How does cost of equity change in recession

A firm's Cost of Equity=Rf+Beta*Market Risk Premium. Treasury bill is low risk investment, does Rf decline during recession? Is this firm more sensitive to market change in recession(Beta)? How about Rmarket? I think Market Risk Premium should be lower because those companies in market portfolio should perform badly in recession therefore the return is lower too.
Can anyone help me with this question?
Thanks

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