The string theory landscape or landscape of vacua refers to the collection of possible
false vacua in
string theory,
[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 fo ...
. 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 th ...
in his book ''
The Life of the Cosmos
''The Life of the Cosmos'' is the debut non-fiction book by American theoretical physicist Lee Smolin. The book was initially published on January 1, 1997 by Oxford University Press.
Overview
In the book, Smolin details his Fecund universes whi ...
'' (1997), 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 commonly thought to be roughly
, but could be
or higher. 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 The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S of integers and a target-sum T, and the question is to decide whether any subset of the integers sum to precisely T''.'' ...
.
A possible mechanism of string theory vacuum stabilization, now known as the KKLT mechanism, was proposed in 2003 by
Shamit Kachru,
Renata Kallosh
Renata Elizaveta Kallosh uk, Рената Єлизавета Каллош; born 1943) is Ukrainian-American a theoretical physicist. She is a Professor of Physics at Stanford University, working there on supergravity, string theory and inflat ...
,
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 ...
.
Fine-tuning by the anthropic principle
Fine-tuning of constants like the
cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant,
is the constant coefficient of a term that Albert Einstein temporarily added to his field eq ...
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 St ...
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, beca ...
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 di ...
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
Steven Weinberg (; May 3, 1933 – July 23, 2021) was an American theoretical physicist and Nobel laureate in physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic inter ...
proposed that the observed value of the
cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant,
is the constant coefficient of a term that Albert Einstein temporarily added to his field eq ...
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 o ...
; interpreting probability in a context where it is only possible to draw one
sample 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 varia ...
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
Max Erik Tegmark (born 5 May 1967) is a Swedish-American physicist, cosmologist and machine learning researcher. He is a professor at the Massachusetts Institute of Technology and the president of the Future of Life Institute. He is also a sci ...
''et al.'' have recently considered these objections and proposed a simplified anthropic scenario for
axion 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 ab ...
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 and
Leonard Susskind advocate it as a solution to the
cosmological constant problem.
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