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We show that the Schwarzschild-(A)dS black hole mechanics possesses a hidden symmetry under the three-dimensional Poincar\'e group. This symmetry shows up after having gauge-fixed the diffeomorphism invariance in the symmetry-reduced homogeneous Einstein-$\Lambda$ model and stands as a physical symmetry of the system. It dictates the geometry both in the black hole interior and exterior regions, as well as beyond the cosmological horizon in the Schwarzschild-dS case. It follows that one can associate a set of non-trivial conserved charges to the Schwarzschild-(A)dS black hole which act in each causally disconnected regions. In T-regions, they act on fields living on spacelike hypersurface of constant time, while in the R-region, they act on time-like hypersurface of constant radius. We find that while the expression of the charges depend explicitly on the location of the hypersurface, the charge algebra remains the same at any radius in R-regions (or time in T-regions). Finally, the analysis of the Casimirs of the charge algebra reveals a new solution-generating map. The sl$(2,\mathbb{R})$ Casimir is shown to generate a one-parameter family of deformation of the black hole geometry labelled by the cosmological constant. This gives rise to a new conformal bridge allowing one to continuously deform the Schwarzschild-AdS geometry to the Schwarzschild and the Schwarzschild-dS solutions., Comment: 22+7 pages, typos corrected, version published in JHEP

We investigate the role played by symmetries in the perturbative expansion of the large-scale structure. In particular, we establish which of the coefficients of the perturbation theory kernels are dictated by symmetries and which not. Up to third order in perturbations, for the dark matter density contrast (and for the dark matter velocity) only three coefficients are not fixed by symmetries and depend on the particular cosmology. For generic biased tracers, where number/mass and momentum conservation cannot be imposed in general, this number rises to seven in agreement with other bias expansions discussed in the literature. A crucial role in our analysis is provided by extended Galilean invariance, which follows from diffeomorphism invariance in the non-relativistic limit. We identify a full hierarchy of extended Galilean invariance constraints, which fix the analytic structure of the perturbation theory kernels as the sums of an increasing number of external momenta vanish. Our approach is especially relevant for non-standard models that respect the same symmetries as $\Lambda$CDM and where perturbation theory at higher orders has not been exhaustively explored, such as dark energy and modified gravity scenarios. In this context, our results can be used to systematically extend the bias expansion to higher orders and set up model independent analyses., Comment: 34 pages, 5 figures. v2: brief revisions and typos corrections

The causal structure of the recent loop quantum gravity black hole collapse model [1] is analysed. As the spacetime is only approximately diffeomorphism invariant up to powers of $\hbar$, it is not straight forwardly possible to find global conformally compactified coordinates and to construct the Penrose diagram. Therefore, radial in- and outgoing light rays are studied to extract the causal features and sketch a causal diagram. It was found that the eternal metric [2], which is the vacuum solution of the collapse model, has a causal horizon. However, in the collapsing case light rays travel through matter to causally connect the regions in- and outside the horizon -- the causal horizon is not present in the collapsing scenario. It is worked out that this is related to the shock wave and spacetime discontinuity, which allows matter travelling super-luminal along a space-like trajectory from the vacuum point of view, but remaining time-like from the matter perspective. The final causal diagram is a compact patch of a Reissner-Nordstr\"om causal diagram. Further, possibilities of a continuous matter collapse with only time-like evolution are studied. It was found that the time-reversed vacuum metric is also a solution of the dynamical equations and a once continuously differentiable matching of the vacuum spacetime across the minimal radius is possible. This allows an everywhere continuous and time-like collapse process at the cost of an infinite extended causal diagram. This solution is part of an infinitely extended eternal black hole solution with a bounce, whose global extension is constructed. Due to the analysis of radial light rays, it is possible to sketch causal diagrams of these spacetimes., Comment: 28 pages, 6 figures. Version accepted for publication in PRD

We formulate the baby universe construction rigorously by giving a primordial role to the algebra of observables of quantum gravity rather than the Hilbert space. Utilizing diffeomorphism invariance, we study baby universe creation and annihilation via change in topology. We then construct the algebra of boundary observables for holographic theories and show that it enhances to contain an 'extra' Abelian tensor factor to describe the bulk in the quantum regime; via the gravitational path integral we realize this extra tensor factor, at the level of the Hilbert space, in the context of the GNS representation. We reformulate the necessary assumptions for the "baby universe hypothesis" using the GNS representation. When the baby universe hypothesis is satisfied, we demonstrate that the "miraculous cancellations" in the corresponding gravitational path integral have a natural explanation in terms of the character theory of Abelian $C^\ast$-algebras. We find the necessary and sufficient mathematical condition for the baby universe hypothesis to hold, and transcribe it into sufficient physical conditions. We find that they are incompatible with a baby universe formation that is influenced by any bulk process from the AdS/CFT correspondence. We illustrate our construction by applying it to two settings, which leads to a re-interpretion of some topological models of gravity, and to draw an analogy with the topological vacua of gauge theory., 35 pages, 4 figures, minor corrections and clarifications added

It is a well-known property of holographic theories that diffeomorphism invariance in the bulk space-time implies Weyl invariance of the dual holographic field theory in the sense that the field theory couples to a conformal class of background metrics. The usual Fefferman-Graham formalism, which provides us with a holographic dictionary between the two theories, breaks explicitly this symmetry by choosing a specific boundary metric and a corresponding specific metric ansatz in the bulk. In this paper, we show that a simple extension of the Fefferman-Graham formalism allows us to sidestep this explicit breaking; one finds that the geometry of the boundary includes an induced metric and an induced connection on the tangent bundle of the boundary that is a Weyl connection (rather than the more familiar Levi-Civita connection uniquely determined by the induced metric). Properly invoking this boundary geometry has far-reaching consequences: the holographic dictionary extends and naturally encodes Weyl-covariant geometrical data, and, most importantly, the Weyl anomaly gains a clearer geometrical interpretation, cohomologically relating two Weyl-transformed volumes. The boundary theory is enhanced due to the presence of the Weyl current, which participates with the stress tensor in the boundary Ward identity., v5; 27 pages, minor typos corrected

Minimally modified gravity theories are modifications of general relativity with two local gravitational degrees of freedom in four dimensions. Their construction relies on the breaking of 4D diffeomorphism invariance keeping however the symmetry under 3D diffeomorphisms. Here, we construct these theories from a Hamiltonian point of view. We start with the phase space of general relativity in the ADM formalism. Then, we find the conditions that the Hamiltonian must satisfy for the theory to propagate (up to) two gravitational degrees of freedom with the assumptions that the lapse and the shift are not dynamical, and the theory remains invariant under 3D diffeomorphisms. This construction enables us to recover the well-known "cuscuton" class of scalar-tensor theories in the unitary gauge. We also exhibit a new class of interesting theories, that we dubb $f({\cal H})$ theories, where the usual Hamiltonian constraint $\cal H$ of general relativity is replaced by $f({\cal H})$ where $f$ is an arbitrary function., 20 pages

We consider theories describing the dynamics of a four-dimensional metric, whose Lagrangian is diffeomorphism invariant and depends at most on second derivatives of the metric. Imposing degeneracy conditions we find a set of Lagrangians that, apart form the Einstein-Hilbert one, are either trivial or contain more than two degrees of freedom. Among the partially degenerate theories, we recover Chern-Simons gravity, endowed with constraints whose structure suggests the presence of instabilities. Then, we enlarge the class of parity violating theories of gravity by introducing new "chiral scalar-tensor theories". Although they all raise the same concern as Chern-Simons gravity, they can nevertheless make sense as low energy effective field theories or, by restricting them to the unitary gauge (where the scalar field is uniform), as Lorentz breaking theories with a parity violating sector., 22 pages, references added, published version

We show that theories of mimetic gravity can be viewed as degenerate higher-order scalar-tensor (DHOST) theories that admit an extra local (gauge) symmetry in addition to the usual diffeomorphism invariance. We reformulate and classify mimetic theories in this perspective. Using the effective theory of dark energy, recently extended to include DHOST theories, we then investigate the linear perturbations about a homogeneous and isotropic background for all mimetic theories. We also include matter, in the form of a $k$-essence scalar field, and we derive the quadratic action for linear perturbations in this case., Comment: 22 pages, 1 figure, references added and discussion on the instability modified. Matches the version published on JCAP

We consider several diffeomorphism invariant field theories of 2- and 3-forms in six dimensions. They all share the same kinetic term $BdC$, but differ in the potential term that is added. The theory $BdC$ with no potential term is topological - it describes no propagating degrees of freedom. We show that the theory continues to remain topological when either the $BBB$ or $C\hat{C}$ potential term is added. The latter theory can be viewed as a background independent version of the 6-dimensional Hitchin theory, for its critical points are complex or para-complex 6-manifolds, but unlike in Hitchin's construction, one does not need to choose of a background cohomology class to define the theory. We also show that the dimensional reduction of the $C\hat{C}$ theory to three dimensions, when reducing on S3, gives 3D gravity., Comment: 24 pages, no figures

In [arXiv:1411.3592] an extension of the Ashtekar-Lewandowski (AL) state space of Loop Quantum Gravity was set up with the help a projective formalism introduced by Kijowski [Kijowski 1977; see also: arXiv:1304.6330, arXiv:1411.3590]. The motivation for this work was to achieve a more balanced treatment of the position and momentum variables (aka. holonomies and fluxes). Indeed, states in the AL Hilbert spaces describe discrete quantum excitations on top of a vacuum which is an eigenstate of the flux variables (a `no-geometry' state): in such states, most holonomies are totally spread, making it difficult to approximate a smooth, classical 4-geometry. However, going beyond the AL sector does not fully resolve this difficulty: one uncovers a deeper issue hindering the construction of states semi-classical with respect to a full set of observables. In the present article, we analyze this issue in the case of real-valued holonomies (we will briefly comment on the heuristic implications for other gauge groups, eg. $\mathcal{SU}(2)$). Specifically, we show that, in this case, there does not exist any state on the holonomy-flux algebra in which the variances of the holonomies and fluxes observables would all be finite, let alone small. It is important to note that this obstruction cannot be bypassed by further enlarging the quantum state space, for it arises from the structure of the algebra itself: as there are too many (uncountably many) non-vanishing commutators between the holonomy and flux operators, the corresponding Heisenberg inequalities force the quantum uncertainties to blow up uncontrollably. A way out would be to suitably restrict the algebra of observables. In a companion paper we take the first steps in this direction by developing a general framework to perform such a restriction without giving up the universality and diffeomorphism invariance of the theory., 51 pages, 1 figure