The string theory landscape or landscape of vacua refers to the collection of possible
false vacua in
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
,
[The number of metastable vacua is not known exactly, but commonly quoted estimates are of the 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).] 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
Evolutionary biology is the subfield of biology that studies the evolutionary processes (natural selection, common descent, speciation) that produced the diversity of life on Earth. It is also defined as the study of the history of life ...
. It was first applied to cosmology by
Lee Smolin
Lee Smolin (; born June 6, 1955) is an American theoretical physicist, a faculty member at the Perimeter Institute for Theoretical Physics, an adjunct professor of physics at the University of Waterloo and a member of the graduate faculty of the ...
in his book ''
The Life of the Cosmos'' (1997), and was first used in the context of string theory by
Leonard Susskind
Leonard Susskind (; born June 16, 1940)his 60th birthday was celebrated with a special symposium at Stanford University.in Geoffrey West's introduction, he gives Suskind's current age as 74 and says his birthday was recent. is an American physicis ...
.
Compactified Calabi–Yau manifolds
In string theory the number of flux vacua is commonly thought to be roughly
, but could be
or higher. The large number of possibilities arises from choices of
Calabi–Yau manifold
In algebraic geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics. Particularly in superstrin ...
s and choices of generalized
magnetic flux
In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the weber ...
es over various
homology cycles, found in
F-theory
In theoretical physics, F-theory is a branch of string theory developed by Iranian physicist Cumrun Vafa. The new vacua described by F-theory were discovered by Vafa and allowed string theorists to construct new realistic vacua — in the fo ...
.
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
Andrei Dmitriyevich Linde (russian: Андре́й Дми́триевич Ли́нде; born March 2, 1948) is a Russian-American theoretical physicist and the Harald Trap Friis Professor of Physics at Stanford University.
Linde is one of the ...
, and
Sandip Trivedi
Sandip Trivedi ( hi, सन्दिप त्रिवेदी; born 1963) is an Indian theoretical physicist working at Tata Institute for Fundamental Research (TIFR) at Mumbai, India, while he is its current director. He is well known for h ...
.
Fine-tuning by the anthropic principle
Fine-tuning of constants like the
cosmological constant or the
Higgs boson
The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the quantum excitation of the Higgs field,
one of the fields in particle physics theory. In the Stan ...
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
The anthropic principle, also known as the "observation selection effect", is the hypothesis, first proposed in 1957 by Robert Dicke, that there is a restrictive lower bound on how statistically probable our observations of the universe are, bec ...
proposes that fundamental constants may have the values they have because such values are necessary for life (and therefore intelligent observers to measure the constants). 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
The multiverse is a hypothetical group of multiple universes. Together, these universes comprise everything that exists: the entirety of space, time, matter, energy, information, and the physical laws and constants that describe them. The dif ...
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
Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification ...
; interpreting probability in a context where it is only possible to draw one
sample
Sample or samples may refer to:
Base meaning
* Sample (statistics), a subset of a population – complete data set
* Sample (signal), a digital discrete sample of a continuous analog signal
* Sample (material), a specimen or small quantity of ...
from a
distribution Distribution may refer to:
Mathematics
* Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations
*Probability distribution, the probability of a particular value or value range of a vari ...
is problematic in
frequentist probability
Frequentist probability or frequentism is an interpretation of probability; it defines an event's probability as the limit of its relative frequency in many trials (the long-run probability). Probabilities can be found (in principle) by a repe ...
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:
* The function
is completely unknown in string theory and may be impossible to define or interpret in any sensible probabilistic way.
* The function
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.
Simplified approaches
Tegmark ''et al.'' have recently considered these objections and proposed a simplified anthropic scenario for
axion
An axion () is a hypothetical elementary particle postulated by the Peccei–Quinn theory in 1977 to resolve the strong CP problem in quantum chromodynamics (QCD). If axions exist and have low mass within a specific range, they are of interest ...
dark matter
Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not ...
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 (depending on one's assumptions) 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
Andrei Linde
Andrei Dmitriyevich Linde (russian: Андре́й Дми́триевич Ли́нде; born March 2, 1948) is a Russian-American theoretical physicist and the Harald Trap Friis Professor of Physics at Stanford University.
Linde is one of the ...
,
Sir Martin Rees
Martin John Rees, Baron Rees of Ludlow One or more of the preceding sentences incorporates text from the royalsociety.org website where: (born 23 June 1942) is a British cosmologist and astrophysicist. He is the fifteenth Astronomer Royal, ...
and
Leonard Susskind
Leonard Susskind (; born June 16, 1940)his 60th birthday was celebrated with a special symposium at Stanford University.in Geoffrey West's introduction, he gives Suskind's current age as 74 and says his birthday was recent. is an American physicis ...
advocate it as a solution to the
cosmological constant problem
In cosmology, the cosmological constant problem or vacuum catastrophe is the disagreement between the observed values of vacuum energy density (the small value of the cosmological constant) and theoretical large value of zero-point energy sugge ...
.
Weak scale supersymmetry from the landscape
The string landscape ideas can be applied to the notion of weak scale supersymmetry and the Little Hierarchy problem.
For string vacua which include the MSSM (Minimal Supersymmetric Standard Model) as the low energy effective field theory, all values of SUSY breaking fields
are expected to be equally likely on the landscape. This led Douglas and others to propose that the SUSY breaking scale is distributed as a power
law in the landscape
where
is the number of F-breaking fields
(distributed as complex numbers) and
is the number of D-breaking fields (distributed as real numbers).
Next, one may impose the Agrawal, Barr, Donoghue, Seckel (ABDS) anthropic requirement that the derived weak scale lie within a factor of a few
of our measured value (lest nuclei as needed for life as we know it become unstable (the atomic principle)).
Combining these effects with a mild power-law draw to large soft SUSY breaking terms,
one may calculate the Higgs boson and superparticle masses expected from the landscape.
The Higgs mass probability distribution peaks around 125 GeV while sparticles (with the exception of light higgsinos) tend to
lie well beyond current LHC search limits. This approach is an example of the application of stringy naturalness.
Scientific relevance
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.
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.
[Motl's blog criticized the anthropic principle and Woit']
blog
frequently attacks the anthropic string landscape.
See also
*
Swampland
*
Extra dimensions
References
External links
String landscape; moduli stabilization; flux vacua; flux compactificationon
arxiv.org.
*
{{DEFAULTSORT:String Theory Landscape
Physical cosmology
String theory
Multiverse