Cosmological predictions of physics beyond general relativity

Abstract

The construction of the teleparallel analogue of Horndeski theory provides the most general second-order scalar-tensor framework within metric-teleparallel gravity for a single scalar field. This formalism opens up the possibility of reviving previously discarded Horndeski gravity models, as the inclusion of an additional teleparallel term allows for a wider range of cosmological solutions consistent with the constraints from gravitational wave event GW170817, particularly the excess speed of the tensor modes. The construction of such a generalised class of teleparallel gravity facilitates the theoretical work by compiling a list of constraints stemming from observational and mathematical limits which would hold for a large class of teleparallel models. In this work, teleparallel Horndeski is explored at both the background and perturbative level. The theory is applied to construct well-tempered models that use a dynamical scalar field to screen vacuum energy contributions, addressing the cosmological constant problem—the large discrepancy between its theoretical and observed values. Upon obtaining the linearised field equations through a scalar-vector-tensor decomposition, the gravitational wave polarisation structure can be realised: a maximum of seven propagating degrees of freedom and four polarisation modes of scalar and tensor nature across the massless and massive sectors for a Minkowski background. The dynamics of scalar-tensor theories provide insight into the physical evolution of cold dark matter, responsible for the formation of large structures such as galaxies and galaxy clusters. The solution of the Mészáros equation is used to derive cosmological parameters such as the growth factor, growth index, fσ8, and S8, highlighting any spatially dependent discrepancies in these models. When it comes to comparing models with observations, it becomes crucial that the choice is taken from healthy branches of teleparallel Horndeski. Ghost and Laplacian instabilities help identify these pathological sectors. Throughout this study, limits of well-established theories such as general relativity, Horndeski gravity, and f(T) gravity are explored to emphasise the ability of generalised teleparallel Horndeski gravity to not only recover these familiar theories but also offer a richer structure of cosmologically viable models.