hi cosmo-torun,
It's my turn to give a talk this Friday @16.00, but i'm still thinking over what i'll present... More soon...
Meanwhile, here's a followup of the discussion we had a few weeks ago.
See Eq.(32), page 11, of Andrew Liddle's 1999 introduction to inflation (quite nice): http://arXiv.org/pdf/astro-ph/9901124.
This quite clearly points out that in comoving units, the horizon including an inflationary epoch is >> than the matter horizon.
More formally:
present particle horizon if there was an inflationary epoch = \int_{t_*}^{t_0}} dt/a(t) > \int_{t_*}^{t_{dec}} dt/a(t) \gg \int_{t_{dec}}^{t_0} dt/a(t) \sim present particle horizon assuming no inflationary epoch
where * the > is because a(t) > 0 and t_0 > t_dec ; * the \gg is Eq. (32), i.e. it's "the basic strategy" that "solves the horizon problem" according to Andrew; * the \sim ignores everything between the end of inflation and decoupling, for simplicity of the discussion
It looks to me like Andrew has been quite careful here - most of the time he uses the term "Hubble length", not "horizon".
i suspect that in general, inflationary people make what is called an "abuse of language" - something that literally is wrong, but is said in practice because it's short and easy to say, and once you know the subject and think about it, it's clear what the correct meaning is even though what you say is literally incorrect. [For example, we often talk about an integral "to infinity", even though really we mean "a limit where N increases without bound", since there is no real number called infinity. It's easier to say "infinity".]
It looks Andrew did fall back into this habit later on - see page 33 first paragraph. However, even on page 11 he was not as careful as he could have been, he wrote "the region of the Universe we can see", which could have been stated more carefully as "the region of the Universe we can see if we assume that there was no inflation".
Back to the subject: compare Equations (25) and (32). Making the particle horizon *much* bigger is the whole point of inflation.
pozdr boud