$$\mathbf {O}(D,D)$$ completion of the Friedmann equations

Abstract

In string theory the closed-string massless NS-NS sector forms a multiplet of $$\mathbf {O}(D,D)$$ O ( D , D ) symmetry. This suggests a specific modification to General Relativity in which the entire NS-NS sector is promoted to stringy graviton fields. Imposing off-shell $$\mathbf {O}(D,D)$$ O ( D , D ) symmetry fixes the correct couplings to other matter fields and the Einstein field equations are enriched to comprise $$D^{2}+1$$ D 2 + 1 components, dubbed recently as the Einstein Double Field Equations. Here we explore the cosmological implications of this framework. We derive the most general homogeneous and isotropic ansatzes for both stringy graviton fields and the $$\mathbf {O}(D,D)$$ O ( D , D ) -covariant energy-momentum tensor. Crucially, the former admits space-filling magnetic H-flux. Substituting them into the Einstein Double Field Equations, we obtain the $$\mathbf {O}(D,D)$$ O ( D , D ) completion of the Friedmann equations along with a generalized continuity equation. We discuss how solutions in this framework may be characterized by two equation-of-state parameters, w and $$\lambda $$ λ , where the latter characterizes the relative intensities of scalar and tensor forces. When $$\lambda +3w=1$$ λ + 3 w = 1 , the dilaton remains constant throughout the cosmological evolution, and one recovers the standard Friedmann equations for generic matter content (i.e. for any w). We further point out that, in contrast to General Relativity, neither an $$\mathbf {O}(D,D)$$ O ( D , D ) -symmetric cosmological constant nor a scalar field with positive energy density gives rise to a de Sitter solution.

Cosmology at the top of the α′ tower

“…This benefits from being a spacetime-covariant approach, which does not have to rely on the assumptions of homogeneity and isotropy. This avenue has led to promising applications in cosmology [33][34][35][36][37]. While this path will not be explored in the present work, we believe that it is worthy of mention.…”

“…Note that this was already partly noticed in the literature (see, e.g., [58] for more details). The difference between an O(d, d)-covariant pressure and a diffeomorphic-covariant one, and its consequences, has also been explored in [37].…”

α′-cosmology: solutions and stability analysis

“…where we have introduced a barotropic equation of state (EOS), w ≡ p/ρ, and the density ratio (DR), λ ≡ σ/ρ, which measures how strongly the matter is coupled to the dilaton in relation to the metric [35]. Throughout this paper, we will assume {w, λ} to be constants, thus we can solve the continuity equation for the energy in terms of the scale factor and shifted dilaton,ρ =ρ 0 a 0 a dw e λ JHEP05(2020)073…”

Dilatonic effect in double field theory cosmology

“…In particular, the concepts of dark matter and dark energy must be introduced in order to provide an explanation for the large-scale dynamics of the universe. Furthermore, in order to solve the horizon and the flatness problems, new dynamics, such as inflation, involving additional degrees of freedom, which may play an important role near the strong-coupling regime at which GR breaks down, are required [1]. In order to make quantitative predictions concerning the early universe a consistent quantum gravity theory needs to be developed.…”