# The Expanding Universe. Prof Jim Dunlop University of Edinburgh

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1 The Expanding Universe Prof Jim Dunlop University of Edinburgh

2 Cosmology: The Study of Structure & Evolution of the Universe Small & Hot Big & Cold

3 Observational Evidence for the Expansion of the Universe Vesto Slipher ( ): studied spectra of several nebulae from Lowell Observatory and noticed almost all of them were moving away from us Slipher s tool: the redshift, z (only for small v/c!!)

4 The Doppler Effect Waves from moving objects will appear to have different wavelengths depending on the relative velocity of the source and observer

5 How This Works in Practice:

6 At around the same time, Edwin Hubble was determining the distance to nearby nebulae using Cepheid variable stars. Remember: Cepheid variable stars are standard candles : period gives actual luminosity which can be compared to observed one to calculate the distance ( )

7 Hubble s Law v=hd Hubble used Slipher s velocity measurements to study the relationship between galaxy velocity and distance. He found a remarkable linear relation!

8 The Hubble Constant, H 0 current best estimate is 70 km/s/mpc it s not really a constant. given an accurate value of H 0, we can measure distances as

9 How to Interpret the Expansion? Tempting to think we are at the centre of the Universe and everything moving away from us But: Copernican Principle: we do not occupy a special place Cosmological Principle: the universe is homogenous and isotropic on large scales Correct View: the entire universe is expanding and all galaxies are moving apart

10 Some Things to Keep in Mind: What is the Universe expanding into? is meaningless - the expansion is creating space itself. It is not really correct to think of the redshift of distant galaxies as a Doppler shift; but rather as a redshift due to the expansion of intervening space. This helps us to understand why distant galaxies are redshifted. As photon travels towards us, its wavelength gets stretched out along with space. The longer it has to travel to reach us, the more stretched it becomes.

11 The Expansion of Space

12 Implications of the Hubble Expansion In the distant past, all galaxies must have been much closer together and the universe much denser - there must have been a huge explosion which started everything in motion. How long ago did this happen? Age of the universe!! Assumes constant v

13 Cosmic Scale Factor and Redshift Consider distribution of galaxies in which all separations increase with time in proportion to scale factor R(t) (but not exactly true!) Wavelength of light also increases with the scale factor:

14 The Expansion of the Universe The expansion of the Universe was implied by Einstein s Theory of General Relativity in its simplest form, which he published in As we have seen, Hubble showed in the 1920s that galaxies were receding from each other according to the relation v = Hd. This implied that the Universe actually was expanding.

15 Einstein s Greatest Blunder Although in their simplest form Einstein s equations implied that the Universe was expanding, Einstein felt convinced that it must be static, and added a balancing term to counteract the expansion. He later realised that he could have predicted the expansion of the Universe, and missing this he called his greatest blunder.

16 Gravity and Expansion The self gravitation of matter in the Universe has the effect of slowing down the expansion. If the average density of matter is large enough, the gravitational attraction will eventually halt the expansion and the Universe will collapse back to a Big Crunch. Otherwise, the Universe will continue to expand forever.

17 Curved Space and General Relativity Einstein s theory of general relativity (1916) introduced idea that space can be curved: Closed Universe: finite volume, positive curvature Open Universe: infinite volume, negative curvature Flat Universe: infinite volume, zero curvature

18 Open and Closed Universes

19 Critical Density Between average matter densities which are large enough to halt the expansion of the Universe and those that are not, there is a special value of the density which divides them. This is known as the critical density ρ crit. The ratio between the actual density of the Universe ρ and ρ crit is known as the cosmological density parameter Ω.

20 Material Content of the Universe Observations of the luminous matter in galaxies show that the mass contained in stars falls far short of the critical density at about 0.5% ρ crit. Nucleosynthesis calculations show that the amount of baryonic matter created in the early Universe was about 4% ρ crit. Studies of the dynamics of clusters suggest that the average mass density on the largest scales is about 25% ρ crit.

21 Model Universes The three diagrams on the left show the evolution of a universe under the influence of gravity alone. The right hand diagram shows the effect of a repulsive force such as dark energy.

22 A Recollapsing Universe If there is no repulsive force and the matter density of the Universe is larger than the critical density, then the collective gravity of all the matter will halt the Universe s expansion and reverse it. The Universe will collapse back into a state similar to its initial state in the Big Bang. Such a universe is said to have positive curvature, like that of a sphere.

23 A Critical Universe In a critical universe there is just enough matter to slow the expansion indefinitely, but not to cause it to collapse. A critical universe will coast for ever, expanding more and more slowly with time. Such a universe is said to have a flat geometry, like that of a plane.

24 A Coasting Universe If there is no repulsive force and the matter density of the universe is less than the critical density, then the collective gravity of all its matter cannot halt the expansion. The universe will keep expanding forever, with little change in its rate of expansion. Such a universe is said to have negative curvature like that of a saddle.

25 An Accelerating Universe If there is a repulsive force, for example in the form of dark energy, then the universe will accelerate from its initial expansion. The universe will expand forever at an ever increasing rate. The curvature of such a universe can be positive, flat or negative depending on the ratio of gravitational to repulsive force.

26 Which Universe? The different model universes can be distinguished by measuring the distance to galaxies at different times in the past.

27 Cosmological Observations Distances can be measured from the apparent brightness of objects of known luminosity. Supernovae are ideal for this as they have well defined luminosities, and are bright enough to be observed at great distances. Time in the past is directly related to redshift, which is quite easily measured even for distant supernovae.

28 The Supernova Project

29 Dark Energy The Supernova Project set out to obtain apparent magnitudes and redshifts for a large sample of very distant supernovae to settle the question of what sort of universe we live in. The results came as a great surprise, implying that we live in an accelerating universe, driven by a repulsive force which has come to be known as Dark Energy.

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