Martin Rees' "Our Complex Cosmos and its Future"

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This is an article published as part of the collected lectures given on Stephen Hawking's 60th birthday. It summarizes our knowledge regarding the origin and fate of the universe (as of 2003), the theory and evidence supporting our beliefs and the open questions yet to be resolved.

Some of us might have encountered similar expositions in e.g. Hawking's "Brief History of Time". Below I am providing a paraphrase that might act as starting point for thoughts over astrophysics/cosmology.

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Einstein : "The most incomprehensible thing about the universe is that it is comprehensible."
John D. Barrow : "Any universe simple enough to be understood is too simple to produce a mind able to understand it."
Emerson Pugh : "If the human brain were so simple that we could understand it, we would be so simple that we couldn’t."

How is matter distributed in the universe on the largest scales?
The distribution of galaxies in the universe is not endlessly hierarchical (i.e. we see clusters and even superclusters but the sequence doesn't continue ad infinitum). There is a global smoothness that vastly simplifies analysis. Thus the universe is homogenous and isotropic on the large scale.

The overall motion is also correspondingly simple. All galaxies recede away from each other at a speed proportional to their distance. One can visualize this as occupying a node on a lattice connected by rods, with the rods stretching in every direction at a speed that increases with the number of nodes between any pair of rods. There is no preferred center - one would make the same observations if one were occupying any other node in the lattice. The expansion is accelerated and happens everywhere.

Since the speed of light is constant, the galaxies that we see farther away appear to us as they were in the distant past. They are crowded together, which implies in the earlier stages of the universe its density and hence temperature were much higher than current values. Extrapolating back to the very beginning gives us the "Big Bang", where everything emerges from a singularity. Note that this is not an "explosion in space-time" but an "expansion of space-time". There is no exterior to this event - it is in the history of all events that ever occurred everywhere.

How do we know the Big Bang happened?
Before the galaxies had time to form, radiation had permeated the universe in the earliest epochs. Today we observe intergalactic space filled with this cosmic microwave background radiation (CMBR) - an afterglow of creation. It demonstrates a blackbody spectrum i.e. equilibrium at extreme heat and density. This gives credence to the big bang cosmological model. The subsequent expansion led to a cooling down and stretching of the wavelengths to their current values of 3 degrees Kelvin and microwaves. This provides the timeline of the Big Bang at roughly 13.8 billion years.

If the early universe was extremely hot and dense, why didn't all the hydrogen undergo fusion, as it does now in stars, to form bigger elements?
This is because the state of high heat/density didn't last for long enough to exhaust all the fuel. The model predicts 23% Helium leftover along with small traces of Deuterium and Lithium, and this is matched by observations.

What dynamical principles lead to the large scale structures we see now?
Gravity clumps together masses and its strength falls as the inverse square of distance. In an expanding universe, if a region has slightly high density, it undergoes greater gravitational attraction and suffers deceleration, while other region with less matter expand away faster. Thus the density contrast is enhanced due to the amplification of gravity.

Collisions of galaxies produce instabilities in huge gas clouds, producing shockwaves travelling through them. This doesn't affect existing stars due to vast intergalactic distances, but triggers gas condensation in the nebulae and new star formation.

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Woody Allen : "Eternity is very long, especially towards the end!"

Will the expansion go on forever?
Calculations suggest a critical density of >5 atoms per cubic meter is needed on average to halt the expansion and reverse it eventually. Current observations produce a value of only 0.2

However, the visible universe is not everything, since dark matter is hypothesized to explain the stability of galaxies and clusters, which in the absence of the missing mass would not have retained their shapes and disintegrated. The gravitational lensing of the light reaching us from other galaxies also needs far greater mass to explain the extent of distortion we observe.

Let S = actual density / critical density. Then taking the proposed dark matter into account, we reach S = 0.3 which should make the geometry of the universe hyperbolic. In such a universe, distant objects look smaller as compared to Euclidean space. However, using the relation between temperature fluctuations in the CMBR and the geometry of the universe, we conclude the universe is flat. Thus there should be around 70% dark matter to account for the observed flatness.

Furthermore, Dark energy is posited to exist as the latent energy of empty space, which has a repulsive effect strong enough to counteract gravity with its high negative pressure and cause a net expansion. This is verified by observing Type 1A supernovae, whose measured brightness acts as a scale of their relative distances, and the gravitational redshift - distance relation confirms the accelerated expansion of the universe.

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What open questions do we have regarding the early universe?

We want explanations of the parameter values needed at the early epochs to lead to current cosmic structure. These include :
Expansion rate
Proportion of atoms, dark matter, dark energy, radiation
Character of fluctuations
Values of fundamental constants of physics

Let Q denote the 'roughness' of the fluctuations in the early microscopic universe that gives rise to present structures observed. Then for
Q << 10^-5 : there would be no stars as the universe would be too smooth for the amorphous hydrogen to condense and gravitate
Q >> 10^-5 : there would be too much aggregation early on in the expansion and the universe would be filled with black holes of the size of galactic clusters
Thus Q must be in a small range around 10^-5 for stars, planets, people to exist. Why does our universe have this value?

Gravity is far weaker than other forces, which either fall with distance or disappear due to opposite charges being balanced out in massive bodies. It is the only force dominating at large distances and its attractive force causes mass to aggregate and lead to star formation, galaxies and clusters. But it can't be too strong, otherwise mass even at small scales would be crushed together and complex life that is usually oblivious to gravity wouldn't emerge.
Why is the value of the gravitational fine structure constant not too low and not too high?

Another conundrum is if the laws governing the universe are derivable from a more fundamental principle i.e. are explainable from purely physical considerations, or should we appeal to anthropic reasoning to rest the case - current laws are just one instance of an "ensemble of possibilities", so we happen to be in a happy accident where the laws are observed to be what they are since they are necessary for conscious observers like us?