctuations in the initial bang. Careful design of the COBE satellite, and a bit of luck, allowed the 30 μK fluctuations in the CMBR temperature (2.73 K) to be pulled out of instrument noise and spurious foreground emissions. Further advances in detector technology and experiment design are allowing current CMBR experiments to search for predicted features in the anisotropy power spectrum at angular scales of 1° and smaller. If they exist, these features were formed at an important epoch in the evolution of the universe—the decoupling of matter and radiation at a temperature of about 4,000 K and a time about 300,000 years after the bang. CMBR anisotropy measurements probe directly some detailed physics of the early universe. Also, parameters of the cosmological model can be measured because the anisotropy power spectrum depends on constituent densities and the horizon scale at a known cosmological epoch. As sophisticated experiments on the ground and on balloons pursue these measurements, two CMBR anisotropy satellite missions are being prepared for launch early in the next century.