Search

The Wheeler-DeWitt equation does not describe any explicit time evolution of the wave function, and somehow related to this issue, there is no natural way of defining an invariant inner product that provides a viable probability interpretation. We show that both of these difficulties are solved in a covariant canonical formulation of general relativity where the configuration space is extended by introducing the embedding coordinates as dynamical variables. The formalism describes the evolution of the wave function from one spacelike slice to another, but as in the case of spatial diffeomorphisms this is simply implemented by a coordinate change in the wave function. We demonstrate how the time equation disappears after gauge fixing that removes the embedding coordinates. These findings indicate that the time evolution is trivial in a background independent formulation of quantum gravity., Comment: 10 pages, v3: comments and references added

There is a common expectation that the big-bang singularity must be resolved in quantum gravity but it is not clear how this can be achieved. A major obstacle here is the difficulty of interpreting wave-functions in quantum gravity. The standard quantum mechanical framework requires a notion of time evolution and a proper definition of an invariant inner product having a probability interpretation, both of which are seemingly problematic in quantum gravity. We show that these two issues can actually be solved by introducing the embedding coordinates as dynamical variables \`a la Isham and Kuchar. The extended theory is identical to general relativity but has a larger group of gauge symmetries. The Wheeler-DeWitt equations describe the change of the wave-function from one arbitrary spacelike slice to another, however the constraint algebra makes this evolution purely kinematical and furthermore enforces the wave-function to be constrained in the subspace of zero-energy states. An inner product can also be introduced having all the necessary requirements. In this formalism big-bang appears as a finite field space boundary on which certain boundary conditions must be imposed for mathematical consistency. We explicitly illustrate this point both in the full theory and in the minisuperspace approximation., Comment: v2: 16 pages, Revtex 4-1, to appear in Annals of Physics

The wave-function in quantum gravity is supposed to obey the Wheeler-DeWitt (WDW) equation, however there is neither a satisfactory probability interpretation nor a successful solution to the problem of time in the WDW framework. To gain some insight on these issues we compare quantization of ordinary systems, first in the usual way having the Schr\"{o}dinger equation and second by promoting them as parametrized theories by introducing embedding coordinate fields, which yields first class constraints and the WDW equation. We observe that the time evolution in the WDW framework can be described with respect to the embedding coordinates, where the WDW equation becomes Schr\"{o}dinger like, i.e. it involves first order timelike functional derivatives. Moreover, the equivalence with the ordinary quantization procedure determines a suitable Hilbert space with a viable probability interpretation. We then apply the same construction to general relativity by adding embedding fields without any prior coordinate choice. The reparametrized general relativity has two different types of diffeomorphism invariance, which arises from world-volume and target-space reparametrizations. As in the case of ordinary systems, the time evolution can be described with respect to the embedding fields and the WDW equation becomes Schr\"{o}dinger like; the construction is almost identical to an ordinary parametrized field theory in terms of time evolution and Hilbert space structure. However, this time, the constraint algebra enforces the wave-function to be in a subspace of states annihilated by an operator that can be identified as the Hamiltonian. The implications of these results for the canonical quantization program, and in particular for the minisuperspace quantum cosmology, are discussed., Comment: 22 pages, revtex4-1, v2: comments and references added, to appear in Annals of Physics

It is shown that membrane and fivebrane of D=11 supergravity theory can support nongauge, linearized spin-3/2 superhairs. Supercharges associated with these fields are calculated. We also generalize the solutions to some overlapping cases and discuss possible implications of their existence., Comment: 16 pages, dedicated to the memory of Rahmi G\"uven, v2: comments and references added, to appear in Phy. Rev. D

The total Hamiltonian in general relativity, which involves the first class Hamiltonian and momentum constraints, weakly vanishes. However, when the action is expanded around a classical solution as in the case of a single scalar field inflationary model, there appears a non-vanishing Hamiltonian and additional first class constraints; but this time the theory becomes perturbative in the number of fluctuation fields. We show that one can reorganize this expansion and solve the Hamiltonian constraint exactly, which yield an explicit all order action. On the other hand, the momentum constraint can be solved perturbatively in the tensor modes $\gamma_{ij}$ by still keeping the curvature perturbation $\zeta$ dependence exact. In this way, after gauge fixing, one can obtain a semi-exact Hamiltonian for $\zeta$ which only gets corrections from the interactions with the tensor modes (hence the Hamiltonian becomes exact when the tensor perturbations set to zero). The equations of motion clearly exhibit when the evolution of $\zeta$ involves a logarithmic time dependence, which is a subtle point that has been debated in the literature. We discuss the long wavelength and late time limits, and obtain some simple but non-trivial classical solutions of the $\zeta$ zero-mode., Comment: 19 pages, revtex 4-1, to appear in Classical and Quantum Gravity

While quantum mechanics allows spooky action at a distance at the level of the wave-function, it also respects locality since there is no instantaneous propagation of real physical effects. We show that this feature can be proved in the standard interpretation of quantum mechanics by a simple general result involving commuting Hermitian operators corresponding to distant (causally disconnected) observables. This is reminiscent of satisfying the locality condition in relativistic quantum field theories., Comment: 6 pages, v3: minor changes

We use the induced geometry on the two dimensional transverse cross section of a photon beam propagating on a perturbed Friedmann-Robertson-Walker (FRW) spacetime to find the Cosmic Microwave Background (CMB) photon distribution over a telescope's collecting area today. It turns out that at each line of sight the photons are diluted along a transverse direction due to gravitational shearing. The effect can be characterized by two spin-weight-two variables, which are reminiscent of the Stokes polarization parameters. Similar to that case, one can construct a scalar and a pseudo-scalar function where the latter only gets contributions from the tensor modes. We analytically determine the power spectrum of the pseudo-scalar at superhorizon scales in a simple inflationary model and briefly discuss possible observational consequences., Comment: 6 pages, 2 figures, to appear in Physics Letters B

It is known that the Cosmic Microwave Background (CMB) temperature fluctuations are modified by gravitational lensing since the angular positions of photons are altered by the metric perturbations. We reconsider this effect in the context of geodesic deviation on a perturbed Friedmann-Robertson-Walker (FRW) spacetime with scalar and tensor modes. We first give an alternative derivation of the Sachs-Wolfe effect by using the solutions of the null geodesic equation. Then, we determine the two-dimensional induced metric on the transverse cross section of the null geodesic congruence corresponding to a beam of photons after decoupling. This metric, whose variation along the congruence can be decomposed as expansion and shear, is shown to produce a nontrivial intensity profile which can be characterized by three variables analogous to the Stokes parameters of the polarization tensor., Comment: 28 pages, 5 figures, v2: comments and references added, to appear in JCAP

We show that the energy density of the superhorizon modes released in a non-Bunch-Davies vacuum can be arbitrarily large during inflation and it decreases like ln(a)/a^4 in the subsequent radiation dominated era. This may constitute a dark radiation component which can sufficiently alter the early cosmological evolution to alleviate the Hubble tension., Comment: 18 pages, 2 figures, v2: references added

Determining the initial state of the universe is a challenging problem in quantum cosmology and we argue that the issue is intractable if the basic postulates of quantum mechanics are not modified in a nontrivial way. Namely a "standard" quantum theory of gravity is expected to resolve the big-bang singularity either by yielding a regular past eternal evolution or by a smooth finite beginning; in both cases the initial state can in principle be totally arbitrary. We illustrate this point in a minisuperspace, gauge fixed, deparametrized toy model where there is a smooth beginning of the universe provided by the matter Hamiltonian degenerating to the zero operator. This arbitrariness is the source of several debates in the literature, especially in relation to inflation, which can only be solved by a new paradigm involving initial conditions that necessarily alters the usual quantum mechanical treatment, but we argue that this is highly improbable., Comment: 10 pages, 2 figures, v2: comments added

We consider quantization of the gravity-scalar field system in the minisuperspace approximation. It turns out that in the gauge fixed deparametrized theory where the scale factor plays the role of time, the Hamiltonian can be uniquely defined without any ordering ambiguity as the square root of a self-adjoint operator. Moreover, the Hamiltonian degenerates to zero and the Schr\"{o}dinger equation becomes well behaved as the scale factor vanishes. Therefore, there is no technical or physical obstruction for the initial wave-function of the universe to be an arbitrary vector in the Hilbert space, which demonstrates the severeness of the initial condition problem in quantum cosmology., Comment: 6 pages, v3: comments added, the results are generalized to the most general spatially flat minisuperspace model

This is a technical note on the $i\epsilon$ prescription in cosmology where we consider a self-interacting scalar field in the Poincare patch of the de Sitter space whose Hamiltonian has explicit time dependence. We use both path integral and operator formalisms to work out the evolution of states from asymptotic past infinity with $i\epsilon$ prescription, which becomes nontrivial even in the free theory, and explicitly show how arbitrary states are projected onto the vacuum. We establish that in perturbation theory the $i\epsilon$ prescription can be implemented in Weinberg's commutator formula by just inserting $\epsilon$ dependent convergence factors that make the oscillating time integrals at infinity meaningful., Comment: 38 pages. v3: comments added, to appear in JCAP

We examine the emergence of the infrared logarithms in the cosmological perturbation theory applied to the minisuperspace scalar slow-roll inflation. Not surprisingly, in the single scalar field model the curvature perturbation $\zeta$ is conserved and no $\ln a_B$ behavior appears, where $a_B(t)$ is the background scale factor of the universe. On the other hand, in the presence of a spectator scalar the $n$'th order perturbation theory gives an $(\ln a_B)^n$ correction to $\zeta$. However, a nonperturbative estimate shows that $\zeta$ actually becomes the sum of a constant and a mildly evolving $\ln a_B$ pieces., Comment: v2: 15 pages, revtex4-1, comments and references added, to appear in Phys. Lett. B

If Higgs is a spectator scalar, i.e. if it is not directly coupled to the inflaton, superhorizon Higgs modes must have been exited during inflation. Since Higgs is unstable its decay into photons is expected to seed superhorizon photon modes. We use in-in perturbation theory to show that this naive physical expectation is indeed fulfilled via loop effects. Specifically, we calculate the first order Higgs loop correction to the magnetic field power spectrum evaluated at some late time after inflation. It turns out that this loop correction becomes much larger than the tree-level power spectrum at the superhorizon scales. This offers a mechanism to generate cosmologically interesting superhorizon vector modes by scalar-vector interactions., Comment: 20 pages, revtex4-1, v3: comments and an appendix discussing dimensional regularization added, other minor changes, to appear in JCAP

In this paper we first discuss how a Noether current corresponding to a gauge or a global symmetry can locally be introduced in a path integral irrespective of the boundary conditions defining the theory. We then consider quantization of gravity plus minimally coupled scalar field system in the phase space path integral approach. The complete gauge fixed action including the Faddeev-Popov determinant is obtained in the so called $\zeta$-gauge. It turns out that in this formalism while the dilatation survives as the residual symmetry of the gauge fixed action, other diffeomorphisms which require field dependent corrections fail to be so. The full Noether current for the dilatation is determined and the spatial boundary conditions that yield a finite and conserved charge are determined. The charge is shown to be expressible as a surface integral at infinity and the corresponding Ward identity gives the standard consistency relation of cosmological perturbations., Comment: 22 pages, revtex4-1, v3: comments and references added, to appear in Phys. Rev. D