There are many different and very theoretical and hypothetical cosmological claims...
...the problems are, that only the observable universe is "observable".
Observable as in being able to "observe", "detect", "measure", "quantify", or any combination of the above.
The furthest and oldest, science and technology have been able to "observe" is currently the Cosmic Microwave Background Radiation or CMBR, which in the Big Bang timeline is the Recombination epoch.
CMBR is the oldest light (radiation) and temperature that we can and are able detect and measure, first from Bell Laboratories, in 1964, by Arno Penzias and Robert Wilson, and later confirmed by space telescopes COBE, and more recently WMAP and Planck. But CMBR was predicted in 1948 by Ralph Alpher and Robert Herman, with Alpher's other colleague and former professor George Gamow.
This radiation (CMBR) was caused by electrons bonding themselves to the hydrogen and helium nuclei for the first time, making these two atoms electrically stable and neutral. These bonding made the universe transparent, and therefore "observable". And the bonding cause light to radiate. And all this, took place in the Recombination epoch.
CMBR is older than the first quasars, older still than the earliest stars.
The universe before the Recombination epoch, is opaque. So we cannot currently view any event from older epochs. So the earlier epochs of the Big Bang cosmology are still hypothetical and theoretical.
Until scientists and engineers build better space probes that can view beyond the CMBR and Recombination epoch, we have no verifiable evidences what really went on before Recombination epoch.
So any theoretical physicist or cosmologist talking about the multiverse models, oscillating universe model (Big Bounce, a cycle of Bang and Crunch...and Bang again, sort of like reincarnation), or the eternal universe model, are all merely highly theoretical and hypothetical speculations.
The only things we can confirm so far, is the existence of CMBR, and seeming likely the existence of Gravitational Waves from the recent images of Planck space probe.
If cannot observe anything before Recombination epoch, then we have no evidences to support the universe is eternal or the universe comes from nothing, both of these scenarios are still just speculations.
Personally, that is all I will accept so far. Until we have more information and more verifiable evidences, I am not going to accept any alternative cosmology to be true. I am willing to wait, though we may not have that answer in our lifetime.