String theory landscape


The string theory landscape refers to the collection of possible false vacua in string theory, together comprising a collective "landscape" of choices of parameters governing compactifications.
The term "landscape" comes from the notion of a fitness landscape in evolutionary biology. It was first applied to cosmology by Lee Smolin in his book The Life of the Cosmos, and was first used in the context of string theory by Leonard Susskind.

Compactified Calabi–Yau manifolds

In string theory the number of flux vacua is thought to be at least. The large number of possibilities arises from choices of Calabi–Yau manifolds and choices of generalized magnetic fluxes over various homology cycles, found in F-theory.
If there is no structure in the space of vacua, the problem of finding one with a sufficiently small cosmological constant is NP complete. This is a version of the subset sum problem.
A possible mechanism of string theory vacuum stabilization, now known as the KKLT mechanism, was proposed in 2003 by Shamit Kachru, Renata Kallosh, Andrei Linde, and Sandip Trivedi.

Fine-tuning by anthropics

of constants like the cosmological constant or the Higgs boson mass are usually assumed to occur for precise physical reasons as opposed to taking their particular values at random. That is, these values should be uniquely consistent with underlying physical laws.
The number of theoretically allowed configurations has prompted suggestions that this is not the case, and that many different vacua are physically realized. The anthropic principle proposes that fundamental constants may have the values they have because such values are necessary for life. The anthropic landscape thus refers to the collection of those portions of the landscape that are suitable for supporting intelligent life.
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.

Weinberg model

In 1987, Steven Weinberg proposed that the observed value of the cosmological constant was so small because it is impossible for life to occur in a universe with a much larger cosmological constant.
Weinberg attempted to predict the magnitude of the cosmological constant based on probabilistic arguments. Other attempts have been made to apply similar reasoning to models of particle physics.
Such attempts are based in the general ideas of Bayesian probability; interpreting probability in a context where it is only possible to draw one sample from a distribution is problematic in frequentist probability but not in Bayesian probability, which is not defined in terms of the frequency of repeated events.
In such a framework, the probability of observing some fundamental parameters is given by,
where is the prior probability, from fundamental theory, of the parameters and is the "anthropic selection function", determined by the number of "observers" that would occur in the universe with parameters.
These probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that:
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.
Vilenkin and collaborators have proposed a consistent way to define the probabilities for a given vacuum.
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 orders of magnitude and hence suggest that the cosmic acceleration should be much more rapid than is observed.

Interpretation

Few dispute the large number of metastable vacua. The existence, meaning, and scientific relevance of the anthropic landscape, however, remain controversial.

Cosmological constant problem

, Sir Martin Rees and Leonard Susskind advocate it as a solution to the cosmological-constant problem.

Scientific relevance

suggests that the idea is inherently unscientific, unfalsifiable or premature. A famous debate on the anthropic landscape of string theory is the Smolin–Susskind debate on the merits of the landscape.

Popular reception

There are several popular books about the anthropic principle in cosmology. The authors of two physics blogs, Lubos Motl and Peter Woit, are opposed to this use of the anthropic principle.