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# 1.2 The cooling Universe

The second piece of evidence for the hot big bang was the discovery in the 1960s by Arno Penzias and Robert Wilson of the cosmic microwave background (CMB) radiation. When observing the sky at microwave wavelengths, a nearly uniform glow can be observed in all directions. The distribution of the radiation corresponds to a blackbody spectrum at a temperature of about 2.7 K (i.e. nearly 3 degrees above absolute zero) and it represents the fading glow of the heat of the big bang. As the Universe expanded and cooled, about 380,000 years after the big bang (known as the time of last scattering), electrons were able to combine with protons for the first time, forming hydrogen atoms. This so-called recombination event happened when the temperature of the Universe was around 3000 K. As photons did not subsequently interact with these electrically neutral atoms, they began to travel freely through space, resulting in the decoupling of matter and radiation. It is this radiation that is observed today as the CMB, redshifted by a factor of about 1100 from the infrared into the microwave part of the spectrum.

Although the CMB is nearly uniform across the whole sky, tiny fluctuations in its temperature and intensity were discovered in the 1990s – see Figure 3. These so-called ‘ripples in the fabric of spacetime’ represent the tiny fluctuations in density in the early Universe from which the galaxies and clusters of galaxies later grew. More recently, detailed observations of the fluctations in the CMB at different angular scales have led to conclusions about the large-scale geometry of the Universe.

Figure 3 An all-sky map of the CMB radiation, as mapped by ESA’s Planck mission. Colour indicates the deviation of temperature from the mean, , at each position on the sky

The behaviour of space and time, described by Einstein’s theory of general relativity, can be expressed by the Friedmann equation. This equation describes how the scale factor of the Universe changes with time and crucially depends on two parameters: the overall matter-energy density of the Universe (represented by ) and the curvature of space (represented by ) which characterises its overall geometry. Broadly speaking there are three possibilities for the Universe’s large-scale geometry: space may either be flat, positively curved or negatively curved (see Figure 4). In flat space, parallel lines remain parallel and the internal angles of a triangle add up to 180 degrees. In positively curved space, parallel lines eventually converge and the internal angles of a triangle add up to more than 180 degrees (as on the two-dimensional surface of a sphere). In negatively curved space, parallel lines eventually diverge and the internal angles of a triangle add up to less than 180 degrees (as on the two-dimensional surface of a saddle). Just which type of geometry the Universe has is determined by the overall matter-energy density of the Universe – if the matter-energy density is higher than some critical value, space is positively curved; if the matter-energy density is lower than this critical value, space is negatively curved.

Perhaps reassuringly, observations of the CMB fluctuations indicate that the large-scale geometry of the Universe is actually flat, as it appears to be locally. This implies that the curvature parameter of the Universe, and that the overall matter-energy density of the Universe is exactly equal to the critical density, kg m-3. The density parameter of the Universe is equal to the ratio of the actual density to the critical density, . In a Universe with flat geometry therefore, .

Figure 4 The geometry of the Universe is determined by whether its overall matter-energy density is greater than, less than or equal to the critical density. (a) A universe with zero curvature has and . (b) A universe with positive curvature has and . (c) A universe with negative curvature has and
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