ASYMPTOTIC BEHAVIOR OF COMPLEX SCALAR FIELDS IN A FRIEDMAN-LEMAITRE UNIVERSE

We study the coupled Einstein-Klein-Gordon equations for a complex scalar field with and without a quartic self-interaction in a curvatureless Friedman-Lema\^{\i}\-tre Universe. The equations can be written as a set of four coupled first order non-linear differential equations, for which we establish the phase portrait for the time evolution of the scalar field. To that purpose we find the singular points of the differential equations lying in the finite region and at infinity of the phase space and study the corresponding asymptotic behavior of the solutions. This knowledge is of relevance, since it provides the initial conditions which are needed to solve numerically the differential equations. For some singular points lying at infinity we recover the expected emergence of an inflationary stage.Comment: uuencoded, compressed tarfile containing a 15 pages Latex file and 2 postscipt figures. Accepted for publication on Phys. Rev.

On Gravitational Waves in Spacetimes with a Nonvanishing Cosmological Constant

We study the effect of a cosmological constant $\Lambda$ on the propagation and detection of gravitational waves. To this purpose we investigate the linearised Einstein's equations with terms up to linear order in $\Lambda$ in a de Sitter and an anti-de Sitter background spacetime. In this framework the cosmological term does not induce changes in the polarization states of the waves, whereas the amplitude gets modified with terms depending on $\Lambda$. Moreover, if a source emits a periodic waveform, its periodicity as measured by a distant observer gets modified. These effects are, however, extremely tiny and thus well below the detectability by some twenty orders of magnitude within present gravitational wave detectors such as LIGO or future planned ones such as LISA.Comment: 8 pages, 4 figures, accepted for publication in Physical Review

Numerical evidence for `multi-scalar stars'

We present a class of general relativistic soliton-like solutions composed of multiple minimally coupled, massive, real scalar fields which interact only through the gravitational field. We describe a two-parameter family of solutions we call ``phase-shifted boson stars'' (parameterized by central density rho_0 and phase delta), which are obtained by solving the ordinary differential equations associated with boson stars and then altering the phase between the real and imaginary parts of the field. These solutions are similar to boson stars as well as the oscillating soliton stars found by Seidel and Suen [E. Seidel and W.M. Suen, Phys. Rev. Lett. 66, 1659 (1991)]; in particular, long-time numerical evolutions suggest that phase-shifted boson stars are stable. Our results indicate that scalar soliton-like solutions are perhaps more generic than has been previously thought.Comment: Revtex. 4 pages with 4 figures. Submitted to Phys. Rev.

What measurable zero point fluctuations can(not) tell us about dark energy

We show that laboratory experiments cannot measure the absolute value of dark energy. All known experiments rely on electromagnetic interactions. They are thus insensitive to particles and fields that interact only weakly with ordinary matter. In addition, Josephson junction experiments only measure differences in vacuum energy similar to Casimir force measurements. Gravity, however, couples to the absolute value. Finally we note that Casimir force measurements have tested zero point fluctuations up to energies of ~10 eV, well above the dark energy scale of ~0.01 eV. Hence, the proposed cut-off in the fluctuation spectrum is ruled out experimentally.Comment: 4 page

Are the singularities stable?

The spacetime singularities play a useful role in gravitational theories by distinguishing physical solutions from non-physical ones. The problem, we studying in this paper is: are these singularities stable? To answer this question, we have analyzed the general problem of stability of the family of the static spherically symmetric solutions of the standard Einstein-Maxwell model coupled to an extra free massless scalar field. We have obtained the equations for the axial and polar perturbations. The stability against axial perturbations has been proven.Comment: 13 pages, LaTeX, no figure

Spontaneous Scalarization and Boson Stars

We study spontaneous scalarization in Scalar-Tensor boson stars. We find that scalarization does not occur in stars whose bosons have no self-interaction. We introduce a quartic self-interaction term into the boson Lagrangian and show that when this term is large, scalarization does occur. Strong self-interaction leads to a large value of the compactness (or sensitivity) of the boson star, a necessary condition for scalarization to occur, and we derive an analytical expression for computing the sensitivity of a boson star in Brans-Dicke theory from its mass and particle number. Next we comment on how one can use the sensitivity of a star in any Scalar-Tensor theory to determine how its mass changes when it undergoes gravitational evolution. Finally, in the Appendix, we derive the most general form of the boson wavefunction that minimises the energy of the star when the bosons carry a U(1) charge.Comment: 23 pages, 5 postscript figures. Typing errors corrected. Includes some new text that relates the paper to several previous results. Accepted for publication in PR

Galactic Halos As Boson Stars

We investigate the boson star with the self-interacting scalar field as a model of galactic halos. The model has slightly increasing rotation curves and allows wider ranges of the mass($m$) and coupling($\lambda$) of the halo dark matter particle than the non-interacting model previously suggested(ref.\cite{sin1}). Two quantities are related by \lambda^{\frac{1}{2}} (m_p/m)^2\st{>}{\sim} 10^{50}.Comment: 15 pages. Standard Latex file with 2 tex figures. Revised version to be published in Phy. Rev. D. (Stability arguments are added.

Charged Scalar-Tensor Boson Stars: Equilibrium, Stability and Evolution

We study charged boson stars in scalar-tensor (ST) gravitational theories. We analyse the weak field limit of the solutions and analytically show that there is a maximum charge to mass ratio for the bosons above which the weak field solutions are not stable. This charge limit can be greater than the GR limit for a wide class of ST theories. We numerically investigate strong field solutions in both the Brans Dicke and power law ST theories. We find that the charge limit decreases with increasing central boson density. We discuss the gravitational evolution of charged and uncharged boson stars in a cosmological setting and show how, at any point in its evolution, the physical properties of the star may be calculated by a rescaling of a solution whose asymptotic value of the scalar field is equal to its initial asymptotic value. We focus on evolution in which the particle number of the star is conserved and we find that the energy and central density of the star decreases as the cosmological time increases. We also analyse the appearance of the scalarization phenomenon recently discovered for neutron stars configurations and, finally, we give a short discussion on how making the correct choice of mass influences the argument over which conformal frame, the Einstein frame or the Jordan frame, is physical.Comment: RevTeX, 27 pages, 9 postscript figures. Minor revisions and updated references. Accepted for publication in Phys. Rev.

Rotating Boson Star with Large Self-interaction in (2+1) dimensions

Solutions for rotating boson stars in (2+1) dimensional gravity with a negative cosmological constant are obtained numerically. The mass, particle number, and radius of the (2+1) dimensional rotating boson star are shown. Consequently we find the region where the stable boson star can exist.Comment: 14 pages, 6 figures, RevTe

Dynamical Evolution of Boson Stars II: Excited States and Self-Interacting Fields

The dynamical evolution of self-gravitating scalar field configurations in numerical relativity is studied. The previous analysis on ground state boson stars of non-interacting fields is extended to excited states and to fields with self couplings. Self couplings can significantly change the physical dimensions of boson stars, making them much more astrophysically interesting (e.g., having mass of order 0.1 solar mass). The stable ($S$) and unstable ($U$) branches of equilibrium configurations of boson stars of self-interacting fields are studied; their behavior under perturbations and their quasi-normal oscillation frequencies are determined and compared to the non-interacting case. Excited states of boson stars with and without self-couplings are studied and compared. Excited states also have equilibrium configurations with $S$ and $U$ branch structures; both branches are intrinsically unstable under a generic perturbation but have very different instability time scales. We carried out a detailed study of the instability time scales of these configurations. It is found that highly excited states spontaneously decay through a cascade of intermediate states similar to atomic transitions.Comment: 16 pages+ 13 figures . All figures are available at http://wugrav.wustl.edu/Paper