Inflationary spectra and partially decohered distributions

It is generally expected that decoherence processes will erase the quantum properties of the inflationary primordial spectra. However, given the weakness of gravitational interactions, one might end up with a distribution which is only partially decohered. Below a certain critical change, we show that the inflationary distribution retains quantum properties. We identify four of these: a squeezed spread in some direction of phase space, non-vanishing off-diagonal matrix elements, and two properties used in quantum optics called non-$P$-representability and non-separability. The last two are necessary conditions to violate Bell's inequalities. The critical value above which all these properties are lost is associated to the `grain' of coherent states. The corresponding value of the entropy is equal to half the maximal (thermal) value. Moreover it coincides with the entropy of the effective distribution obtained by neglecting the decaying modes. By considering backreaction effects, we also provide an upper bound for this entropy at the onset of the adiabatic era.Comment: 42 pages, 9 figures; 1 ref. adde

Probing the Equation of State of Nuclear Matter via Neutron Star Asteroseismology

We general relativistically calculate the frequency of fundamental torsional oscillations of neutron star crusts, where we focus on the crystalline properties obtained from macroscopic nuclear models in a way depending on the equation of state of nuclear matter. We find that the calculated frequency is sensitive to the density dependence of the symmetry energy, but almost independent of the incompressibility of symmetric nuclear matter. By identifying the lowest-frequency quasi-periodic oscillation in giant flares observed from soft gamma-ray repeaters as the fundamental torsional mode and allowing for the dependence of the calculated frequency on stellar models, we provide a lower limit of the density derivative of the symmetry energy as $L\simeq 50$ MeV.Comment: 4 pages, 4 figure

Oscillations of rapidly rotating relativistic stars

Non-axisymmetric oscillations of rapidly rotating relativistic stars are studied using the Cowling approximation. The oscillation spectra have been estimated by Fourier transforming the evolution equations describing the perturbations. This is the first study of its kind and provides information on the effect of fast rotation on the oscillation spectra while it offers the possibility in studying the complete problem by including spacetime perturbations. Our study includes both axisymmetric and non-axisymmetric perturbations and provides limits for the onset of the secular bar mode rotational instability. We also present approximate formulae for the dependence of the oscillation spectrum from rotation. The results suggest that it is possible to extract the relativistic star's parameters from the observed gravitational wave spectrum.Comment: this article will be published in Physical Review

Maximum elastic deformations of relativistic stars

We present a method for calculating the maximum elastic quadrupolar deformations of relativistic stars, generalizing the previous Newtonian, Cowling approximation integral given by [G. Ushomirsky et al., Mon. Not. R. Astron. Soc. 319, 902 (2000)]. (We also present a method for Newtonian gravity with no Cowling approximation.) We apply these methods to the m = 2 quadrupoles most relevant for gravitational radiation in three cases: crustal deformations, deformations of crystalline cores of hadron-quark hybrid stars, and deformations of entirely crystalline color superconducting quark stars. In all cases, we find suppressions of the quadrupole due to relativity compared to the Newtonian Cowling approximation, particularly for compact stars. For the crust these suppressions are up to a factor ~6, for hybrid stars they are up to ~4, and for solid quark stars they are at most ~2, with slight enhancements instead for low mass stars. We also explore ranges of masses and equations of state more than in previous work, and find that for some parameters the maximum quadrupoles can still be very large. Even with the relativistic suppressions, we find that 1.4 solar mass stars can sustain crustal quadrupoles of a few times 10^39 g cm^2 for the SLy equation of state or close to 10^40 g cm^2 for equations of state that produce less compact stars. Solid quark stars of 1.4 solar masses can sustain quadrupoles of around 10^44 g cm^2. Hybrid stars typically do not have solid cores at 1.4 solar masses, but the most massive ones (~2 solar masses) can sustain quadrupoles of a few times 10^41 g cm^2 for typical microphysical parameters and a few times 10^42 g cm^2 for extreme ones. All of these quadrupoles assume a breaking strain of 0.1 and can be divided by 10^45 g cm^2 to yield the fiducial "ellipticities" quoted elsewhere.Comment: 21 pages, 11 figures, version accepted by PRD, including the corrected maximum hybrid star quadrupoles (from the erratum to the shear modulus calculation) and the corrected binding energy computatio

Crustal Oscillations of Slowly Rotating Relativistic Stars

We study low-amplitude crustal oscillations of slowly rotating relativistic stars consisting of a central fluid core and an outer thin solid crust. We estimate the effect of rotation on the torsional toroidal modes and on the interfacial and shear spheroidal modes. The results compared against the Newtonian ones for wide range of neutron star models and equations of state.Comment: 15 page

Cosmological Perturbations of Quantum-Mechanical Origin and Anisotropy of the Microwave Background

Cosmological perturbations generated quantum-mechanically (as a particular case, during inflation) possess statistical properties of squeezed quantum states. The power spectra of the perturbations are modulated and the angular distribution of the produced temperature fluctuations of the CMBR is quite specific. An exact formula is derived for the angular correlation function of the temperature fluctuations caused by squeezed gravitational waves. The predicted angular pattern can, in principle, be revealed by the COBE-type observations.Comment: 9 pages, WUGRAV-92-17 Accepted for Publication in Phys. Rev. Letters (1993

ASTROD, ASTROD I and their gravitational-wave sensitivities

ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) is a mission concept with three spacecraft -- one near L1/L2 point, one with an inner solar orbit and one with an outer solar orbit, ranging coherently with one another using lasers to test relativistic gravity, to measure the solar system and to detect gravitational waves. ASTROD I with one spacecraft ranging optically with ground stations is the first step toward the ASTROD mission. In this paper, we present the ASTROD I payload and accelerometer requirements, discuss the gravitational-wave sensitivities for ASTROD and ASTROD I, and compare them with LISA and radio-wave PDoppler-tracking of spacecraft.Comment: presented to the 5th Edoardo Amaldi Conference (July 6-11, 2003) and submitted to Classical and Quantum Gravit