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A couple of inflationary problems

  1. Apr 12, 2015 #1
    Hi guys.

    I'm new here and I want to ask you if anybody of you have some ideas to solve this two problems:

    1. Consider single field inflation in slow roll regime, at which the slow roll parameter ǫ
    decreases in time. Take any inflaton potential consistent with the CMB and galaxy distri-
    bution data. Show that during the period at inflation, which is responsible for generating
    the adiabatic perturbations, the inflaton field rolls down at least by

    \begin{equation} \Delta \phi \gtrsim 10rM_{planck}

    where r is the tensor-to-scalar ratio. [This means, in particular, that the discovery of tensor
    modes with r ∼ 0.2, as originally claimed by BICEP-2, would imply that the variation of
    the inflaton over the relevant period of time at inflationary epoch was super-Planckian.]

    Relatively short gravity waves, created at inflation, after horizon re-entry at radiation
    domination can be viewed as a collection of gravitons (just like electromagnetic waves emitted
    by antenna can be viewed as a collection of photons). Assuming that the Hubble parameter
    H some 60 e-foldings before inflation end is known, calculate the average (over enesemble of
    universes) number of gravitons <N(k,\Delta k)> in the present visible Universe in the interval of
    momenta from k/a0 to (k +\Delta k)/a0, and relative variance of this number

    \begin{equation} \frac{ \sqrt{ <N^{2}(k,\Delta k)> - <N(k,\Delta k)>^{2} }}{<N(k,\Delta k)>}

    Dropping the assumption about the value of the Hubble parameter, calculate these quantities
    for the inflaton potential V = (m^2φ^2)/2. Give numerical estimates in the latter case for
    k/a0 = 1 Mpc^(−1), \Delta k = k.

    I thank you in advance for any kind of helps
    Last edited by a moderator: Apr 12, 2015
  2. jcsd
  3. Apr 12, 2015 #2


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    Staff: Mentor

    Thread closed temporarily for Moderation...
  4. Apr 12, 2015 #3


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    Staff: Mentor

    Thread reopened.

    @supertramp87 -- Welcome to the PF.

    Per the PF Rules (see Info at the top of the page), we do allow graduate school-level questions in the general technical PF forums (all others go in the Homework Help forums). But this exception is only allowed if you show lots of work and effort on the question. Can you please make a follow-up post that shows how you are approaching the problem? Thanks! :smile:
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