174 Cosmic Inflation
- Show that the number of e-foldings of inflation in the푉(휙)=−휆휙^4 model is of
order
푁≈퐻2
휆휙^2 푖
fromthetimeatwhichthefieldhasthevalue휙푖to the end of inflation (휙≪휙푖).
Hence show that the density perturbations in this model are of order
(
훿휌
휌)
퐻≈
√
휆푁^3. (7.62)
Deduce that휆< 10 −^14 is required if the fluctuations are to be compatible with
the CMB. This of course amounts to the fine-tuning that inflation is supposed to
avoid [8].References
[1] Kaiser, N. and Silk, J. 1986Nature 324 , 529.
[2] Guth, A. H. 1981Phys. Rev.D 23 , 347.
[3] Kenney, W. H. 2009TASI Lectures on Inflation, Boulderand preprint arXiv: 0902.1529
astro-ph.CO.
[4] Linde, A. D. 1990Particle physics and inflationary cosmology. Harwood Academic
Publishers, London.
[5] Linde, A. D. 2002 Inflationary cosmology and creation of matter in the Universe. InModern
cosmology(ed. S. Bonometto, V. Gorini and U. Moschella). Institute of Physics Publishing,
Bristol.
[6] Steinhardt, P. J. and Turok, N. 2002Science 296 , 1496; 2005New Astron. Rev. 49 , 43.
[7] Peebles, P. J. E. 1993Principles of physical cosmology. Princeton University Press,
Princeton, NJ.
[8] Raine, D. J. and Thomas, E. G. 2001An introduction to the science of cosmology. Institute
of Physics Publishing, Bristol.