Background: Thomas Stearns Eliot,  (26 September 1888 - 4 January 1965) was a British essayist, publisher, playwright, literary and social critic, and "one of the twentieth century's major poets". He moved from his native United States to England in 1914 at the age of 25, settling, working, and marrying there. He eventually became a British subject in 1927 at the age of 39, renouncing his American passport. Eliot attracted widespread attention for his poem "The Love Song of J. Alfred Prufrock" (1915), which was seen as a masterpiece of the Modernist movement.
Context: In a letter to Aiken late in December 1914, Eliot, aged 26, wrote, "I am very dependent upon women (I mean female society)." Less than four months later, Thayer introduced Eliot to Vivienne Haigh-Wood, a Cambridge governess. They were married at Hampstead Register Office on 26 June 1915.  After a short visit alone to his family in the United States, Eliot returned to London and took several teaching jobs, such as lecturing at Birkbeck College, University of London. The philosopher Bertrand Russell took an interest in Vivienne while the newlyweds stayed in his flat. Some scholars have suggested that she and Russell had an affair, but the allegations were never confirmed.  The marriage was markedly unhappy, in part because of Vivienne's health issues. In a letter addressed to Ezra Pound, she covers an extensive list of her symptoms, which included a habitually high temperature, fatigue, insomnia, migraines, and colitis. This, coupled with apparent mental instability, meant that she was often sent away by Eliot and her doctors for extended periods of time in the hope of improving her health, and as time went on, he became increasingly detached from her. The couple formally separated in 1933 and in 1938 Vivienne's brother, Maurice, had her committed to a lunatic asylum, against her will, where she remained until her death of heart disease in 1947. Their relationship became the subject of a 1984 play Tom & Viv, which in 1994 was adapted as a film.  In a private paper written in his sixties, Eliot confessed: "I came to persuade myself that I was in love with Vivienne simply because I wanted to burn my boats and commit myself to staying in England. And she persuaded herself (also under the influence of [Ezra] Pound) that she would save the poet by keeping him in England. To her, the marriage brought no happiness. To me, it brought the state of mind out of which came The Waste Land."  By 1932, Eliot had been contemplating a separation from his wife for some time. When Harvard offered him the Charles Eliot Norton professorship for the 1932-1933 academic year, he accepted and left Vivienne in England. Upon his return, he arranged for a formal separation from her, avoiding all but one meeting with her between his leaving for America in 1932 and her death in 1947. Vivienne was committed to the Northumberland House mental hospital, Stoke Newington, in 1938, and remained there until she died. Although Eliot was still legally her husband, he never visited her.  From 1938 to 1957 Eliot's public companion was Mary Trevelyan of London University, who wanted to marry him and left a detailed memoir.  From 1946 to 1957, Eliot shared a flat at 19 Carlyle Mansions, Chelsea, with his friend John Davy Hayward, who collected and managed Eliot's papers, styling himself "Keeper of the Eliot Archive". Hayward also collected Eliot's pre-Prufrock verse, commercially published after Eliot's death as Poems Written in Early Youth. When Eliot and Hayward separated their household in 1957, Hayward retained his collection of Eliot's papers, which he bequeathed to King's College, Cambridge, in 1965.  On 10 January 1957, at the age of 68, Eliot married Esme Valerie Fletcher, who was 30. In contrast to his first marriage, Eliot knew Fletcher well, as she had been his secretary at Faber and Faber since August 1949. They kept their wedding secret; the ceremony was held in a church at 6:15 am with virtually no one in attendance other than his wife's parents. Eliot had no children with either of his wives. In the early 1960s, by then in failing health, Eliot worked as an editor for the Wesleyan University Press, seeking new poets in Europe for publication. After Eliot's death, Valerie dedicated her time to preserving his legacy, by editing and annotating The Letters of T. S. Eliot and a facsimile of the draft of The Waste Land. Valerie Eliot died on 9 November 2012 at her home in London.  For a poet of his stature, Eliot produced a relatively small number of poems. He was aware of this even early in his career. He wrote to J.H. Woods, one of his former Harvard professors, "My reputation in London is built upon one small volume of verse, and is kept up by printing two or three more poems in a year. The only thing that matters is that these should be perfect in their kind, so that each should be an event."  Typically, Eliot first published his poems individually in periodicals or in small books or pamphlets, and then collected them in books. His first collection was Prufrock and Other Observations (1917). In 1920, he published more poems in Ara Vos Prec (London) and Poems: 1920 (New York). These had the same poems (in a different order) except that "Ode" in the British edition was replaced with "Hysteria" in the American edition. In 1925, he collected The Waste Land and the poems in Prufrock and Poems into one volume and added The Hollow Men to form Poems: 1909-1925. From then on, he updated this work as Collected Poems. Exceptions are Old Possum's Book of Practical Cats (1939), a collection of light verse; Poems Written in Early Youth, posthumously published in 1967 and consisting mainly of poems published between 1907 and 1910 in The Harvard Advocate, and Inventions of the March Hare: Poems 1909-1917, material Eliot never intended to have published, which appeared posthumously in 1997.  During an interview in 1959, Eliot said of his nationality and its role in his work: "I'd say that my poetry has obviously more in common with my distinguished contemporaries in America than with anything written in my generation in England. That I'm sure of. ... It wouldn't be what it is, and I imagine it wouldn't be so good; putting it as modestly as I can, it wouldn't be what it is if I'd been born in England, and it wouldn't be what it is if I'd stayed in America. It's a combination of things. But in its sources, in its emotional springs, it comes from America."  Cleo McNelly Kearns notes in her biography that Eliot was deeply influenced by Indic traditions, notably the Upanishads. From the Sanskrit ending of The Waste Land to the "What Krishna meant" section of Four Quartets shows how much Indic religions and more specifically Hinduism made up his philosophical basic for his thought process. It must also be acknowledged, as Chinmoy Guha showed in his book Where the Dreams Cross: T S Eliot and French Poetry (Macmillan, 2011), that he was deeply influenced by French poets from Baudelaire to Paul Valery. He himself wrote in his 1940 essay on W.B. Yeats: "The kind of poetry that I needed to teach me the use of my own voice did not exist in English at all; it was only to be found in French." ("Yeats," On Poetry and Poets, 1948)
Question: Did they have any children?

Answer:
The marriage was markedly unhappy, in part because of Vivienne's health issues. In a letter addressed to Ezra Pound, she covers an extensive list of her symptoms,