# 17.17 Precision Cosmology

Cosmology has entered a new era in the past decade. In ancient times, people could only guess about the size and shape and age of the universe, and they has trouble contemplating something so much larger and grander than the Earth. In the early 20th century, cosmology matured using a new theory of gravity — Einstein's general relativity — and new data to show that we lived in an expanding universe filled with countless galaxies. However, Hubble's first attempt to measure the expansion rate and age was in error by a factor of eight, and even into the 1980s, astronomers claimed values for the Hubble constant that differed by a factor of two. The subject has matured rapidly. Part of this is the impact of the Hubble Space Telescope and large new ground-based telescopes. But the most dramatic improvement has been the increased quality and sensitivity of observations of the microwave background radiation. This has ushered in the era of "precision cosmology."

The first observations by Penzias and Wilson were just good enough to say that the temperature of the radiation was around 3 Kelvin and that it didn't vary in intensity by more than a few percent across the sky. In the early 1990s, COBE improved the angular resolution to about 7 degrees and the sensitivity to 10^{-4} Kelvin, both improvements of factors of a hundred. In the 2000s, WMAP and Planck improved on COBE by another factor of 30, reaching an angular resolution of 0.1-0.2 degrees and a sensitivity of 3 × 10^{-6} Kelvin. Data of this quality allow the angular variations on many different scales to be measured, in what is called the angular "power spectrum." Looking at a map of the CMB, there seems to be a characteristic scale of the variations or "speckles" at an angular scale of about 1 degree, and this is confirmed by a mathematical analysis. The power spectrum has many undulations and they all give information on the physical conditions in the universe when it was 380,000 years old.

To see how the CMB data has led to precision cosmology, let's look at the parameters of the standard cosmological model as derived using data from the current state-of-the-art mission, the Planck satellite. Some measurements come purely from the CMB data, and others are derived in combination with ground-based surveys of galaxies.In each case, the measurement is accompanied by the uncertainty or error, where ± indicates the range above or below the measurement that could be accommodated with 68% certainty (also referred to as 1σ). A range of twice the uncertainty above or below the measurement is the 95% certainty level (2σ), and three times the uncertainty above or below the measurement is the 99.5% certainty level (3σ).

With Planck data released in 2015, the age of the universe is 13.799 ± 0.021 billion years. The total matter density is Ω_{m} = 0.3089 ± 0.0062 and the dark energy density is Ω_{&Lambda} = 0.6911 ± 0.0062. Of that matter density, 19% is normal matter and 81% is dark matter. The universe is flat to within 0.4%. The Hubble constant calculated in this analysis is 67.74 ± 0.46 km/s/Mpc. The spectrum of the fluctuations has an index of 0.9667 ± 0.0040, or very close to one. This last number indicate equal amounts of microwave power of different anghular scales and it agrees with a central prediction of the inflationary big bang model. Astronomers hope to refine these measurements even further to improve our understanding of the very early universe.