String theory landscape

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.[7]

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.[8]

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 ${\displaystyle P(x)}$ of observing some fundamental parameters ${\displaystyle x}$ is given by,

${\displaystyle P(x)=P_{\mathrm {prior} }(x)\times P_{\mathrm {selection} }(x),}$

where ${\displaystyle P_{\mathrm {prior} }}$ is the prior probability, from fundamental theory, of the parameters ${\displaystyle x}$ and ${\displaystyle P_{\mathrm {selection} }}$ is the "anthropic selection function", determined by the number of "observers" that would occur in the universe with parameters ${\displaystyle x}$.

These probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that:

• The function ${\displaystyle P_{\mathrm {prior} }}$ is completely unknown in string theory and may be impossible to define or interpret in any sensible probabilistic way.
• The function ${\displaystyle P_{\mathrm {selection} }}$ 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.

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.[9]

Vilenkin and collaborators have proposed a consistent way to define the probabilities for a given vacuum.[10]

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 (depending on one's assumptions) and hence suggest that the cosmic acceleration should be much more rapid than is observed.[11][12][13]

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

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

David Gross 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.

There are several popular books about the anthropic principle in cosmology.[14] The authors of two physics blogs, Lubos Motl and Peter Woit, are opposed to this use of the anthropic principle.[15]