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I am new on here, so please forgive me if this is in the wrong place. I am currently an Undergraduate physics major at UCLA, and want to pursue cosmology as a career eventually.

A few of my friends are big fans of Lawrence Krauss, and recommended his book, a Universe from Nothing. I searched for it in Google, and found an arXiv article by a mathematical physicist, who has disproved many of the claims in the book. Since the article has mathematics that is way above my head, I'm wondering if other experts could analyze some of the claims? The author even acknowledges George Ellis, which may indicate that it is on firm ground. If so, why does Krauss continue to garner so much attention, if his claims are imcorrect. Here is the article: https://inspirehep.net/record/1298212?ln=en