String theory landscape

The string theory landscape or anthropic landscape refers to the large number of possible false vacua in string theory.The most commonly quoted number is of order 10⁵⁰⁰. See M. Douglas, "The statistics of string / M theory vacua", "JHEP" 0305, 46 (2003). arxiv|archive=hep-th|id=0303194; S. Ashok and M. Douglas, "Counting flux vacua", "JHEP" 0401, 060 (2004). ] The "landscape" includes so many possible configurations that it is thought by some physicists that the known laws of physics, the Standard Model and General relativity with a positive cosmological constant, occurs in at least one of them. The "anthropic landscape" refers to the collection of those portions of the landscape that are suitable for supporting human life, an application of the anthropic principle that selects a subset of the theoretically possible configurations.

In string theory the number of false vacua is commonly quoted as 10⁵⁰⁰. The large number of possibilities arises from different choices of Calabi-Yau manifolds and different values of generalized magnetic fluxes over different homology cycles. If one assumes that there is no structure in the space of vacua, the problem of finding one with a sufficiently small cosmological constant is NP complete [cite arxiv|title=Computational complexity of the landscape|author=F. Denef and M. R. Douglas|eprint=hep-th/0602072|year=2006|version=] , being a version of the subset sum problem.

Anthropic principle

The idea of the string theory landscape has been used to propose a concrete implementation of the anthropic principle, the idea that fundamental constants may have the values they have not for fundamental physical reasons, but rather because such values are necessary for life (and hence intelligent observers to measure the constants). In 1987, Steven Weinberg proposed that the observed value of the cosmological constant was so small because it is not possible for life to occur in a universe with a much larger cosmological constant. [S. Weinberg, "Anthropic bound on the cosmological constant", "Phys. Rev. Lett." 59, 2607 (1987).] In order to implement this idea in a concrete physical theory, it is necessary to postulate a multiverse in which fundamental physical parameters can take different values. This has been realized in the context of eternal inflation.

Bayesian probability

Some physicists, starting with Weinberg, have proposed that Bayesian probability can be used to compute probability distributions for fundamental physical parameters, where the probability $P(x)$ of observing some fundamental parameters $x$ is given by,:$P(x)=P\_mathrm\{prior\}(x)\; imes\; P\_mathrm\{selection\}(x),$where $P\_mathrm\{prior\}$ is the prior probability, from fundamental theory, of the parameters $x$ and $P\_mathrm\{selection\}$ is the anthropic selection function, determined by the number of "observers" that would occur in the universe with parameters $x$. These probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that:
* The function $P\_mathrm\{prior\}$ is completely unknown in string theory and may be impossible to define or interpret in any sensible probabilistic way.
* The function $P\_mathrm\{selection\}$ is completely unknown, since so little is known about the origin of life. Simplified criteria (such as the number of galaxies) must be used as a proxy for the number of observers. Moreover, it may never be possible to compute it for parameters radically different from those of the observable universe.
* Interpreting probability in a context where it is only possible to draw one sample from a distribution is problematic.

Various physicists have tried to address these objections, and the ideas remain extremely controversial both within and outside the string theory community. These ideas have been reviewed by Carroll [S. M. Carroll, "Is our universe natural?", arxiv|archive=hep-th|id=0512148.] .

implified approaches

Tegmark "et al." have recently considered these objections and proposed a simplified anthropic scenario for axion dark matter in which they argue that the first two of these problems do not apply. [M. Tegmark, A. Aguirre, M. Rees and F. Wilczek, "Dimensionless constants, cosmology and other dark matters", arxiv|archive=astro-ph|id=0511774. F. Wilczek, "Enlightenment, knowledge, ignorance, temptation," arxiv|archive=hep-ph|id=0512187. See also the discussion at [http://www.math.columbia.edu/~woit/wordpress/?p=310] .]

Vilenkin and collaborators have proposed a consistent way to define the probabilities for a given vacuum. [See, "e.g." cite arxiv|author=A. Vilenkin|year=2006|title=A measure of the multiverse|eprint=hep-th/0609193|version=]

A problem with many of the simplified approaches people have tried is that they "predict" a cosmological constant that is too large by a factor of 10–1000 (depending on one's assumptions) and hence suggest that the cosmic acceleration should be much more rapid than is observed. [cite journal|title=An observational test for the anthropic origin of the cosmological constant|author=Abraham Loeb|date=2006|journal=JCAP|volume=0605|pages=009|url=http://www.arxiv.org/astro-ph/0604242|format=subscription required] [cite journal|title=Anthropic prediction for Lambda and the Q catastrophe|author=Jaume Garriga and Alexander Vilenkin|year=2006|volume=163|pages=245–57|journal=Prog. Theor.Phys. Suppl.|url=http://www.arxiv.org/hep-th/0508005|doi=10.1143/PTPS.163.245|format=subscription required] [cite journal|title=Probabilities in the Bousso-Polchinski multiverse|author=Delia Schwartz-Perlov and Alexander Vilenkin|date=2006|journal=JCAP|volume=0606|pages=010|url=http://www.arxiv.org/hep-th/0601162|format=subscription required]

Proponents and opponents of the idea

Although few dispute the idea that string theory appears to have an unimaginably large number of metastable vacua, the existence, meaning and scientific relevance of the anthropic landscape remain highly controversial. Prominent proponents of the idea include Andrei Linde, Sir Martin Rees and especially Leonard Susskind who advocate it as a solution to the cosmological constant problem. Opponents, such as David Gross, suggest that the idea is inherently unscientific, unfalsifiable or premature.

The term "landscape" comes from evolutionary biology (see "Fitness landscape") and was first applied to cosmology by Lee Smolin in his book. [L. Smolin, "Did the universe evolve?," "Classical and Quantum Gravity" 9, 173–191 (1992). L. Smolin, "The Life of the Cosmos" (Oxford, 1997)] It was first used in the context of string theory by Susskind. [L. Susskind, "The anthropic landscape of string theory", arxiv|archive=hep-th|id=0302219.]

There are several popular books about the anthropic principle in cosmology. [L. Susskind, "The cosmic landscape: string theory and the illusion of intelligent design" (Little, Brown, 2005). M. J. Rees, "Just six numbers: the deep forces that shape the universe" (Basic Books, 2001). R. Bousso and J. Polchinski, "The string theory landscape", "Sci. Am." 291, 60–69 (2004).] Two popular physics blogs are opposed to this use of the anthropic principle. [ Lubos Motl's [http://motls.blogspot.com blog] criticized the anthropic principle and Peter Woit's [http://www.math.columbia.edu/~woit/blog/ blog] frequently attacks the anthropic string landscape.]

References

External links

* [http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=hep-th&level=1&index1=5460697 String theory landscape on arxiv.org]