I would say that the alternative that gets the best scientific support has to be the Quasi Steady State Cosmology (QSSC) developed by Fred Hoyle and his students, out of the old & untenable steady state cosmology from the 50's (which was also essentially Hoyle's baby).
- On searches for gravitational waves from mini-creation events by laser interferometric detectors, Sarmah, et al., MNRAS, June 2006
- Inhomogeneities in the Microwave Background Radiation Interpreted within the Framework of the Quasi-Steady State Cosmology, Narlikar, et al., ApJ, 2003
- Action at a Distance Cosmology: A Historical Perspective, Jayant Narlikar, ARA&A, 2003
- Interpretations of the Accelerating Universe, Narlikar, Vishwakarma & Burbidge, PASP, 2002
- Standard Cosmology and Alternatives: A Critical Appraisal, Narlikar & Padmanabhan, ARA&A, 2001
- Structure Formation in the Quasi-Steady State Cosmology, Narlikar, GReGr, 2000
- Structure Formation in the Quasi-Steady State Cosmology: A Toy Model, Nayeri, et al., ApJ, 1999
There are more references out there, but an exhaustive list is unnecessary. The point is that serious scientists are seriously working on this cosmological model. Narlikar himself, in his 2001 ARA&A review admits that standard big bang cosmolgy is a better fit to observation, but feels that the alternative viewpoint should always be presented as best it can be.
My opinion is that the QSSC is the
only serious alternative to standard big bang cosmology, and all the rest are of no serious value. I also suspect that it was
Nereid's intention, perhaps, that the alternative cosmologies be presented by adherents of same. I do not support the QSSC, and I think that standard big bang cosmology is now, and will remain, the most appropriate class of cosmological models. But I have much respect for Narlikar, and his co-authors, for maintaining high standards of scientific inquiry.