String theory suggests a unique and unambiguous modification to General Relativity : the symmetry of \mathbf { O } ( D,D ) T-duality promotes the entire closed-string massless NS-NS sector to stringy graviton fields .
The symmetry fixes the couplings to other matter fields unambiguously and the Einstein field equations are enriched to comprise D ^ { 2 } +1 components , dubbed recently as the Einstein Double Field Equations .
Here we explore the cosmological implications of this ‘ Stringy Gravity ’ .
We derive the most general homogeneous and isotropic ansatzes for both stringy graviton fields and the stringy energy-momentum tensor .
Substituting them into the Einstein Double Field Equations , we obtain the \mathbf { O } ( D,D ) completion of the Friedmann equations along with a generalized continuity equation .
We discuss how this gives an enriched and novel framework beyond typical string cosmology , with solutions that may be characterized by two equation-of-state parameters , w ( conventional ) and \lambda ( new ) .
When \lambda + 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 ) , an improvement over conventional string cosmology where this occurs only for a radiation equation of state ( w = 1 / 3 ) .
We further point out that , in contrast to General Relativity , in Stringy Gravity there is no de Sitter solution arising from either an \mathbf { O } ( D,D ) -symmetric cosmological constant or scalar field with positive energy density .