On the contribution of density perturbations and gravitational waves to the lower order multipoles of the Cosmic Microwave Background Radiation

The important studies of Peebles, and Bond and Efstathiou have led to the formula C_l = const/[l(l +1)] aimed at describing the lower order multipoles of the CMBR temperature variations caused by density perturbations with the flat spectrum. Clearly, this formula requires amendments, as it predicts an infinitely large monopole C_0, and a dipole moment C_1 only 6/2 times larger than the quadrupole C_2, both predictions in conflict with observations. We restore the terms omitted in the course of the derivation of this formula, and arrive at a new expression. According to the corrected formula, the monopole moment is finite and small, while the dipole moment is sensitive to short-wavelength perturbations, and numerically much larger than the quadrupole, as one would expect on physical grounds. At the same time, the function l(l +1)C_l deviates from a horizontal line and grows with l, for l \geq 2. We show that the inclusion of the modulating (transfer) function terminates the growth and forms the first peak, recently observed. We fit the theoretical curves to the position and height of the first peak, as well as to the observed dipole, varying three parameters: red-shift at decoupling, red-shift at matter-radiation equality, and slope of the primordial spectrum. It appears that there is always a deficit, as compared with the COBE observations, at small multipoles, l \sim 10. We demonstrate that a reasonable and theoretically expected amount of gravitational waves bridges this gap at small multipoles, leaving the other fits as good as before. We show that the observationally acceptable models permit somewhat `blue' primordial spectra. This allows one to avoid the infra-red divergence of cosmological perturbations, which is otherwise present.Comment: prints to 25 pages including 14 figures, several additional sentences on interpretation, new references, to appear in Int. Journ. Mod. Physics

Cooper Pairs with Broken Parity and Time-Reversal Symmetries in D-wave Superconductors

Paramagnetic effects are shown to result in the appearance of a triplet component of order parameter in a vortex phase of a d-wave superconductor in the absence of impurities. This component, which breaks both parity and time-reversal symmetries of Cooper pairs, is expected to be of the order of unity in a number of modern superconductors such as organic, high-Tc, and some others. A generic phase diagram of such type-IV superconductors, which are singlet ones at H=0 and characterized by singlet-triplet mixed Copper pairs with broken time-reversal symmetry in a vortex phase, is discussed.Comment: 10 pages, 1 figures, Phys. Rev. Lett., submitted (July 25 2005

In-plane magnetic field phase diagram of superconducting Sr2RuO4

We develop the Ginzburg - Landau theory of the upper critical field in the basal plane of a tetragonal multiband metal in two-component superconducting state. It is shown that typical for the two component superconducting state the upper critical field basal plane anisotropy and the phase transition splitting still exist in a multiband case. However, the value of anisotropy can be effectively smaller than in the single band case. The results are discussed in the application to the superconducting Sr2RuO4.Comment: 4 pages, no figure

Quantum Effects In Cosmology

Contents: Introduction. The Present State of the Universe. What Can We Expect From a Complete Cosmological Theory? An Overview of Quantum Effects in Cosmology. Parametric (Superadiabatic) Amplification of Classical Waves. Graviton Creation in the Inflationary Universe. Quantum States of a Harmonic Oscillator. Squeezed Quantum States of Relic Gravitons and Primordial Density Perturbations. Quantum Cosmology, Minisuperspace Models and Inflation. From the Space of Classical Solutions to the Space of Wave Functions. On the Probability of Quantum Tunneling From "Nothing". Duration of InflationComment: (43 pages, to be published in "The Origin of Structure in the Universe", ed. P.Nardone

Cooling system for high speed aircraft

The system eliminates the necessity of shielding an aircraft airframe constructed of material such as aluminum. Cooling is accomplished by passing a coolant through the aircraft airframe, the coolant acting as a carrier to remove heat from the airframe. The coolant is circulated through a heat pump and a heat exchanger which together extract essentially all of the added heat from the coolant. The heat is transferred to the aircraft fuel system via the heat exchanger and the heat pump. The heat extracted from the coolant is utilized to power the heat pump. The heat pump has associated therewith power turbine mechanism which is also driven by the extracted heat. The power turbines are utilized to drive various aircraft subsystems, the compressor of the heat pump, and provide engine cooling

Fictitious Level Dynamics: A Novel Approach to Spectral Statistics in Disordered Conductors

We establish a new approach to calculating spectral statistics in disordered conductors, by considering how energy levels move in response to changes in the impurity potential. We use this fictitious dynamics to calculate the spectral form factor in two ways. First, describing the dynamics using a Fokker-Planck equation, we make a physically motivated decoupling, obtaining the spectral correlations in terms of the quantum return probability. Second, from an identity which we derive between two- and three-particle correlation functions, we make a mathematically controlled decoupling to obtain the same result. We also calculate weak localization corrections to this result, and show for two dimensional systems (which are of most interest) that corrections vanish to three-loop order.Comment: 35 pages in REVTeX format including 10 postscript figures; to be published in a special issue (on Topics in Mesoscopic Physics) of the Journal of Mathematical Physics, October 199

Relic gravitational waves in the light of 7-year Wilkinson Microwave Anisotropy Probe data and improved prospects for the Planck mission

The new release of data from Wilkinson Microwave Anisotropy Probe improves the observational status of relic gravitational waves. The 7-year results enhance the indications of relic gravitational waves in the existing data and change to the better the prospects of confident detection of relic gravitational waves by the currently operating Planck satellite. We apply to WMAP7 data the same methods of analysis that we used earlier [W. Zhao, D. Baskaran, and L.P. Grishchuk, Phys. Rev. D 80, 083005 (2009)] with WMAP5 data. We also revised by the same methods our previous analysis of WMAP3 data. It follows from the examination of consecutive WMAP data releases that the maximum likelihood value of the quadrupole ratio $R$, which characterizes the amount of relic gravitational waves, increases up to $R=0.264$, and the interval separating this value from the point $R=0$ (the hypothesis of no gravitational waves) increases up to a $2\sigma$ level. The primordial spectra of density perturbations and gravitational waves remain blue in the relevant interval of wavelengths, but the spectral indices increase up to $n_s =1.111$ and $n_t=0.111$. Assuming that the maximum likelihood estimates of the perturbation parameters that we found from WMAP7 data are the true values of the parameters, we find that the signal-to-noise ratio $S/N$ for the detection of relic gravitational waves by the Planck experiment increases up to $S/N=4.04$, even under pessimistic assumptions with regard to residual foreground contamination and instrumental noises. We comment on theoretical frameworks that, in the case of success, will be accepted or decisively rejected by the Planck observations.Comment: 27 pages, 12 (colour) figures. Published in Phys. Rev. D. V.3: modifications made to reflect the published versio

Relic gravitational waves: latest revisions and preparations for new data

The forthcoming release of data from the Planck mission, and possibly from the next round of Wilkinson Microwave Anisotropy Probe (WMAP) observations, make it necessary to revise the evaluations of relic gravitational waves in the existing data and, at the same time, to refine the assumptions and data analysis techniques in preparation for the arrival of new data. We reconsider with the help of the commonly used CosmoMC numerical package the previously found indications of relic gravitational waves in the 7-year (WMAP7) data. The CosmoMC approach reduces the confidence of these indications from approximately 2$\sigma$ level to approximately 1$\sigma$ level, but the indications do not disappear altogether. We critically analyze the assumptions that are currently used in the Cosmic Microwave Background (CMB) data analyzes and outline the strategy that should help avoid the oversight of relic gravitational waves in the future CMB data. In particular, it is important to keep away from the unwarranted assumptions about density perturbations. The prospects of confident detection of relic gravitational waves by the Planck satellite have worsened, but they are still good. It appears that more effort will be required in order to mitigate the foreground contamination.Comment: 11 pages, 4 figures, 3 tables; v.3: improvements, published versio