Thursday, April 4, 2013

What is the End State of the Universe?

It is tantalizing to look at history and predict the future. People (and later scientists, i.e., people who dedicate their lives to answering questions) wanted to know "why life formed? why are we here?" almost from the beginning of mankind. The answer to these questions has never been fully understood. In our most recent paper [arXiv:1304.0594 - Title: "Merging Gravitation with Thermodynamics to Understand Cosmology"], Andrew Lundgren, Mihai (my brother) and I discuss why the universe evolved from a hot and uniform past to its cold, clumpy state where planets and stars and humans exist, what will be the final state of the universe, and how to compute the total entropy inside a star. It is believed that the evolution of the universe is dictated by the second law of thermodynamics, which states that entropy (the degree of disorder or the number of indistinguishable configurations of a system) always increases.

However, in general, a hot and uniform gas has higher entropy than a solid or liquid because in a gas particles can move around freely and the degree of disorder is higher. So, why did stars form? we are "clumpier" than gas and so why are we here? Well... because of gravity. Gravity has entropy too. As a gas collapses to a star and later forms a black hole, the entropy increases.

The largest repositories of entropy are gravitational: the cosmic microwave background, the cosmological horizon and the supermassive black holes.

 Brief History of the Universe:
How do we know the universe was uniform and hot early on? From the WMAP and more recently from the Planck satellite who mapped residual light from the Big Bang. The largest temperature difference seen by WMAP in this primordial light was 0.0004 K! Planck has provided an even more detailed map of temperature fluctuations that will lead to more realistic models of the beginning of the universe.

The Clumpy Universe.
As the universe expanded, it became colder and clumpier, and more and more structure formed. Radiation and later matter dominated the early universe. In time, the concentration of matter and radiation decreased, and then dark energy, which causes the accelerated expansion observed today, started to dominate the universe. Leading theories propose dark energy is either a constant energy density or a scalar field (quintessence) that mimics the cosmological constant, but can vary in space and decays away in time. 

The Frozen Far Future.

The future of our local supercluster
  Over the next 1012 years most matter will stream beyond the cosmological horizon, leaving dark energy to completely dominate the large scale of the universe on scales above 100 Mpc. However, the local supercluster is decoupled from the expansion of the universe, and will remain gravitationally bound. Everything in the local universe will coalesce into supermassive black holes that slowly evaporate or be ejected (Adams and Laughlin 1997)

The far future of the Universe.
Schematic BH Evaporation. Cosmological horizon = blue.
The cosmological horizon is colder than anything else in the universe. Since heat flows from hot to cold, the horizon is slowly absorbing the contents of the universe producing entropy and grows in response. In time, all that will be left is supermassive black holes that slowly evaporate transferring more heat over the horizon and producing entropy. The emptying of universe is an approach to equilibrium.

The end state of the universe?
The equilibrium state of a system is its most generic state. The equilibrium state of gas in a box is one where the gas is uniformly distributed. Flat Minkowski space and deSitter space (the space with a cosmological constant) are both maximally symmetric. This means that they have a full set of ten symmetries: three rotations, three boosts, one time and three space translations. However, deSitter has a cosmological constant, which restricts the wavelength of gravitational waves, which are modes of the Weyl tensor (a mathematical quantity that measures the curvature of spacetime). When the cosmological horizon grows, the number of accessible microstates in the Weyl tensor increase leading to an increase in the total entropy of the universe.

 Mathematically, one recovers flat space from deSitter space in the limit in which the cosmological constant is zero. In that case the temperature of flat space is zero and its entropy is divergent. This divergence is first mentioned by Curir and Demianski in 1979, and then later mentioned in passing in other papers. This finding has been largely ignored and there is no discussion in the literature of its potential impact.

Since flat space has higher entropy than deSitter, the second law of thermodynamics favors a decay from deSitter to flat space, which could happen if deSitter is unstable when quantum effects are considered or if the cosmological constant is mimicked by a scalar field that slow rolls to flat space.

 Gravitational Entropy.
 I hope have convinced you that gravitational entropy is important in the evolution of the universe. But how do we compute it? It's difficult to define gravitational entropy in the absence of a horizon (otherwise, one can use the Bekenstein-Hawking formula - the entropy of a black hole is a quarter the area of its horizon; this formula applies to the cosmological horizon and to other horizons as well). Gravitational thermodynamics is challenging because gravity is non-local. Energy cannot be defined at a point in general relativity because of the equivalence principle. Switching to a free falling elevator removes all local gravitational effects. So, scientists define quasi-local quantities, which are hard to compute for general situations because they involve surface integrals and it is also not clear which formalism to use. We use the Brown-York quasi-local energy, which counts the total energy inside the surface, and write the first law of thermodynamics in terms of quasi-local quantities to compute the total entropy inside a star.  The result is fairly simple. The entropy of the star is not constant inside and it is smaller than the entropy outside the star.


  1. when the big bang blew, seems like all the matter from the inside would have been equal, and all the matter would be the same, but we have empty spaces- outer space, kool so that means that when the big bang blasted that their was more mass on one side than the other, if their is more star trash or star in one part of the cosmo, that means more energy was different all around the big bang. so we need to look in space where the most stars are to see father back in time cause that's where the big bang had the most blast. what ever

  2. Hi Robert! Thanks for reading my blog and for thinking about cosmology. It is believed that the pre-inflation early universe was almost perfectly homogeneous with very tiny over-densities. It was also the same in all directions. Then the universe inflated like a balloon you blow in and then these tiny over-densities grew with the universe. At the end of the inflationary period the universe was still very small - perhaps the size of a small ball, and afterwards it kept growing and cooling only at a slower rate. As it grew and these over-densities acted as seeds for the dark matter halos. Eventually, the first atoms formed, and later the first stars and galaxies we see today. People simulate structure formation on big supercomputers. Getting the universe how we see it today and explaining the voids is a very complicated yet unsolved problem, but we are making progress as computers get better and we get more data from satellites. Now, there is some asymmetry in the data from the Planck satellite that is not understood.