papers on inflation
Alan Guth has a couple of recent ones (2003)
"Time since the beginning"
http://arxiv.org/astro-ph/0301199
(quote: "'eternal' inflation...proposes that our universe evolved
from an infinite tree of inflationary spacetime")
"Inflation and cosmological perturbations"
http://arxiv.org/astro-ph/0306275
Stephen Hawking has a recent one (2003)
"Cosmology from the top down"
http://www.arxiv.org/ftp/astro-ph/papers/0305/0305562.pdf
Alan Guth has an older, more wide-audience, talk too (2001)
"Eternal Inflation"
http://arxiv.org/astro-ph/0101507
-------------
In eternal inflation an inflating patch expands so fast that even tho the vacuum energy driving it decays exponentially (causing pockets of non-inflating space to form) there is always a larger patch still inflating. Once, by some quantum mechanical accident, this process begins, it must continue forever, and create a welter of pockets of space that have finished inflating.
In a curious way, it appears as if the "eternal" inflation story was invented to take care of the the question of how inflation gets started-----in all spacetime it never has to start more than once (by some no-matter-how-unlikely quantum hiccup) and once started goes on forever making jillions of universes like ours. So the question of how it got started in OUR little universe is dispelled.
If this "starting problem" had never appeared---say the standard models of physics and cosmology had, from the outset, always predicted an inflaton field causing brief exponential expansion and then decaying---then quite possibly no one would have bothered to think up this "eternal" tree of pocket universes outside our own.
Hawking's critique of the "eternal" scenario is an example of someone who disposes of it because he thinks he doesn't need it---he thinks he has a way to describe how what we see came about (without going outside the universe we see).
-------------------
For a mainstream cosmologist's view (simple oneshot inflation, no fancy theory)
Lineweaver
"Inflation and the Cosmic Microwave Background"
http://arxiv.org/astro-ph/0305179
------------------------
Another recent paper (November 2003)
Tsujikawa, Singh, Maartens
"Loop quantum gravity effects on inflation and the CMB"
"Time since the beginning"
http://arxiv.org/astro-ph/0311015
Loop gravity predicts a quantum bounce with a peak density and predicts this will trigger inflation, so no other story is needed about how it gets started. So topic of "eternal" never comes up.
For other papers see references in this one. Tsujikawa and Maartens are string theorists---this is their only contribution so far to Loop gravity---so their examination of the loop gravity mechanism for inflation is especially interesting I think.