Turning on gravity with the Higgs mechanism

We investigate how a Higgs mechanism could be responsible for the emergence of gravity in extensions of Einstein theory, with a suitable low energy limit. In this scenario, at high energies, symmetry restoration could 'turn off' gravity, with dramatic implications for cosmology and quantum gravity. The sense in which gravity is muted depends on the details of the implementation. In the most extreme case gravity's dynamical degrees of freedom would only be unleashed after the Higgs field acquires a non-trivial vacuum expectation value, with gravity reduced to a topological field theory in the symmetric phase. We might also identify the Higgs and the Brans-Dicke fields in such a way that in the unbroken phase Newton's constant vanishes, decoupling matter and gravity. We discuss the broad implications of these scenarios

The cosmology of minimal varying Lambda theories

Inserting a varying Lambda in Einstein's field equations can be made consistent with the Bianchi identities by allowing for torsion, without the need to add scalar field degrees of freedom. In the minimal such theory, Lambda is totally free and undetermined by the field equations in the absence of matter. Inclusion of matter ties Lambda algebraically to it, at least when homogeneity and isotropy are assumed, i.e. when there is no Weyl curvature. We show that Lambda is proportional to the matter density, with a proportionality constant depending on the equation of state. Unfortunately, the proportionality constant becomes infinite for pure radiation, ruling out the minimal theory prima facie despite of its novel internal consistency. It is possible to generalize the theory still without the addition of kinetic terms, leading to a new algebraically-enforced proportionality between Lambda and the matter density. Lambda and radiation may now coexist in a form consistent with Big Bang Nucleosynthesis, though this places strict constraints on the single free parameter of the theory, $\theta$. In the matter epoch Lambda behaves just like a dark matter component. Its density is proportional to the baryonic and/or dark matter, and its presence and gravitational effects would need to be included in accounting for the necessary dark matter in our Universe. This is a companion paper to Ref. [1] where the underlying gravitational theory is developed in detail.Comment: Companion paper to arXiv:1905.10380. Minor updates to match published versio

Developments in noncommutative differential geometry

One of the great outstanding problems of theoretical physics is the quantisation of gravity, and an associated description of quantum spacetime. It is often argued that, at short distances, the manifold structure of spacetime breaks down and is replaced by some sort of algebraic structure. Noncommutative geometry is a possible candidate for the mathematics of this structure. However, physical theories on noncommutative spaces are still essentially classical and need to be quantised. We present a path integral formalism for quantising gravity in the form of the spectral action. Our basic principle is to sum over all Dirac operators. The approach is demonstrated on two simple finite noncommutative geometries (the two-point space and the matrix geometry M(_2)(C)) and a circle. In each case, we start with the partition function and calculate the graviton propagator and Greens functions. The expectation values of distances are also evaluated. We find on the finite noncommutative geometries, distances shrink with increasing graviton excitations, while on a circle, they grow. A comparison is made with Rovelli's canonical quantisation approach, and with his idea of spectral path integrals. We also briefly discuss the quantisation of a general Riemannian manifold. Included, is a comprehensive overview of the homological aspects of noncommutative geometry. In particular, we cover the index pairing between K-theory and K-homology, KK-theory, cyclic homology/cohomology, the Chern character and the index theorem. We also review the various field theories on noncommutative geometries