The string theory landscape or anthropic landscape refers to the large number of different false vacua in string theory. It arises from the idea that there are an extremely large number of metastable vacua (ground states) in string theory. The large number of possibilites arise from different choices of Calabi-Yau manifolds and different values of generalized magnetic fluxes over different homology cycles. This large number of de-Sitter like metastable vacua is thought by some physicists to be large enough that the known laws of physics, the Standard Model and General relativity with a positive cosmological constant, occurs in at least one, although computing quantities such as masses of particles and Yukawa couplings for even a single vacuum is a technically difficult problem.

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. 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. 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,

$P(x)=P\_\backslash mathrm\{prior\}(x)\backslash times\; P\_\backslash mathrm\{selection\}(x),$

where $P\_\backslash mathrm\{prior\}$ is the prior probability, from fundamental theory, of the parameters $x$ and $P\_\backslash mathrm\{selection\}$ 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 $P\_\backslash mathrm\{prior\}$ is completely unknown in string theory and may be impossible to define or interpret in any sensible probablistic way.
• The function $P\_\backslash mathrm\{selection\}$ is completely unknown, since so little is known about the origin of life and 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, but as yet there is no widespread agreement. These ideas have been reviewed by Carroll . 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.

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. Many other physicists retain a suspicious or neutral view about the scenario of the anthropic landscape and hope to have in the future a better and more scientific explanation.

The term "landscape" comes from evolutionary biology (see Fitness landscape) and was first applied to cosmology by Lee Smolin in his book . It was first used in the context of string theory by Susskind. There are several popular books about the anthropic principle in cosmology. Two popular physics blogs are opposed to the anthropic principle.

References

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1. The most commonly quoted number is of order 10⁵⁰⁰. See M. Douglas, "The statistics of string / M theory vacua", JHEP 0305, 46 (2003). ; S. Ashok and M. Douglas, "Counting flux vacua", JHEP 0401, 060 (2004).
2. R. Bousso and J. Polchinski, "Quantization of four-form fluxes and dynamical neutralization of the cosmological constant", JHEP 06, 006 (2000). S. Kachru, R. Kallosh, A. Linde and S. Trivedi, "de Sitter vacua in string theory", Phys. Rev. D68, 046005 (2003).
3. S. Weinberg, "Anthropic bound on the cosmological constant", Phys. Rev. Lett. 59, 2607 (1987).
4. S. M. Carroll, "Is our universe natural?", .
5. M. Tegmark, A. Aguirre, M. Rees and F. Wilczek, "Dimensionless constants, cosmology and other dark matters", . F. Wilczek, "Enlightenment, knowledge, ignorance, temptation," . See also the discussion at ^*.
6. L. Smolin, "Did the universe evolve?," Classical and Quantum Gravity 9, 173–191 (1992). L. Smolin, The Life of the Cosmos (Oxford, 1997)
7. L. Susskind, "The anthropic landscape of string theory", .
8. 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).
9. Lubos Motl's blog criticized the anthropic principle and Peter Woit's blog frequently attacks the anthropic string landscape.

• landscape on arxiv.org

Physical cosmology | String theory

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