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I'm curious about the difference between low redshift and high redshift universe. Is there any defined limit of redshift beyond which we call things high redshifted?

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There definitely is no definition of what is low and what is high redshift — it is always seen in relation to something. An astronomer working in, say, the interstellar medium of the Milky Way ($z\sim0$) might talk about the ISM of a $z\sim2$ galaxy as being high redshift, whereas another astronomer working the reionization of the Universe (which took place around $z\sim10$) would consider $z\sim2$ to be low redshift. A cosmologist working in the CMB or inflation, however, would probably call $z\sim10$ low redshift. It all depends on the context.

Nevertheless I think that most people would consider $z\lesssim0.1$ to be low redshift.

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