Abstract
While the classification of $\alpha'$ corrections of string inspired effective theories remains an unsolved problem, we show how to classify duality invariant $\alpha'$ corrections for purely time-dependent (cosmological) backgrounds. We determine the most general duality invariant theory to all orders in $\alpha'$ for the metric, $b$-field, and dilaton. The resulting Friedmann equations are studied when the spatial metric is a time-dependent scale factor times the Euclidean metric and the $b$-field vanishes. These equations can be integrated perturbatively to any order in $\alpha'$. We construct non-perturbative solutions and display duality invariant theories featuring string-frame de Sitter vacua.
Highlights
String theory is arguably the most promising candidate for a theory of quantum gravity
As a theory of gravity, the prospect for a confrontation between string theory and observation seems to be promising in the realm of cosmology, where the effects of fundamental physics at very small scales may be amplified to very large scales
Two such features of classical string theory will be central for the present paper: (i) the existence of dualities that for cosmological backgrounds send the scale factor aðtÞ of the universe to 1=aðtÞ, in sharp contrast to Einstein gravity, and (ii) the presence of infinitely many higher-derivative α0 corrections
Summary
String theory is arguably the most promising candidate for a theory of quantum gravity. Our analysis is based on the result by Veneziano and Meissner [24], extended by Sen [25], concerning the classical field theory of the metric, the b-field, and the dilaton arising from D 1⁄4 d þ 1 dimensional string theory This field theory displays an Oðd; d; RÞ symmetry to all orders in α0 provided the fields do not depend on the d spatial coordinates. We will assume that there are field variables so that duality transformations remain unchanged to all orders in α0 (this certainly happens in conventional string field theory variables [27]) With this assumption we are able to classify completely the duality invariant α0 corrections. As it turns out, this result is valid even when the action contains the most general multitrace terms. This was partially done in [28], whose results will here be completed by allowing for Oðd; dÞ covariant field redefinitions of the lapse function
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