Modern Cosmology A/Prof Geraint Lewis University of Sydney

Historically, “cosmology” was the realm of philosophers.

Isaac Newton First mathematical laws of gravity and motion. Thought that an isolated group of stars would collapse in on itself. An infinite universe of stars should collapse into isolated islands of mass. A finely tuned universe could be balanced and static.

Albert Einstein General Relativity: viewing gravity as curved space time (1915). “Cosmological considerations on the general theory of relativity” (1917). Einstein thought the universe was static and unchanging, although his equations were dynamic. Added a cosmological constant term which acts as an repulsive force, balancing gravity.

Alexander Friedmann Friedmann wrote “On the curvature of space” in He came to the conclusion that Einstein’s cosmological equations predicted that the universe evolved with time, either expanding or collapsing. Einstein wrote that Friedmann had made a mathematical error and his results were invalid. In 1923, Einstein retracted his objection and agreed relativistic universe was dynamic.

Einstein’s Biggest Blunder? After Friedmann’s work, Einstein threw away his Cosmological Constant, calling it his biggest blunder. There is a persistent myth that Einstein fudged the equations of relativity, adding anti-gravity to make a static universe. However, this is not correct. The addition of a cosmological constant term was a completely legitimate mathematical exercise. Einstein’s blunder was choosing a specific value for the cosmological constant to balance gravity, not its addition. It was not discarded, just set to zero.

Edwin Hubble In the 1920s, Hubble measured the speeds of nearby galaxies. He found nearly all were rushing away from us, with their velocity increasing with distance, exactly as predicted in the relativistic model of the universe.

Modern Measurement The search for Hubble’s Constant, the rate of the expansion of the universe, has dominated astronomy since Hubble’s day. Velocities are easy to measure, distances are hard. The issue was only resolved in the last decade with use of the Hubble Space Telescope.

Understanding Expansion A good way to understand expansion is with a “conformal diagram”. It simply has us and all other objects in the universe as a series of straight lines.

Understanding Expansion Friedmann’s equations give us the “Scale Factor” and the distances as a function of time are;

Understanding Expansion Notice how as we go back in time, R(t) goes to zero. This means the distance between any two objects also goes to zero. This is the location of the “Big Bang”.

Which Scale Factor? The shape of the scale factor depends upon the mix of energies (matter, radiation, other stuff) in the universe. Universes only containing matter slow down over time, while other universes slow and then accelerate. Which is our universe?

Which Scale Factor? On conformal diagrams, light rays travel at 45 degrees and it’s simple to see that light we receive now set out from distant objects long ago.

Which Scale Factor? The velocity of an object (its redshift) tells us the scale factor at the time the light set out, while the brightness of an object tells us how far the light has travelled.

Cosmological Supernovae Supernovae are exploding stars whose true brightness is well known. Using the Keck and Hubble Space Telescope, ten years ago we were able to do this experiment.

Which Universe? The supernovae appeared fainter than expected, showing that the universe does not contain only matter. A third of the cosmos is matter, the most of which is dark (does not radiate, but we can feel its gravitational pull). Heavy elements (that’s us!) make up 0.03% of the universe. Some mysterious substance, dark energy, make up 70% of the universe.

The Future of the Universe The mix of matter and energy imply that the expansion of the universe is beginning to accelerate, and in the future, the universe will dilute and dim.

The Future of the Universe In the future, there will be no cosmology as there will be nothing to see out there.

Well, we know what it isn’t. It isn’t dark or normal matter. It has to possess a negative pressure (a tension) to cause the universe to accelerate. With quantum physics, the vacuum is not empty but seethes with particles popping in and out of existence. Such a vacuum possesses precisely the tension of dark energy Only problem is that the density is wrong by a factor of What is dark energy?

Particle physics is trying to understand what dark energy is (although they still haven’t sorted out dark matter). Observations reveal that dark energy has the same properties as Einstein’s cosmological constant. However, the properties could have changed with time and the goal of several proposed telescopes will be to uncover any such change. Any change will have a big impact on our understanding. What now? Proposed Thirty Metre Telescope

Georges Lemaître Friedmann died soon after he published his work. Georges Lemaitre examined the equations of cosmology, especially the point where the scale factor goes to zero. Running the universe backwards, he realized that it must have been hotter in the past. He proposed the “Hot Big Bang” model of the universe, where the universe was born in a hot, dense state and has been cooling and expanding ever since.

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Large Hadron Collider CERN, on the Swiss-French Border, will recreate the conditions when the universe was seconds old.

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Cosmic Microwave Background Penzias & Wilson won the 1978 Nobel Prize for detecting the cosmic microwave background radiation. Mather & Smoot won the 2006 Nobel prize for showing this radiation has a blackbody spectrum (2.7K) and for revealing that it is not smoothly distributed over the sky.

Cosmic Microwave Background While the mean temperature of the sky is 2.7K, some regions are hotter and some cooler, with a temperature difference of 0.001K. Where did these temperature differences come from?

CMB Hot & Cool Spots At the time of reionization (when the universe became neutral) there were regions of slightly higher and slightly lower density. Where did these come from?

Inflation & the Quantum The quantum fluctuations we met earlier were stretched out during a period of rapid expansion know as “Inflation”, with the pattern we see matching theoretical expectations. These slight over densities became the seeds of stars and galaxies, including our own Milky Way galaxy.

Universe in a Computer It is too difficult to follow the complex evolution of matter on a piece of paper. This is especially true for gas which can collapse and form stars, which can then explode. A large number of astronomers now build their own universes within computers. Swinburne Green Machine

2dF Galaxy Redshift Survey Mapping out the locations of galaxies show that they sit on just the kind of foamy structure we expect from the lumps in the Cosmic Microwave Background. This directly connects the universe today to its very birth.

How Big is the Universe? Given our mix of dark energy and matter, the universe is infinite in extent, but we can only see the “observable universe”. As time proceeds, more and more is revealed.

Where did it come from? Bohr & Einstein The truth is we just don’t know. We have a major problem in physics, namely our best and most accurate theories (quantum mechanics and general relativity) just do not work together; we don’t have a theory of “quantum gravity”. Without this, we cannot work out what happened before inflation.

Possibilities? Reproducing Universe: Linde Colliding Branes: Turok & Stienhardt Perhaps one of your students will work this out. The End