The author of The Golden Bough, a text that influenced Eliot’s poetry and criticism substantially, is:

The correct option is James George Frazer.

Detailed Explanation:
Sir James George Frazer (1854–1941) was a prominent Scottish social anthropologist, folklorist, and classical scholar. He is widely remembered for his landmark work, The Golden Bough: A Study in Comparative Religion (first published in 1890), which presents a massive comparative study of mythology, magic, ritual, and religion across diverse global cultures.

Influence on T. S. Eliot:
Frazer's concepts of the dying-and-reviving god, vegetation rites, and the cycle of fertility deeply resonated with modernists who were seeking archetypal structures to address the spiritual crisis of the post-World War I era.
T. S. Eliot drew heavily on The Golden Bough for both his poetry and literary criticism. Most famously, in his notes to the landmark modernist poem The Waste Land (1922), Eliot explicitly acknowledged his debt to Frazer, noting that the work was influenced by Jessie L. Weston's study of the Grail legend, From Ritual to Romance, and by Frazer's The Golden Bough, particularly the volumes dealing with the mythologies of Adonis, Attis, and Osiris.

Distinction from Other Options:
• John Ruskin was a prominent Victorian art critic, social thinker, and philanthropist.
• Thomas Carlyle was an influential Victorian essayist, historian, and philosopher known for his "Great Man" theory of history.
• David Wilson is not associated with this work, serving as a distractor option.