Inflation: Observations and Attractors

  • Diederik Roest
  • Marco Scalisi
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 176)


In these lecture notes, we present the latest status of CMB observations and outline a particular set of inflationary models to explain these data. As an introduction, we provide the necessary background to understand the Planck results on the temperature fluctuations of the CMB. We then explain how these results can be interpreted in terms of the number of e-folds during inflation. Finally, we discuss theoretical models that underpin this interpretation and yield robust predictions for future CMB observables.


Cosmic Microwave Background Quantum Fluctuation Inflationary Model Hubble Radius Inflaton Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We are grateful to our collaborators John Joseph Carrasco, Mario Galante, Juan Garcia-Bellido, Renata Kallosh and Andrei Linde, who have all contributed in a major way to the results described in the last chapters. Moreover, DR would like to thank the organization of the school on “Theoretical Frontiers in Black Holes and Cosmology” in Natal, Brasil, from June 8 to 12, 2015, for a stimulating atmosphere.


  1. 1.
    A.D. Linde, Particle physics and inflationary cosmology. Contemp. Concepts Phys. 5, 1 (1990). arXiv:hep-th/0503203 Google Scholar
  2. 2.
    S. Dodelson, Modern Cosmology (Academic Press, Amsterdam, 2003)Google Scholar
  3. 3.
    V. Mukhanov, Physical Foundations of Cosmology (Cambridge University Press, Oxford, 2005)CrossRefzbMATHGoogle Scholar
  4. 4.
    S. Weinberg, Cosmology (Oxford University Press, Oxford, 2008)zbMATHGoogle Scholar
  5. 5.
    D. Baumann, Inflation, in Physics of the large and the small, TASI 09, proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics, Boulder, Colorado, USA, 1–26 June 2009 (2011) pp. 523-686, arXiv:0907.5424 [hep-th]
  6. 6.
    E. Hubble, A relation between distance and radial velocity among extra-galactic nebulae. Proc. Natl. Acad. Sci. 15, 168 (1929)ADSCrossRefzbMATHGoogle Scholar
  7. 7.
    A.H. Guth, The inflationary universe: a possible solution to the horizon and flatness problems. Phys. Rev. D 23, 347 (1981)ADSCrossRefGoogle Scholar
  8. 8.
    A.D. Linde, A new inflationary universe scenario: a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems. Phys. Lett. B 108, 389 (1982)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    A. Albrecht, P.J. Steinhardt, Cosmology for grand unified theories with radiatively induced symmetry breaking. Phys. Rev. Lett. 48, 1220 (1982)ADSCrossRefGoogle Scholar
  10. 10.
    U. Seljak, Measuring polarization in cosmic microwave background. Astrophys. J. 482, 6 (1997). arXiv:astro-ph/9608131 ADSCrossRefGoogle Scholar
  11. 11.
    M. Kamionkowski, A. Kosowsky, A. Stebbins, A Probe of primordial gravity waves and vorticity. Phys. Rev. Lett. 78, 2058 (1997). arXiv:astro-ph/9609132 ADSCrossRefGoogle Scholar
  12. 12.
    U. Seljak, M. Zaldarriaga, Signature of gravity waves in polarization of the microwave background. Phys. Rev. Lett. 78, 2054 (1997). arXiv:astro-ph/9609169 ADSCrossRefGoogle Scholar
  13. 13.
    M. Zaldarriaga, U. Seljak, An all sky analysis of polarization in the microwave background. Phys. Rev. D 55, 1830 (1997). arXiv:astro-ph/9609170 ADSCrossRefGoogle Scholar
  14. 14.
    M. Kamionkowski, A. Kosowsky, A. Stebbins, Statistics of cosmic microwave background polarization. Phys. Rev. D 55, 7368 (1997). arXiv:astro-ph/9611125 ADSCrossRefGoogle Scholar
  15. 15.
    W. Hu, M.J. White, A CMB polarization primer. New Astron. 2, 323 (1997). arXiv:astro-ph/9706147 ADSCrossRefGoogle Scholar
  16. 16.
    T.S. Bunch, P.C.W. Davies, Quantum field theory in de sitter space: renormalization by point splitting. Proc. R. Soc. Lond. A 360, 117 (1978)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    A.H. Guth, S.Y. Pi, Fluctuations in the new inflationary universe. Phys. Rev. Lett. 49, 1110 (1982)ADSCrossRefGoogle Scholar
  18. 18.
    A.A. Penzias, R.W. Wilson, A measurement of excess antenna temperature at 4080-Mc/s. Astrophys. J. 142, 419 (1965)ADSCrossRefGoogle Scholar
  19. 19.
    W. Hu, Lecture Notes on CMB Theory: From Nucleosynthesis to Recombination. arXiv:0802.3688 [astro-ph]
  20. 20.
    P.A.R. Ade et al., Planck Collaboration, Planck 2015 results. XIII. Cosmological parameters. arXiv:1502.01589 [astro-ph.CO]
  21. 21.
    P.A.R. Ade et al., Planck Collaboration, Planck 2015 results. XX. Constraints on inflation. arXiv:1502.02114 [astro-ph.CO]
  22. 22.
    G.F. Smoot et al., Structure in the COBE differential microwave radiometer first year maps. Astrophys. J. 396, L1 (1992)ADSCrossRefGoogle Scholar
  23. 23.
    V. Mukhanov, Quantum cosmological perturbations: predictions and observations. Eur. Phys. J. C 73, 2486 (2013) arXiv:1303.3925 [astro-ph.CO]
  24. 24.
    D. Roest, Universality classes of inflation. JCAP 1401, 007 (2014). arXiv:1309.1285 [hep-th]ADSCrossRefGoogle Scholar
  25. 25.
    J. Garcia-Bellido, D. Roest, Large-\(N\) running of the spectral index of inflation. Phys. Rev. D 89(10), 103527 (2014) arXiv:1402.2059 [astro-ph.CO]
  26. 26.
    J. Garcia-Bellido, D. Roest, M. Scalisi, I. Zavala, Can CMB data constrain the inflationary field range? JCAP 1409, 006 (2014). arXiv:1405.7399 [hep-th]ADSCrossRefGoogle Scholar
  27. 27.
    J. Garcia-Bellido, D. Roest, M. Scalisi, I. Zavala, Lyth bound of inflation with a tilt. Phys. Rev. D 90(12), 123539 (2014). arXiv:1408.6839 [hep-th]ADSCrossRefGoogle Scholar
  28. 28.
    P. Creminelli, S. Dubovsky, D.L. Nacir, M. Simonovic, G. Trevisan, G. Villadoro, M. Zaldarriaga, Implications of the scalar tilt for the tensor-to-scalar ratio. arXiv:1412.0678 [astro-ph.CO]
  29. 29.
    D.Z. Freedman, A. Van Proeyen, Supergravity (Cambridge University Press, Cambridge, 2012)CrossRefzbMATHGoogle Scholar
  30. 30.
    E.J. Copeland, A.R. Liddle, D.H. Lyth, E.D. Stewart, D. Wands, False vacuum inflation with Einstein gravity. Phys. Rev. D 49, 6410 (1994). arXiv:astro-ph/9401011 ADSCrossRefGoogle Scholar
  31. 31.
    M. Kawasaki, M. Yamaguchi, T. Yanagida, Natural chaotic inflation in supergravity. Phys. Rev. Lett. 85, 3572 (2000). arXiv:hep-ph/0004243 ADSCrossRefGoogle Scholar
  32. 32.
    R. Kallosh, A. Linde, T. Rube, General inflaton potentials in supergravity. Phys. Rev. D 83, 043507 (2011). arXiv:1011.5945 [hep-th]ADSCrossRefGoogle Scholar
  33. 33.
    J.J.M. Carrasco, R. Kallosh, A. Linde, D. Roest, Hyperbolic geometry of cosmological attractors. Phys. Rev. D 92(4), 041301 (2015). arXiv:1504.05557 [hep-th]ADSCrossRefGoogle Scholar
  34. 34.
    R. Kallosh, A. Linde, Universality class in conformal inflation. JCAP 1307, 002 (2013). arXiv:1306.5220 [hep-th]ADSCrossRefGoogle Scholar
  35. 35.
    S. Ferrara, R. Kallosh, A. Linde, M. Porrati, Minimal supergravity models of inflation. Phys. Rev. D 88(8), 085038 (2013). arXiv:1307.7696 [hep-th]ADSCrossRefGoogle Scholar
  36. 36.
    R. Kallosh, A. Linde, D. Roest, Superconformal inflationary \(\alpha \)-attractors. JHEP 1311, 198 (2013). arXiv:1311.0472 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    R. Kallosh, A. Linde, D. Roest, Large field inflation and double \(\alpha \)-attractors. JHEP 1408, 052 (2014). arXiv:1405.3646 [hep-th]ADSCrossRefGoogle Scholar
  38. 38.
    M. Galante, R. Kallosh, A. Linde, D. Roest, Unity of cosmological inflation attractors. Phys. Rev. Lett. 114(14), 141302 (2015). arXiv:1412.3797 [hep-th]ADSCrossRefGoogle Scholar
  39. 39.
    D. Roest, M. Scalisi, Cosmological attractors from a-scale supergravity. Phys. Rev. D 92, 043525 (2015). arXiv:1503.07909 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    M. Scalisi, Cosmological \(\alpha \)-Attractors and de Sitter Landscape. arXiv:1506.01368 [hep-th]

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Van Swinderen Institute for Particle Physics and GravityUniversity of GroningenGroningenThe Netherlands

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