Motivated by the recent work of Saridakis [1], we generalize this work to the noninteracting case. Using an additional canonical scalar field, we formulate HořavaLifshitz cosmology with an effective interacting dark energy sector. ∗E-mail: [email protected]

Monads are of interest both in semantics and in higher dimensional algebra. It turns out that the idea behind usual notion finitary monads (whose values on all sets can be computed from their values on finite sets) extends to a more general class of monads called monads with arities, so that not only algebraic theories can be computed from a proper set of arities, but also more general structur...

This is a nontechnical introduction to recent work on quantum gravity using ideas from higher-dimensional algebra. We argue that reconciling general relativity with the Standard Model requires a ‘background-free quantum theory with local degrees of freedom propagating causally’. We describe the insights provided by work on topological quantum field theories such as quantum gravity in 3-dimensio...

A 2-group is a ‘categorified’ version of a group, in which the underlying set G has been replaced by a category and the multiplication map m: G×G → G has been replaced by a functor. Various versions of this notion have already been explored; our goal here is to provide a detailed introduction to two, which we call ‘weak’ and ‘coherent’ 2-groups. A weak 2-group is a weak monoidal category in whi...

We study the phase space of spatially homogeneous and isotropic cosmology in general scalar-tensor theories. A reduction to a two-dimensional phase space is performed when possible — in these situations the phase space is usually a twodimensional curved surface embedded in a three-dimensional space and composed of two sheets attached to each other, possibly with complicated topology. The result...

We study anisotropic cosmology in Hořava’s gravity theory and obtain Kasner type solutions, valid for any number d of spatial dimensions. The corresponding exponents satisfy two relations, one involving the marginal coupling λ . Also, Hořava’s (super)renormalisable theory predicts (super)stiff matter whose equation of state is p = wρ with w ≥ 1 . We discuss the implications of these results for...