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I am trying to find some nice explanatory books about neutrino effects on the cosmic structure. I did not take GR so I prefer sources that contain not much GR.

I prefer lecture note series or books rather than articles. I mean I want to understand the idea behind it.

For instance, I looked at Neutrino Cosmology but it contains a lot of GR and it's kind of hard to read as an undergrad. I am looking for something simpler but also explanatory as well.

seVenVo1d
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My favorite book on this topic is Soler, Froggatt & Muheim's Neutrinos in Particle Physics, Astrophysics and Cosmology. They start with neutrinos in the standard model and go over neutrino oscillation, and then go onto look at neutrinos emitted from stellar objects. Experimental neutrino detection is emphasized, and then finally leptogenesis. If I remember correctly, GR discussion is minimal.

Another good resource is Zuber's Neutrino Physics. It has a nice introduction to neutrinos in the standard model, and then goes onto discuss possible experimental ways of detecting them. The connection between neutrinos and several phenomena (neutrino oscillations, atmospheric neutrinos, neutrinos from supernovae, and connections to dark matter) are discussed in an introductory manner.

Finally, I would recommend the excellent lecture notes of Dolgov, Neutrinos in cosmology. Basic cosmology is introduced before neutrinos are formally introduced. Primordial nucleosynthesis, cosmological lepton asymmetry, dark matter, and neutrino oscillations in the early universe are discussed. It also contains over 800 references to relevant articles and additional books.