Enlarging the continuum with $\sigma$-centered forcing

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How large can we force the continuum to be if we force with a $\sigma$-centered forcing notion?

References to texts discussing the subject would be much appreciated.

[A forcing notion $P$ is called $\sigma$-centered if it can be written as $\bigcup _{n<\omega}P_n$ where for each $n$, every finite subset of $P_n$ has a lower bound in $P$.]