I'm not sure, what the "standard cosmology" should mean. Approximatelly one half of cosmologists are believing in inflationary hypothesis, approximatelly one third is believing in expyrotic model by my estimations. The least common denominator is supposedly BigBang event and the birth of Universe in "singularity". But such singularity doesn't mean the pin-point Universe from high dimensional perspective, which nobody is able to verify. The singularity means the Universe size from the perspective of Planck length distance scale - i.e. single graviton wave (which is illustrated by green color on the animated scheme bellow). Such wave gradually expands and the number of wave peaks increases - so that the observer formed by such wave will obtain an illusion of fast inflation of the space. The right animation is illustrating, how the expansion of brane surface would appear from the surface cosmologist's perspective.
We can consider the classical "expanding balloon example", where the observer is living on the surface of balloon (mem)brane. Such brane can condense as a surface of droplet from the outer environment. A. Linde, the author of inflationary hypothesis is talking about phase transition of so called "
false vacuum", i.e. hypothetical former generation of Universe. We can see, from the perspective of creatures, living at the surface of such membrane the Universe really expands from minute size. Nevertheless, from the perspective of the outer observer in higher dimensions (which cannot be verified, of course), the size of Universe remains the same all the time, or it even collapses - while just a density of brane is changing. Note, that such model fills both the initial singularity concept (as required by BigBang model), both the brane concept (as required by ekpyrotic cosmology), both the inflationary model (A. Linde), both the concept of phase transition of classical matter at the same time. At the very beginning of Universe condensation, every droplet is formed by single surface wave, because the difference between both phases remains minute. In fact, it doesn't differ from classical physics by any way - but in space-time scale.