A solution of the (4 + n)-dimensional vacuum Einstein equations is found for which spacetime is compactified on an n-dimensional compact hyperbolic manifold (n ≥ 2) of time-varying volume to a flat four-dimensional FLRW cosmology undergoing a period of accelerated expansion in Einstein conformal frame. This shows that the 'no-go' theorem forbidding acceleration in 'standard' (time-independent) compactifications of string/M-theory does not apply to 'cosmological' (timedependent) hyperbolic compactifications.PACS numbers: 98.80. Cq, 11.25.Mj, 11.25.Yb, 98.80.Jk Astronomical observations appear to show that the universe is not only expanding but is undergoing accelerated expansion, see e.g. [1]. In addition, recent measurements of the cosmic microwave background provide support for the hypothesis of accelerated expansion in a much earlier inflationary cosmological epoch, see e.g. [2,3]. Although it is not difficult to find cosmological models that exhibit these features, one would wish any such model to be derivable from a fundamental, and mathematically consistent, theory that incorporates both gravity and the standard model of particle physics. Most current attempts to place the standard model within such a framework start from the ten or eleven-dimensional spacetime of superstring/M-theory, in which case one needs a compactification of ten or eleven dimensional supergravity in which an effective four-dimensional cosmology undergoes one or more periods of accelerated expansion. However, it has been shown that no such solution exists when the six or seven dimensional 'internal' space is a time-independent non-singular compact manifold without boundary [4,5]. Three observations go into the derivation of this 'no-go' theorem. The first is that accelerated expansion requires a violation of the strong-energy condition. This is the condition on the stress tensor that, given the Einstein equations, implies R 00 ≥ 0, but the acceleration of a FLRW (homogeneous and isotropic) universe is positive if and only if R 00 is negative. The strong energy condition is violated in many four-dimensional supergravity theories but, and this is the second observation, it is not violated by either elevendimensional supergravity or any of the ten-dimensional supergravity theories that serve as effective field theories for a superstring theory. The third observation is generic to any compactification of the type specified in the theorem: if the higher-dimensional stress tensor satisfies the strong energy condition then so will the lowerdimensional stress tensor.Clearly, any attempt to derive a viable cosmology from string/M-theory must circumvent this no-go theorem, and this is possible in one of two ways. Either one rejects ten or eleven-dimensional supergravity as the relevant starting point or one relaxes one or more of the premises of the theorem. Attempts to circumvent the theorem by the addition of higher-derivative 'quantum correction' terms to the supergravity action, or appeals to non-geometrical solutions of string theory wit...

We construct gravitational dynamics for Finsler spacetimes in terms of an action integral on the unit tangent bundle. These spacetimes are generalizations of Lorentzian metric manifolds which satisfy necessary causality properties. A coupling procedure for matter fields to Finsler gravity completes our new theory that consistently becomes equivalent to Einstein gravity in the limit of metric geometry. We provide a precise geometric definition of observers and their measurements, and show that the transformations by means of which different observers communicate form a groupoid that generalizes the usual Lorentz group. Moreover, we discuss the implementation of Finsler spacetime symmetries. We use our results to analyze a particular spacetime model that leads to Finsler geometric refinements of the linearized Schwarzschild solution.Comment: 39 pages, 4 figures, journal references adde

We present a concise new definition of Finsler spacetimes that generalize Lorentzian metric manifolds and provide consistent backgrounds for physics. Extending standard mathematical constructions known from Finsler spaces we show that geometric objects like the Cartan non-linear connection and its curvature are well-defined almost everywhere on Finsler spacetimes, also on their null structure. This allows us to describe the complete causal structure in terms of timelike and null curves; these are essential to model physical observers and the propagation of light. We prove that the timelike directions form an open convex cone with null boundary as is the case in Lorentzian geometry. Moreover, we develop action integrals for physical field theories on Finsler spacetimes, and tools to deduce the corresponding equations of motion. These are applied to construct a theory of electrodynamics that confirms the claimed propagation of light along Finsler null geodesics.Comment: 27 pages, 4 figures, additional comment

In crystal optics and quantum electrodynamics in gravitational vacua, the propagation of light is not described by a metric, but an area metric geometry. In this article, this prompts us to study conditions for linear electrodynamics on area metric manifolds to be well-posed. This includes an identification of the timelike future cones and their duals associated to an area metric geometry, and thus paves the ground for a discussion of the related local and global causal structures in standard fashion. In order to provide simple algebraic criteria for an area metric manifold to present a consistent spacetime structure, we develop a complete algebraic classification of area metric tensors up to general transformations of frame. This classification, valuable in its own right, is then employed to prove a theorem excluding the majority of algebraic classes of area metrics as viable spacetimes. Physically, these results classify and drastically restrict the viable constitutive tensors of non-dissipative linear optical media.

Area metric manifolds emerge as effective classical backgrounds in quantum string theory and quantum gauge theory, and present a true generalization of metric geometry. Here, we consider area metric manifolds in their own right, and develop in detail the foundations of area metric differential geometry. Based on the construction of an area metric curvature scalar, which reduces in the metric-induced case to the Ricci scalar, we re-interpret the Einstein-Hilbert action as dynamics for an area metric spacetime. In contrast to modifications of general relativity based on metric geometry, no continuous deformation scale needs to be introduced; the extension to area geometry is purely structural and thus rigid. We present an intriguing prediction of area metric gravity: without dark energy or fine-tuning, the late universe exhibits a small acceleration. INVITATIONA new theoretical concept which, once formulated, naturally emerges in many related contexts, deserves further study. Even more so, if it makes us view well-established theories in a novel way, and meaningfully points beyond standard theory.Area metrics, we argue in this paper, are such an emerging notion in fundamental physics.An area metric may be defined as a fourth rank tensor field which allows to assign a measure to two-dimensional tangent areas, in close analogy to the way a metric assigns a measure to tangent vectors. In more than three dimensions, area metric geometry is a true generalization of metric geometry; although every metric induces an area metric, not every area metric comes from an underlying metric. The mathematical constructions, and physical conclusions, of the present paper are then based on a single principle:Spacetime is an area metric manifold.We will be concerned with justifying this rather bold idea by a detailed construction of the geometry of area metric manifolds, followed by providing an appropriate theory of gravity, which finally culminates in an application of our ideas to cosmology. In the highly symmetric cosmological area metric spacetimes, we can compare our results easily to those of Einstein gravity. We obtain the interesting result that the simplest type of area metric cosmology, namely a universe filled with non-interacting string matter, may be solved exactly and is able to explain the observed [1,2] very small late-time acceleration of our Universe, see the figure on page 40, without introducing any notion of dark energy, nor by invoking fine-tuning arguments.It may come as a surprise, but standard physical theory itself predicts the departure from metric to true area metric manifolds. More precisely, the quantization of classical theories based on metric geometry generates, in a number of interesting cases, area metric geometries: back-reacting photons in quantum electrodynamics effectively propagate in an area metric background [3]; the massless states of quantum string theory give rise to the Neveu-Schwarz two-form potential and dilaton besides the graviton, producing a generalized geometry which may be neatly...