An ${\alpha }^{\prime }$-complete theory of cosmology and its tensionless limit

Abstract

We explore the exactly duality invariant higher-derivative extension of double field theory due to Hohm, Siegel and Zwiebach (HSZ) specialized to cosmological backgrounds. Despite featuring a finite number of derivatives in its original formulation, this theory encodes infinitely many ${\alpha }^{\prime }$ corrections for metric, B-field and dilaton, which are obtained upon integrating out certain extra fields. We perform a cosmological reduction with fields depending only on time and show consistency of this truncation. We compute the ${\alpha }^{\prime 4}$ coefficients of the general cosmological classification. As a possible model for how to deal with all ${\alpha }^{\prime }$ corrections in string theory we give a two-derivative reformulation in which the extra fields are kept. The corresponding Friedmann equations are then ordinary second order differential equations that capture all ${\alpha }^{\prime }$ corrections. We explore the tensionless limit ${\alpha }^{\prime }\to \infty$, which features string frame de Sitter vacua, and we set up perturbation theory in $\frac{1}{{\alpha }^{\prime }}$.

38 pages

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• Massive Gravity in Three Dimensions
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Cited by in corpus (4)

• Double Field Theory with matter and the generalized Bergshoeff-de Roo identification
• 2D Black Holes, Bianchi I Cosmologies, and ${\alpha }^{\prime }$
• Non-linear stability of ${\alpha }^{\prime }$-corrected Friedmann equations
• Massive strings from a haunted field theory