String theory landscape

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In string theory, the string theory landscape (or landscape of vacua) is the collection of possible false vacua, [1] together comprising a collective "landscape" of choices of parameters governing compactifications.

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The term "landscape" comes from the notion of a fitness landscape in evolutionary biology. [2] It was first applied to cosmology by Lee Smolin in his book The Life of the Cosmos (1997), and was first used in the context of string theory by Leonard Susskind. [3]

Compactified Calabi–Yau manifolds

In string theory the number of flux vacua is commonly thought to be roughly , [4] but could be [5] 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. [6] 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. [7]

Fine-tuning by the anthropic principle

Fine-tuning 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[ according to whom? ] that this is not the case, and that many different vacua are physically realized. [8] The anthropic principle 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.

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. [9]

Weinberg attempted to predict the magnitude of the cosmological constant based on probabilistic arguments. Other attempts[ which? ] have been made to apply similar reasoning to models of particle physics. [10]

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 .[ citation needed ]

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

Simplified approaches

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. [11]

Vilenkin and collaborators have proposed a consistent way to define the probabilities for a given vacuum. [12]

A problem with many of the simplified approaches people[ who? ] 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. [13] [14] [15]

Interpretation

Few dispute the large number of metastable vacua.[ citation needed ] The existence, meaning, and scientific relevance of the anthropic landscape, however, remain controversial.[ further explanation needed ]

Cosmological constant problem

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

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 [16] 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 [17] 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. [18] 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[ citation needed ] 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. [19] The authors of two physics blogs, Lubos Motl and Peter Woit, are opposed to this use of the anthropic principle.[ why? ] [20]

See also

Related Research Articles

The anthropic principle, also known as the observation selection effect, is the hypothesis, first proposed in 1957 by Robert Dicke, that the range of possible observations that could be made about the universe is limited by the fact that observations could happen only in a universe capable of developing intelligent life. As Steven Weinberg puts it: "Where else could we be, except on a planet that can sustain life?" Proponents of the anthropic principle argue that it explains why the universe has the age and the fundamental physical constants necessary to accommodate conscious life, since if either had been different, no one would have been around to make observations. Anthropic reasoning is often used to deal with the idea that the universe seems to be finely tuned for the existence of life.

<span class="mw-page-title-main">Inflation (cosmology)</span> Theory of rapid universe expansion

In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch is believed to have lasted from 10−36 seconds to between 10−33 and 10−32 seconds after the Big Bang. Following the inflationary period, the universe continued to expand, but at a slower rate. The re-acceleration of this slowing expansion due to dark energy began after the universe was already over 7.7 billion years old.

<span class="mw-page-title-main">Multiverse</span> Hypothetical group of multiple universes

The multiverse is the hypothetical set of all universes. Together, these universes are presumed to comprise everything that exists: the entirety of space, time, matter, energy, information, and the physical laws and constants that describe them. The different universes within the multiverse are called "parallel universes", "flat universes", "other universes", "alternate universes", "multiple universes", "plane universes", "parent and child universes", "many universes", or "many worlds". One common assumption is that the multiverse is a "patchwork quilt of separate universes all bound by the same laws of physics."

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 interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. Thus, string theory is a theory of quantum gravity.

<span class="mw-page-title-main">Cosmological constant</span> Constant representing stress–energy density of the vacuum

In cosmology, the cosmological constant, alternatively called Einstein's cosmological constant, is the constant coefficient of a term that Albert Einstein temporarily added to his field equations of general relativity. He later removed it; however, much later it was revived and reinterpreted as the energy density of space, or vacuum energy, that arises in quantum mechanics. It is closely associated with the concept of dark energy.

<span class="mw-page-title-main">Brane cosmology</span> Several theories in particle physics and cosmology related to superstring theory and M-theory

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<span class="mw-page-title-main">Leonard Susskind</span> American theoretical physicist (born 1940)

Leonard Susskind is an American theoretical physicist, Professor of theoretical physics at Stanford University and founding director of the Stanford Institute for Theoretical Physics. His research interests are string theory, quantum field theory, quantum statistical mechanics and quantum cosmology. He is a member of the US National Academy of Sciences, and the American Academy of Arts and Sciences, an associate member of the faculty of Canada's Perimeter Institute for Theoretical Physics, and a distinguished professor of the Korea Institute for Advanced Study.

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<span class="mw-page-title-main">Andrei Linde</span> Russian-American theoretical physicist

Andrei Dmitriyevich Linde is a Russian-American theoretical physicist and the Harald Trap Friis Professor of Physics at Stanford University.

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Cosmological natural selection, also called the fecund universes, is a hypothesis proposed by Lee Smolin intended as a scientific alternative to the anthropic principle. It addresses the problem of complexity in our universe, which is largely unexplained. The hypothesis suggests that a process analogous to biological natural selection applies at the grandest of scales. Smolin published the idea in 1992 and summarized it in a book aimed at a lay audience called The Life of the Cosmos.

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<span class="mw-page-title-main">Cosmological constant problem</span> Concept in cosmology

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<span class="mw-page-title-main">Renata Kallosh</span> Theoretical physicist

Renata Elizaveta Kallosh is a Russian-American theoretical physicist. She is a professor of physics at Stanford University, working there on supergravity, string theory and inflationary cosmology.

Raphael Bousso is a theoretical physicist and cosmologist. He is a professor at the Berkeley Center for Theoretical Physics in the Department of Physics, UC Berkeley. He is known for the Bousso bound on the information content of the universe. With Joseph Polchinski, Bousso proposed the string theory landscape as a solution to the cosmological constant problem.

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The measure problem in cosmology concerns how to compute the ratios of universes of different types within a multiverse. It typically arises in the context of eternal inflation. The problem arises because different approaches to calculating these ratios yield different results, and it is not clear which approach is correct.

References

  1. 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", JHEP0305, 46 (2003). arXiv : hep-th/0303194; S. Ashok and M. Douglas, "Counting flux vacua", JHEP0401, 060 (2004).
  2. Baggott, Jim (2018). Quantum Space Loop Quantum Gravity and the Search for the Structure of Space, Time, and the Universe. Oxford University Press. p. 288. ISBN   978-0-19-253681-5.
  3. L. Smolin, "Did the universe evolve?", Classical and Quantum Gravity9, 173–191 (1992). L. Smolin, The Life of the Cosmos (Oxford, 1997)
  4. Read, James; Le Bihan, Baptiste (2021). "The landscape and the multiverse: What's the problem?". Synthese. 199 (3–4): 7749–7771. doi: 10.1007/s11229-021-03137-0 . S2CID   234815857.
  5. Taylor, Washington; Wang, Yi-Nan (2015). "The F-theory geometry with most flux vacua". Journal of High Energy Physics. 2015 (12): 164. arXiv: 1511.03209 . Bibcode:2015JHEP...12..164T. doi:10.1007/JHEP12(2015)164. S2CID   41149049.
  6. Frederik Denef; Douglas, Michael R. (2007). "Computational complexity of the landscape". Annals of Physics. 322 (5): 1096–1142. arXiv: hep-th/0602072 . Bibcode:2007AnPhy.322.1096D. doi:10.1016/j.aop.2006.07.013. S2CID   281586.
  7. Kachru, Shamit; Kallosh, Renata; Linde, Andrei; Trivedi, Sandip P. (2003). "de Sitter Vacua in String Theory". Physical Review D. 68 (4): 046005. arXiv: hep-th/0301240 . Bibcode:2003PhRvD..68d6005K. doi:10.1103/PhysRevD.68.046005. S2CID   119482182.
  8. L. Susskind, "The anthropic landscape of string theory", arXiv : hep-th/0302219.
  9. S. Weinberg, "Anthropic bound on the cosmological constant", Phys. Rev. Lett.59, 2607 (1987).
  10. S. M. Carroll, "Is our universe natural?" (2005) arXiv : hep-th/0512148 reviews a number of proposals in preprints dated 2004/5.
  11. M. Tegmark, A. Aguirre, M. Rees and F. Wilczek, "Dimensionless constants, cosmology and other dark matters", arXiv : astro-ph/0511774. F. Wilczek, "Enlightenment, knowledge, ignorance, temptation", arXiv : hep-ph/0512187. See also the discussion at .
  12. See, e.g.Alexander Vilenkin (2007). "A measure of the multiverse". Journal of Physics A: Mathematical and Theoretical. 40 (25): 6777–6785. arXiv: hep-th/0609193 . Bibcode:2007JPhA...40.6777V. doi:10.1088/1751-8113/40/25/S22. S2CID   119390736.
  13. Abraham Loeb (2006). "An observational test for the anthropic origin of the cosmological constant". Journal of Cosmology and Astroparticle Physics. 0605 (5): 009. arXiv: astro-ph/0604242 . Bibcode:2006JCAP...05..009L. doi:10.1088/1475-7516/2006/05/009. S2CID   39340203.
  14. Jaume Garriga & Alexander Vilenkin (2006). "Anthropic prediction for Lambda and the Q catastrophe". Prog. Theor. Phys. Suppl. 163: 245–57. arXiv: hep-th/0508005 . Bibcode:2006PThPS.163..245G. doi:10.1143/PTPS.163.245. S2CID   118936307.
  15. Delia Schwartz-Perlov & Alexander Vilenkin (2006). "Probabilities in the Bousso-Polchinski multiverse". Journal of Cosmology and Astroparticle Physics. 0606 (6): 010. arXiv: hep-th/0601162 . Bibcode:2006JCAP...06..010S. doi:10.1088/1475-7516/2006/06/010. S2CID   119337679.
  16. M. R. Douglas, "Statistical analysis of the supersymmetry breaking scale", arXiv : hep-th/0405279.
  17. V. Agrawal, S. M. Barr, J. F. Donoghue and D. Seckel, "Anthropic considerations in multiple domain theories and the scale of electroweak symmetry breaking", Phys. Rev. Lett.80, 1822 (1998).arXiv : hep-ph/9801253
  18. H. Baer, V. Barger, H. Serce and K. Sinha, "Higgs and superparticle mass predictions from the landscape", JHEP03, 002 (2018), arXiv : 1712.01399 .
  19. 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).
  20. Motl's blog criticized the anthropic principle and Woit's blog frequently attacks the anthropic string landscape.