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Textbooks on Cosmic Inflation?

Anonymous Wed 05 Aug 23:24:54 2020 No.11978746 View Reply Original Report

Quoted By: >>11981251 >>11981462

Textbook recommendations for topics around cosmic inflation and the infinitude of the universe. Thanks guys, can't seem to find anything good on this

Anonymous

Anonymous Thu 06 Aug 2020 16:34:09 No.11980893 Report

Quoted By:

$\textrm{Denote a normal p-Sylow subgroup of} \ G \ \textrm{as}\ P. \textrm{Assume} \ p \ \textrm{does not divide} \ |H|, \textrm{then it must follow that} \ |K|=p^an, \ \textrm{where} \ n \ \textrm{and} \ p \ \textrm{are coprime, since} \ |G|=p^am=|K||P| \ \textrm{where} \ m \ \textrm{and} \ p \ \textrm{are coprime. Therefore,} \ K \ \textrm{must contain a normal p-Sylow subgroup} \ P'. \textrm{Then,} \ (1,K) \ \textrm{is a subgroup of G and} \ (1,K) \cong K, \ \textrm{must also contain a normal p-Sylow subgroup. Per Sylow's theorems, there can only be one normal Sylow p-subgroup contained in G. From this, it follows that} \ P \leq (1,K) \ \textrm{meaning that} \ P=(1,P') \ \textrm{because} \ (1,P') \ \textrm{is a normal subgroup of} \ (1,K)\ \textrm{that has order} \ p^a. \\ \textrm{Because} \ P \trianglelefteq (1,K) \leq G \ \textrm{and} \ (H,1) \trianglelefteq G \Rightarrow (H,1) \cap P=1. \textrm{So,} \ (H,1)P \leq G \ \textrm{and} \ |(H,1)P| = |H| |P|. \\ \textrm{Now, let} \ G'= H \ltimes_\varphi P' \ \textrm{where} \ \varphi: P' \rightarrow Aut(H) \ \textrm{and} \ \forall k \in P', \varphi(k) = \theta(k). \textrm{Because} \ P' \leq K \ \varphi \ \textrm{is well defined}. \varphi \ \textrm{is homomorphic because}\ \theta \ \textrm{is also homomorphic: take any} \ k_1,k_2 \in P \leq K, \ \textrm{and} \ \varphi(k_1 k_2) = \theta(k_1 k_2) = \varphi(k_1) \varphi(k_2) = \theta(k_1) \theta(k_2). \textrm{From this, it follows that} \ G' \textrm{is a group, and since} \ G' \subseteq G, G' \leq G. (1,P') = P \trianglelefteq G \ \textrm{meaning that} \ (1,P') \trianglelefteq G' \ \textrm{and that} \ \varphi \ \textrm{must be trivial, since} \ \forall k \in P', \varphi(k) = \theta(k) = 1. \textrm{From this it follows that} \ P' \leq \ker (\theta) \ \textrm{and Lagrange's theorem tells us that} \ | \ker(\theta)| = p^a \lambda, \lambda \in \mathbb{Z}^+.[\math]$

Anonymous

Anonymous Thu 06 Aug 2020 18:54:23 No.11981251 Report

Quoted By: >>11981258

>>11978746
Dan Baum's set of notes is really nice for inflation. other than that, you might also check out mukhanovs book

Anonymous

Anonymous Thu 06 Aug 2020 18:56:06 No.11981258 Report

Quoted By:

>>11981251
I'm sorry, Daniel Baumann, the physics of inflation

Anonymous

Anonymous Thu 06 Aug 2020 20:04:40 No.11981462 Report

Quoted By:

>>11978746
Wow, this is actually a decent book rec from /sci/. I'm shocked. Schwarz' new book is gaining attention quickly which is good because it's a terrific book, too.
Schutz fucking sucks though.

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