This is way out of my field, but I'm going to report my first impressions of the paper.
The sentences quoted by
DeiRenDopa are, as you say, quite similar to what you can read in many other popular expositions of the Big Bang. Note that this is not a research paper; of the five kinds of article published by the
Journal of Cosmology, I'd guess that this paper falls into the review, commentary, or speculation categories. Note also that the
Journal of Cosmology is a pay-to-publish online journal founded in 2009. If you click on their
book review page, you'll find a review of science fiction. Note also the
contents of its first volume. The first few paragraphs of
the first paper in that first volume may give you some idea of what that journal is willing to publish.
Eastman's review is clearly partial to the steady-state models advocated by Burbridge, Hoyle, etc. Not that there's anything wrong with that, but there appear to be good reasons for the general opinion that these steady-state models are incorrect. Eastman's main source is another review paper by Geoffrey Burbridge, whose
web page lists his collaborators as Fred Hoyle and Jayant Narlikar, who have been prominent advocates of steady state cosmology. If you look at Burbridge's web page, you will see a short explanation of "quasi-steady state cosmology", including a graph of the cosmic scale factor that resembles a graph you might see for the so-called standard model, surrounded on either side by an infinite number of universes that also resemble the standard model. In other words, even the steady state cosmologists have pretty much given up on traditional steady state cosmology and are now incorporating variations of the Big Bang and Big Crunch into their cosmologies.
Back to Eastland's article. In the first paragraph of section 2, he quotes Burbridge saying "while the black body nature of the radiation was predicted by the big bang theory, the numerical value of the temperature was not, and cannot be". That's pretty misleading. The famous Alpher-Bethe-Gamow paper
WP of 1948 argued for Big Bang nucleosynthesis. In 1948 through 1953, Gamow, Alpher, and Herman estimated temperatures ranging from 5 through 50 K; the higher estimates were based on an estimated age for the universe that is now believed to be too low by a factor of 4 to 5. Eastman actually mentions those predictions in paragraph 6 of section 2. When measured in 1965 for the first time, the actual temperature turned out to be 3 K. Eastman acts as though that discrepancy is strong evidence against the Big Bang model.
Ignorant though I be, I could point to several other problems I see in the paper. The above should be enough to give you some idea of why I wasn't impressed.