Completeness of non-normalizable modes

We establish the completeness of some characteristic sets of non-normalizable modes by constructing fully localized square steps out of them, with each such construction expressly displaying the Gibbs phenomenon associated with trying to use a complete basis of modes to fit functions with discontinuous edges. As well as being of interest in and of itself, our study is also of interest to the recently introduced large extra dimension brane-localized gravity program of Randall and Sundrum, since the particular non-normalizable mode bases that we consider (specifically the irregular Bessel functions and the associated Legendre functions of the second kind) are associated with the tensor gravitational fluctuations which occur in those specific brane worlds in which the embedding of a maximally four-symmetric brane in a five-dimensional anti-de Sitter bulk leads to a warp factor which is divergent. Since the brane-world massless four-dimensional graviton has a divergent wave function in these particular cases, its resulting lack of normalizability is thus not seen to be any impediment to its belonging to a complete basis of modes, and consequently its lack of normalizability should not be seen as a criterion for not including it in the spectrum of observable modes. Moreover, because the divergent modes we consider form complete bases, we can even construct propagators out of them in which these modes appear as poles with residues which are expressly finite. Thus even though normalizable modes appear in propagators with residues which are given as their finite normalization constants, non-normalizable modes can just as equally appear in propagators with finite residues too -- it is just that such residues will not be associated with bilinear integrals of the modes.Comment: 34 pages, 6 figures. Revte

Implications of Cosmic Repulsion for Gravitational Theory

In this paper we present a general, model independent analysis of a recently detected apparent cosmic repulsion, and discuss its potential implications for gravitational theory. In particular, we show that a negatively spatially curved universe acts like a diverging refractive medium, to thus naturally cause galaxies to accelerate away from each other. Additionally, we show that it is possible for a cosmic acceleration to only be temporary, with some accelerating universes actually being able to subsequently recontract.Comment: RevTeX, 13 page

Open Questions in Classical Gravity

We discuss some outstanding open questions regarding the validity and uniqueness of the standard second order Newton-Einstein classical gravitational theory. On the observational side we discuss the degree to which the realm of validity of Newton's Law of Gravity can actually be extended to distances much larger than the solar system distance scales on which the law was originally established. On the theoretical side we identify some commonly accepted but actually still open to question assumptions which go into the formulating of the standard second order Einstein theory in the first place. In particular, we show that while the familiar second order Poisson gravitational equation (and accordingly its second order covariant Einstein generalization) may be sufficient to yield Newton's Law of Gravity they are not in fact necessary. The standard theory thus still awaits the identification of some principle which would then make it necessary too. We show that current observational information does not exclusively mandate the standard theory, and that the conformal invariant fourth order theory of gravity considered recently by Mannheim and Kazanas is also able to meet the constraints of data, and in fact to do so without the need for any so far unobserved non-luminous or dark matter.Comment: UCONN-93-1, plain TeX format, 22 pages (plus 7 figures - send requests to [email protected]). To appear in a special issue of Foundations of Physics honoring Professor Fritz Rohrlich on the occasion of his retirement, L. P. Horwitz and A. van der Merwe Editors, Plenum Publishing Company, N.Y., Fall 199

Broadband study of blazar 1ES 1959+650 during flaring state in 2016

Aim : The nearby TeV blazar 1ES 1959+650 (z=0.047) was reported to be in flaring state during June - July 2016 by Fermi-LAT, FACT, MAGIC and VERITAS collaborations. We studied the spectral energy distributions (SEDs) in different states of the flare during MJD 57530 - 57589 using simultaneous multiwaveband data to understand the possible broadband emission scenario during the flare. Methods : The UV/optical and X-ray data from UVOT and XRT respectively on board Swift and high energy $\gamma$-ray data from Fermi-LAT are used to generate multiwaveband lightcurves as well as to obtain high flux states and quiescent state SEDs. The correlation and lag between different energy bands is quantified using discrete correlation function. The synchrotron self Compton (SSC) model was used to reproduce the observed SEDs during flaring and quiescent states of the source. Results : A decent correlation is seen between X-ray and high energy $\gamma$-ray fluxes. The spectral hardening with increase in the flux is seen in X-ray band. The powerlaw index vs flux plot in $\gamma$-ray band indicates the different emission regions for 0.1 - 3 GeV and 3-300 GeV energy photons. Two zone SSC model satisfactorily fits the observed broadband SEDs. The inner zone is mainly responsible for producing synchrotron peak and high energy $\gamma$-ray part of the SED in all states. The second zone is mainly required to produce less variable optical/UV and low energy $\gamma$-ray emission. Conclusions : Conventional single zone SSC model does not satisfactorily explain broadband emission during observation period considered. There is an indication of two emission zones in the jet which are responsible for producing broadband emission from optical to high energy $\gamma$-rays.Comment: 11 pages, 12 figures, Accepted in A&

Constraints on AdS5AdS_5 Embeddings

We show that the embedding of either a static or a time dependent maximally 3-symmetric brane with non-zero spatial curvature $k$ into a non-compactified $AdS_5$ bulk does not yield exponential suppression of the geometry away from the brane. Implications of this result for brane-localized gravity are discussed.Comment: RevTeX, 9 pages (updated version v2, conclusions unchanged after extension to the non-static case

Multi-frequency, Multi-Epoch Study of Mrk 501: Hints for a two-component nature of the emission

Since the detection of very high energy (VHE) $\gamma$-rays from Mrk 501, its broad band emission of radiation was mostly and quite effectively modeled using one zone emission scenario. However, broadband spectral and flux variability studies enabled by the multiwavelength campaigns carried out during the recent years have revealed rather complex behavior of Mrk 501. The observed emission from Mrk 501 could be due to a complex superposition of multiple emission zones. Moreover new evidences of detection of very hard intrinsic $\gamma$-ray spectra obtained from {\it Fermi}--LAT observations have challenged the theories about origin of VHE $\gamma$-rays. Our studies based on {\it Fermi}--LAT data indicate the existence of two separate components in the spectrum, one for low energy $\gamma$-rays and the other for high energy $\gamma$-rays. Using multiwaveband data from several ground and space based instruments, in addition to HAGAR data, the spectral energy distribution of Mrk~501 is obtained for various flux states observed during 2011. In the present work, this observed broadband spectral energy distribution is reproduced with a leptonic, multi-zone Synchrotron Self-Compton model.Comment: Published in Astrophysical Journal (ApJ

Coherent Neutrino Interactions in a Dense Medium

Motivated by the effect of matter on neutrino oscillations (the MSW effect) we study in more detail the propagation of neutrinos in a dense medium. The dispersion relation for massive neutrinos in a medium is known to have a minimum at nonzero momentum p \sim (G_F\rho)/\sqrt{2}. We study in detail the origin and consequences of this dispersion relation for both Dirac and Majorana neutrinos both in a toy model with only neutral currents and a single neutrino flavour and in a realistic "Standard Model" with two neutrino flavours. We find that for a range of neutrino momenta near the minimum of the dispersion relation, Dirac neutrinos are trapped by their coherent interactions with the medium. This effect does not lead to the trapping of Majorana neutrinos.Comment: 28 pages, 6 figures, Latex; minor changes, one reference added; version to appear in Phys. Rev.

Causal Structure of Vacuum Solutions to Conformal(Weyl) Gravity

Using Penrose diagrams the causal structure of the static spherically symmetric vacuum solution to conformal (Weyl) gravity is investigated. A striking aspect of the solution is an unexpected physical singularity at $r=0$ caused by a linear term in the metric. We explain how to calculate the deflection of light in coordinates where the metric is manifestly conformal to flat i.e. in coordinates where light moves in straight lines.Comment: 18 pages, 2 figures, title and abstract changed, contents essentially unaltered accepted for publication in General Relativity and Gravitatio

Oscillating instanton solutions in curved space

We investigate oscillating instanton solutions of a self-gravitating scalar field between degenerate vacua. We show that there exist O(4)-symmetric oscillating solutions in a de Sitter background. The geometry of this solution is finite and preserves the $Z_{2}$ symmetry. The nontrivial solution corresponding to tunneling is possible only if the effect of gravity is taken into account. We present numerical solutions of this instanton, including the phase diagram of solutions in terms of the parameters of the present work and the variation of energy densities. Our solutions can be interpreted as solutions describing an instanton-induced domain wall or braneworld-like object rather than a kink-induced domain wall or braneworld. The oscillating instanton solutions have a thick wall and the solutions can be interpreted as a mechanism providing nucleation of the thick wall for topological inflation. We remark that $Z_{2}$ invariant solutions also exist in a flat and anti-de Sitter background, though the physical significance is not clear.Comment: 25 pages, 11 figues. Some typos corrected, references added, and Ch3. modified according to referee's comment

A possible origin of superconducting currents in cosmic strings

The scattering and capture of right-handed neutrinos by an Abelian cosmic string in the SO(10) grand unification model are considered. The scattering cross-section of neutrinos per unit length due to the interaction with the gauge and Higgs fields of the string is much larger in its scaling regime than in the friction one because of the larger infrared cutoff of the former.The probability of capture in a zero mode of the string accompanied by the emission of a gauge or Higgs boson shows a resonant peak for neutrino momentum of the order of its mass. Considering the decrease of number of strings per unit comoving volume in the scaling epoch the cosmological consequences of the superconducting strings formed in this regime will be much smaller than those which could be produced already in the friction one.Comment: 14 pages Latex, 4 figues/ep