Astroparticle Physics

256 12 InflationFig. 12.3Schematic illustration of thepotential V(φ)for ‘new inflation’quantum fluctuationsend of inflationdensity fluctuationsAs in Guth’s original theory, however, new inflation doesnot end everywhere at the same time. But now this featureis turned to an advantage. It is used to explain the structureor clumpiness of the universe currently visible on distancescales less than around 100 Mpc. Because of quantum fluctuations,the value of the field φ at the start of the inflationaryphase will not be exactly the same at all places. As with therandomness of quantum-mechanical tunneling, these quantumfluctuations lead to differences, depending on position,in the time needed to move to the true vacuum state.When a volume of space is undergoing inflation, the energydensity ϱ ≈ V(0) is essentially constant. After inflationends, the energy is transferred to particles such as photons,electrons, etc. Their energy density then decreases as theuniverse continues to expand, e.g., ϱ ∼ R −4 for relativisticparticles. The onset of this decrease is therefore delayed inregions where inflation goes on longer. Thus, the variation inthe time of the end of inflation provides a natural mechanismto explain spatial variations in energy density. These densityfluctuations are then amplified by gravity and finally resultin the structures that one sees today, e.g., galaxies, clusters,and superclusters.12.6 Solution to the Flatness Problem“I have just invented an anti-gravitymachine. It’s called a chair.”Richard P. Feynmanwhy is ϱ = ϱ c ?It will now be shown that an early period of inflationary expansioncan explain the flatness problem, i.e., why the energydensity today is so close to the critical density. Supposethat inflation starts at some initial time t i and continues until