11,514 research outputs found
Exact String Solutions in 2+1-Dimensional De Sitter Spacetime
Exact and explicit string solutions in de Sitter spacetime are found. (Here,
the string equations reduce to a sinh-Gordon model). A new feature without flat
spacetime analogy appears: starting with a single world-sheet, several (here
two) strings emerge. One string is stable and the other (unstable) grows as the
universe grows. Their invariant size and energy either grow as the expansion
factor or tend to constant. Moreover, strings can expand (contract) for large
(small) universe radius with a different rate than the universe.Comment: 11 pages, Phyzzx macropackage used, PAR-LPTHE 92/32. Revised version
with a new understanding of the previous result
Infinitely Many Strings in De Sitter Spacetime: Expanding and Oscillating Elliptic Function Solutions
The exact general evolution of circular strings in dimensional de
Sitter spacetime is described closely and completely in terms of elliptic
functions. The evolution depends on a constant parameter , related to the
string energy, and falls into three classes depending on whether
(oscillatory motion), (degenerated, hyperbolic motion) or
(unbounded motion). The novel feature here is that one single world-sheet
generically describes {\it infinitely many} (different and independent)
strings. The world-sheet time is an infinite-valued function of the
string physical time, each branch yields a different string. This has no
analogue in flat spacetime. We compute the string energy as a function of
the string proper size , and analyze it for the expanding and oscillating
strings. For expanding strings : even at ,
decreases for small and increases for large .
For an oscillating string , the average energy
over one oscillation period is expressed as a function of as a
complete elliptic integral of the third kind.Comment: 32 pages, Latex file, figures available from the authors under
request. LPTHE-PAR 93-5
Semi-Classical Quantization of Circular Strings in De Sitter and Anti De Sitter Spacetimes
We compute the {\it exact} equation of state of circular strings in the (2+1)
dimensional de Sitter (dS) and anti de Sitter (AdS) spacetimes, and analyze its
properties for the different (oscillating, contracting and expanding) strings.
The string equation of state has the perfect fluid form with
the pressure and energy expressed closely and completely in terms of elliptic
functions, the instantaneous coefficient depending on the elliptic
modulus. We semi-classically quantize the oscillating circular strings. The
string mass is being the Casimir operator,
of the -dS [-AdS] group, and is
the Hubble constant. We find \alpha'm^2_{\mbox{dS}}\approx 5.9n,\;(n\in N_0),
and a {\it finite} number of states N_{\mbox{dS}}\approx 0.17/(H^2\alpha') in
de Sitter spacetime; m^2_{\mbox{AdS}}\approx 4H^2n^2 (large ) and
N_{\mbox{AdS}}=\infty in anti de Sitter spacetime. The level spacing grows
with in AdS spacetime, while is approximately constant (although larger
than in Minkowski spacetime) in dS spacetime. The massive states in dS
spacetime decay through tunnel effect and the semi-classical decay probability
is computed. The semi-classical quantization of {\it exact} (circular) strings
and the canonical quantization of generic string perturbations around the
string center of mass strongly agree.Comment: Latex, 26 pages + 2 tables and 5 figures that can be obtained from
the authors on request. DEMIRM-Obs de Paris-9404
The Statistical Mechanics of the Self-Gravitating Gas: Equation of State and Fractal Dimension
We provide a complete picture of the self-gravitating non-relativistic gas at
thermal equilibrium using Monte Carlo simulations (MC), analytic mean field
methods (MF) and low density expansions. The system is shown to possess an
infinite volume limit, both in the canonical (CE) and in the microcanonical
ensemble (MCE) when N, V \to \infty, keeping N/ V^{1/3} fixed. We {\bf compute}
the equation of state (we do not assume it as is customary), the entropy, the
free energy, the chemical potential, the specific heats, the compressibilities,
the speed of sound and analyze their properties, signs and singularities. The
MF equation of state obeys a {\bf first order} non-linear differential equation
of Abel type. The MF gives an accurate picture in agreement with the MC
simulations both in the CE and MCE. The inhomogeneous particle distribution in
the ground state suggest a fractal distribution with Haussdorf dimension D with
D slowly decreasing with increasing density, 1 \lesssim D < 3.Comment: LaTex, 7 pages, 2 .ps figures, minor improvements, to appear in
Physics Letters
Mass Spectrum of Strings in Anti de Sitter Spacetime
We perform string quantization in anti de Sitter (AdS) spacetime. The string
motion is stable, oscillatory in time with real frequencies and the string size and energy are bounded. The
string fluctuations around the center of mass are well behaved. We find the
mass formula which is also well behaved in all regimes. There is an {\it
infinite} number of states with arbitrarily high mass in AdS (in de Sitter (dS)
there is a {\it finite} number of states only). The critical dimension at which
the graviton appears is as in de Sitter space. A cosmological constant
(whatever its sign) introduces a {\it fine structure} effect
(splitting of levels) in the mass spectrum at all states beyond the graviton.
The high mass spectrum changes drastically with respect to flat Minkowski
spacetime. For {\it
independent} of and the level spacing {\it grows} with the
eigenvalue of the number operator, The density of states grows
like \mbox{Exp}[(m/\sqrt{\mid\Lambda\mid}\;)^{1/2}] (instead of
\rho(m)\sim\mbox{Exp}[m\sqrt{\alpha'}] as in Minkowski space), thus {\it
discarding} the existence of a critical string temperature.
For the sake of completeness, we also study the quantum strings in the black
string background, where strings behave, in many respects, as in the ordinary
black hole backgrounds. The mass spectrum is equal to the mass spectrum in flat
Minkowski space.Comment: 31 pages, Latex, DEMIRM-Paris-9404
Galaxy phase-space density data exclude Bose-Einstein condensate Axion Dark Matter
Light scalars (as the axion) with mass m ~ 10^{-22} eV forming a
Bose-Einstein condensate (BEC) exhibit a Jeans length in the kpc scale and were
therefore proposed as dark matter (DM) candidates. Our treatment here is
generic, independent of the particle physics model and applies to all DM BEC,
in or out of equilibrium. Two observed quantities crucially constrain DM in an
inescapable way: the average DM density rho_{DM} and the phase-space density Q.
The observed values of rho_{DM} and Q in galaxies today constrain both the
possibility to form a BEC and the DM mass m. These two constraints robustly
exclude axion DM that decouples just after the QCD phase transition. Moreover,
the value m ~ 10^{-22} eV can only be obtained with a number of
ultrarelativistic degrees of freedom at decoupling in the trillions which is
impossible for decoupling in the radiation dominated era. In addition, we find
for the axion vacuum misalignment scenario that axions are produced strongly
out of thermal equilibrium and that the axion mass in such scenario turns to be
17 orders of magnitude too large to reproduce the observed galactic structures.
Moreover, we also consider inhomogenous gravitationally bounded BEC's supported
by the bosonic quantum pressure independently of any particular particle
physics scenario. For a typical size R ~ kpc and compact object masses M ~ 10^7
Msun they remarkably lead to the same particle mass m ~ 10^{-22} eV as the BEC
free-streaming length. However, the phase-space density for the gravitationally
bounded BEC's turns to be more than sixty orders of magnitude smaller than the
galaxy observed values. We conclude that the BEC's and the axion cannot be the
DM particle. However, an axion in the mili-eV scale may be a relevant source of
dark energy through the zero point cosmological quantum fluctuations.Comment: 8 pages, no figures. Expanded versio
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