ما هو الدليل من القرآن والسنة على عدم وجوب إخبار الرجل زوجته بزواجه من أخرى، وعلى جواز كذبه عليها إذا شكت في ذلك؟

There is no evidence from the Quran or Sunnah that obligates a man to inform his wife of his marriage to another woman; the default is the exoneration of responsibility. It is permissible for a man to lie to his wife if there is a legitimate benefit, such as concealing his marriage to another, and this is established in the authentic Sunnah.