The issue of time in generally covariant theories and the Komar-Bergmann approach to observables in general relativity

Diffeomorphism-induced symmetry transformations and time evolution are distinct operations in generally covariant theories formulated in phase space. Time is not frozen. Diffeomorphism invariants are consequently not necessarily constants of the motion. Time-dependent invariants arise through the choice of an intrinsic time, or equivalently through the imposition of time-dependent gauge fixation conditions. One example of such a time-dependent gauge fixing is the Komar-Bergmann use of Weyl curvature scalars in general relativity. An analogous gauge fixing is also imposed for the relativistic free particle and the resulting complete set time-dependent invariants for this exactly solvable model are displayed. In contrast with the free particle case, we show that gauge invariants that are simultaneously constants of motion cannot exist in general relativity. They vary with intrinsic time

Massive spin 2 propagator on de Sitter space

We compute the Pauli-Jordan, Hadamard and Feynman propagators for the massive metrical perturbations on de Sitter space. They are expressed both in terms of mode sums and in invariant forms.Comment: 30 pages + 1 eps fi

Type I vacuum solutions with aligned Papapetrou fields: an intrinsic characterization

We show that Petrov type I vacuum solutions admitting a Killing vector whose Papapetrou field is aligned with a principal bivector of the Weyl tensor are the Kasner and Taub metrics, their counterpart with timelike orbits and their associated windmill-like solutions, as well as the Petrov homogeneous vacuum solution. We recover all these metrics by using an integration method based on an invariant classification which allows us to characterize every solution. In this way we obtain an intrinsic and explicit algorithm to identify them.Comment: 14 pages; v2: added new section, references and tabl

Naturalness in Cosmological Initial Conditions

We propose a novel approach to the problem of constraining cosmological initial conditions. Within the framework of effective field theory, we classify initial conditions in terms of boundary terms added to the effective action describing the cosmological evolution below Planckian energies. These boundary terms can be thought of as spacelike branes which may support extra instantaneous degrees of freedom and extra operators. Interactions and renormalization of these boundary terms allow us to apply to the boundary terms the field-theoretical requirement of naturalness, i.e. stability under radiative corrections. We apply this requirement to slow-roll inflation with non-adiabatic initial conditions, and to cyclic cosmology. This allows us to define in a precise sense when some of these models are fine-tuned. We also describe how to parametrize in a model-independent way non-Gaussian initial conditions; we show that in some cases they are both potentially observable and pass our naturalness requirement.Comment: 35 pages, 8 figure

On the algebraic classification of spacetimes

We briefly overview the Petrov classification in four dimensions and its generalization to higher dimensions.Comment: Submitted to Journal of Physics, conference series, proceedings of 4th meeting on constrained dynamics and quantum gravity, 12-16 September 2005, Sardinia, Ital

Holographic dark matter and dark energy with second order invariants

One of the main goals of modern cosmology remains to summon up a self consistent policy, able to explain, in the framework of the Einstein's theory, the cosmic speed up and the presence of Dark Matter in the Universe. Accordingly to the Holographic principle, which postulates the existence of a minimal size of a physical region, we argue, in this paper, that if this size exists for the Universe and it is accrued from the independent geometrical second order invariants, it would be possible to ensure a surprising source for Dark Matter and a viable candidate for explaining the late acceleration of the Universe. Along the work, we develop low redshift tests, such as Supernovae Ia and kinematical analysis complied by the use of Cosmography and we compare the outcomes with higher redshift tests, such as CMB peak and anisotropy of the cosmic power spectrum. All the results indicate that the models presented here can be interpreted as unified models that are capable to describe both the dark matter and the dark energy.Comment: 12 figures, revtex styl

Curvature invariants in type N spacetimes

Scalar curvature invariants are studied in type N solutions of vacuum Einstein's equations with in general non-vanishing cosmological constant Lambda. Zero-order invariants which include only the metric and Weyl (Riemann) tensor either vanish, or are constants depending on Lambda. Even all higher-order invariants containing covariant derivatives of the Weyl (Riemann) tensor are shown to be trivial if a type N spacetime admits a non-expanding and non-twisting null geodesic congruence. However, in the case of expanding type N spacetimes we discover a non-vanishing scalar invariant which is quartic in the second derivatives of the Riemann tensor. We use this invariant to demonstrate that both linearized and the third order type N twisting solutions recently discussed in literature contain singularities at large distances and thus cannot describe radiation fields outside bounded sources.Comment: 17 pages, to appear in Class. Quantum Gra

Group theoretical approach to quantum fields in de Sitter space I. The principal series

Using unitary irreducible representations of the de Sitter group, we construct the Fock space of a massive free scalar field. In this approach, the vacuum is the unique dS invariant state. The quantum field is a posteriori defined by an operator subject to covariant transformations under the dS isometry group. This insures that it obeys canonical commutation relations, up to an overall factor which should not vanish as it fixes the value of hbar. However, contrary to what is obtained for the Poincare group, the covariance condition leaves an arbitrariness in the definition of the field. This arbitrariness allows to recover the amplitudes governing spontaneous pair creation processes, as well as the class of alpha vacua obtained in the usual field theoretical approach. The two approaches can be formally related by introducing a squeezing operator which acts on the state in the field theoretical description and on the operator in the present treatment. The choice of the different dS invariant schemes (different alpha vacua) is here posed in very simple terms: it is related to a first order differential equation which is singular on the horizon and whose general solution is therefore characterized by the amplitude on either side of the horizon. Our algebraic approach offers a new method to define quantum field theory on some deformations of dS space.Comment: 35 pages, 2 figures ; Corrected typo, Changed referenc

All spacetimes with vanishing curvature invariants

All Lorentzian spacetimes with vanishing invariants constructed from the Riemann tensor and its covariant derivatives are determined. A subclass of the Kundt spacetimes results and we display the corresponding metrics in local coordinates. Some potential applications of these spacetimes are discussed.Comment: 24 page

Reparameterization invariants for anisotropic Bianchi I cosmology with a massless scalar source

Intrinsic time-dependent invariants are constructed for classical, flat, homogeneous, anisotropic cosmology with a massless scalar material source. Invariance under the time reparameterization-induced canonical symmetry group is displayed explicitly.Comment: 28 pages, to appear in General Relativity and Gravitation. Substantial revisions: added foundational overview section 2, chose new intrinsic time variable, worked with dimensionless variables, added appendix with comparison and criticism of other approache