Exponential expansion in Unimodular Gravity is possible even in the absence of a constant potential; {em id est} for free fields. This is at variance with the case in General Relativity.
The full one-loop (scalar) effective action is computed for both hyperbolic and elliptic spacetimes.
This paper studies both existence and spectral stability properties of bounded spatially periodic traveling wave solutions to a large class of scalar viscous balance laws in one space dimension with a reaction function of monostable or Fisher-KPP typ
e. Under suitable structural assumptions, it is shown that this class of equations underlies two families of periodic waves. The first family consists of small amplitude waves with finite fundamental period which emerge from a Hopf bifurcation around a critical value of the wave speed. The second family pertains to arbitrarily large period waves which arise from a homoclinic bifurcation and tend to a limiting traveling (homoclinic) pulse when their fundamental period tends to infinity. For both families, it is shown that the Floquet (continuous) spectrum of the linearization around the periodic waves intersects the unstable half plane of complex values with positive real part, a property known as spectral instability. For that purpose, in the case of small-amplitude waves it is proved that the spectrum of the linearized operator around the wave can be approximated by that of a constant coefficient operator around the zero solution and determined by a dispersion relation which intersects the unstable complex half plane. In the case of large period waves, we verify that the family satisfies the assumptions of the seminal result by Gardner (1997, J. Reine Angew. Math. 491, pp. 149-181) of convergence of periodic spectra in the infinite-period limit to that of the underlying homoclinic wave, which is unstable. A few examples are discussed.
This paper is concerned with the structural stability of spherical horizons. By this we mean stability with respect to variations of the second member of the corresponding differential equations, corresponding to the inclusion of the contribution of
operators quadratic in curvature. This we do both in the usual second order approach (in which the independent variable is the spacetime metric) and in the first order one (where the independent variables are the spacetime metric and the connection field). In second order, it is claimed that the generic solution in the asymptotic regime (large radius) can be matched not only with the usual solutions with horizons (like Schwarzschild-de Sitter) but also with a more generic (in the sense that it depends on more arbitrary parameters) horizonless family of solutions. It is however remarkable that these horizonless solutions are absent in the {em restricted} (that is, when the background connection is the metric one) first order approach.
The presence of gravity generalizes the notion of scale invariance to Weyl invariance, namely, invariance under local rescalings of the metric. In this work, we have computed the Weyl anomaly for various classically scale or Weyl invariant theories,
making particular emphasis on the differences that arise when gravity is taken as a dynamical fluctuation instead of as a non-dynamical background field. We find that the value of the anomaly for the Weyl invariant coupling of scalar fields to gravity is sensitive to the dynamical character of the gravitational field, even when computed in constant curvature backgrounds. We also discuss to what extent those effects are potentially observable.
The most general lagrangian describing spin 2 particles in flat spacetime and containing operators up to (mass) dimension 6 is carefully analyzed, determining the precise conditions for it to be invariant under linearized (transverse) diffeomorphisms
, linearized Weyl rescalings, and conformal transformations.
A definition of quasi-local energy in a gravitational field based upon its embedding into flat space is discussed. The outcome is not satisfactory from many points of view.
A ghost free massive deformation of unimodular gravity (UG), in the spirit of {em mimetic massive gravity}, is shown to exist. This construction avoids the no-go theorem for a Fierz-Pauli type of mass term in UG by giving up on Lorentz invariance. In
our framework, the mimetic degree of freedom vanishes on-shell.
