Monday, August 30, 2004

Fine Tuning the Cosmological Constant

Don't miss the article by Raphael Bousso and Joseph Polchinski in the September, 2004 issue of Scientific American. Entitled "The String Theory Landscape", this article presents a user friendly discussion of the existence of a huge number of environments allowed by string theory, each one of which can be the "vacuum state" of a universe. The vacuum energy of each such universe, existing in different 3D spatial parts of the "megaverse", would be the local measured "cosmological constant". The graphics in this article are very helpful in getting some intuition going.

Recall that the simplest explanation for the origin of the dark energy which is driving the accelerated expansion of the universe is a spatially constant positive vacuum energy proportional to the "cosmological constant" which exerts a negative pressure tending to drive clusters of galaxies apart. As the 3D space of our universe has expanded from the moment of the "big bang", the spatial density of matter and radiation has steadily decreased, while the spatial density of the vacuum energy has remained constant and now dominates the energy density of space.

The "fine tuning problem" is that the measured cosmological constant in our universe is tiny but not zero, and if it were much larger, galaxies could not have formed and galaxies are needed to provide an environment for successive generations of stars to form and die, some of their deaths resulting in the crucial production of chemical elements necessary for our (carbon based) form of life to evolve on suitable planets formed together with second generation stars (like our sun).

The other part of this fine tuning problem is that it would be incredible that one could ever find some deep physics reason (related, say, to some symmetry principle) for there being one unique solution allowed for the vacuum state of any universe such that the cosmological constant was close to the tiny positive value we measure.

A good review of the general "problem" of a non-zero cosmological constant is given by Sean Carroll in his Living Reviews in Relativity (Dec. 99) article: "The Cosmological Constant" (also available at here ).

In the Sept. Sci. Amer. article, Bousso and Polchinski review how recent "countings" of string theory vacua have revealed astoundingly large numbers, like 10^(500) (ie. 1 followed by 500 zeros) vacua having positive vacuum energy. They also discuss how such vacua are unstable to decay to vacua with other values of the cosmological constant (mainly lower values but still positive), allowing a universe to nucleate a baby universe (like a bubble starting somewhere) which expands at a lower rate (if its cosmological constant is smaller than its parent), and this process can continue with the baby universe nucleating out grandchildren universes contained within the prior universe boundaries (a concrete version of "eternal inflation" and the "self-reproducing universe").

String theory suggests that we can regard the "dark energy" component of our universe to be the metastable value of an effective scalar field potential energy density, spatially constant in our local universe, but taking different values in each subuniverse.

If one imagines some effective semi-classical scalar field starting out at a high value of potential energy (but in a local minimum of the effective 3D potential energy), and take into account the quantum fluctuations which can allow the scalar field to tunnel to other minima with lower values of the effective potential energy, eventually the metaverse is populated by a "hierarchy of nested bubbles, or subuniverses."

"In each bubble, an observer conducting experiments at low energies (like we do) will see a specific four-dimensional universe [3 spatial and one time dimension(s)] with its own characteristic laws of physics. Information from outside our bubble cannot reach us, because the intermediate space is expanding too rapidly for light to outrun it."

We are here (ie., life and human life has evolved) because "We live where we can" (to quote Leonard Susskind). The basic physics parameters (including the cosmological constant) of our universe are in the "sweet spot" where life is possible.

No one "ordered" this particular sweet spot for us, but there must be a huge number (actually an infinite number ) of other "pocket universes" (which we cannot communicate with) which also have the requisite physics parameters suitable for the evolution of intelligent life, capable of eventually doing physics and developing a gradual understanding of the universe and meta-universe of which our universe is a part. (And of course also gaining the requisite understanding to develop nuclear weapons and toxic pathogens, etc, which can easily end the local human experiment before long.)

If you have broadband internet service, you might enjoy seeing and listening to Leonard Susskind presenting an informal discussion of these ideas to a group of experts on Friday, Oct. 24, 2003, during one of the sessions of the Conference on Superstring Cosmology (10-20 thru 10-24) at the Kavli Institute for Theoretical Physics at UC Santa Barbara. Susskind's talk can be viewed and heard using Real Player software. You can also download the audio alone and listen at your leisure. Note that there was also a semester long "Program" in Superstring Cosmology at KITP which extended from Aug. 4 to Dec. 19 (2003), which has much of interest.

Don't miss the interview with Susskind on the Edge website. Some of the flavor is suggested by the following Susskind quote from that website:

"The beginning of the 21st century is a watershed in modern science, a time that will forever change our understanding of the universe. Something is happening which is far more than the discovery of new facts or new equations. This is one of those rare moments when our entire outlook, our framework for thinking, and the whole epistemology of physics and cosmology are suddenly undergoing real upheaval. The narrow 20th-century view of a unique universe, about ten billion years old and ten billion light years across with a unique set of physical laws, is giving way to something far bigger and pregnant with new possibilities.

"Gradually physicists and cosmologists are coming to see our ten billion light years as an infinitesimal pocket of a stupendous megaverse. At the same time theoretical physicists are proposing theories which demote our ordinary laws of nature to a tiny corner of a gigantic landscape of mathematical possibilities

"This landscape of possibilities is a mathematical space representing all of the possible environments that theory allows. Each possible environment has its own laws of physics, elementary particles and constants of nature. Some environments are similar to our own corner of the landscape but slightly different. They may have electrons, quarks and all the usual particles, but gravity might be a billion times stronger. Others have gravity like ours but electrons that are heavier than atomic nuclei. Others may resemble our world except for a violent repulsive force (called the cosmological constant) that tears apart atoms, molecules and even galaxies. Not even the dimensionality of space is sacred. Regions of the landscape describe worlds of 5,6…11 dimensions. The old 20th century question, 'What can you find in the universe?' is giving way to 'What can you not find?' "

A deeper look at these ideas can be found in Susskind's "The Anthropic Landscape of String Theory": preprint available here. (, or archive/gr-qc, or
archive/astro-ph are full of fascinating physics. )

If you go to this hep-th section of and use an author search on Susskind, you will get 542 hits (as of today: Mon. Aug 30, 2004), and hit number 5 is this paper. I recommend the Adobe Acrobat "PDF" version.


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