23,191 research outputs found
Quantum fields near phantom-energy `sudden' singularities
This paper is committed to calculations near a type of future singularity
driven by phantom energy. At the singularities considered, the scale factor
remains finite but its derivative diverges. The general behavior of barotropic
phantom energy producing this singularity is calculated under the assumption
that near the singularity such fluid is the dominant contributor. We use the
semiclassical formula for renormalized stress tensors of conformally invariant
fields in conformally flat spacetimes and analyze the softening/enhancing of
the singularity due to quantum vacuum contributions. This dynamical analysis is
then compared to results from thermodynamical considerations. In both cases,
the vacuum states of quantized scalar and spinor fields strengthen the
accelerating expansion near the singularity whereas the vacuum states of vector
fields weaken it.Comment: 6 pages RevTe
Superpotentials from variational derivatives rather than Lagrangians in relativistic theories of gravity
The prescription of Silva to derive superpotential equations from variational
derivatives rather than from Lagrangian densities is applied to theories of
gravity derived from Lovelock Lagrangians in the Palatini representation.
Spacetimes are without torsion and isolated sources of gravity are minimally
coupled. On a closed boundary of spacetime, the metric is given and the
connection coefficients are those of Christoffel. We derive equations for the
superpotentials in these conditions. The equations are easily integrated and we
give the general expression for all superpotentials associated with Lovelock
Lagrangians. We find, in particular, that in Einstein's theory, in any number
of dimensions, the superpotential, valid at spatial and at null infinity, is
that of Katz, Bicak and Lynden-Bell, the KBL superpotential. We also give
explicitly the superpotential for Gauss-Bonnet theories of gravity. Finally, we
find a simple expression for the superpotential of Einstein-Gauss-Bonnet
theories with an anti-de Sitter background: it is minus the KBL superpotential,
confirming, as it should, the calculation of the total mass-energy of spacetime
at spatial infinity by Deser and Tekin.Comment: Scheduled to appear in Class. Quantum Grav. August 200
A-infinity algebra of an elliptic curve and Eisenstein series
We compute explicitly the A-infinity structure on the Ext-algebra of the
collection , where is a line bundle of degree 1 on an
elliptic curve . The answer involves higher derivatives of Eisenstein
series.Comment: 13 pages, 3 figures; v3: added remark on the limit at the cus
On the Evolutionary History of Stars and their Fossil Mass and Light
The total extragalactic background radiation can be an important test of the
global star formation history (SFH). Using direct observational estimates of
the SFH, along with standard assumptions about the initial mass function (IMF),
we calculate the total extragalactic background radiation and the observed
stellar density today. We show that plausible SFHs allow a significant range in
each quantity, but that their ratio is very tightly constrained. Current
estimates of the stellar mass and extragalactic background are difficult to
reconcile, as long as the IMF is fixed to the Salpeter slope above 1 Msun. The
joint confidence interval of these two quantities only agrees with that
determined from the allowed range of SFH fits at the 3-sigma level, and for our
best-fit values the discrepancy is about a factor of two. Alternative energy
sources that contribute to the background, such as active galactic nuclei
(AGN), Population III stars, or decaying particles, appear unlikely to resolve
the discrepancy. However, changes to the IMF allow plausible solutions to the
background problem. The simplest is an average IMF with an increased
contribution from stars around 1.5--4 Msun. A ``paunchy'' IMF of this sort
could emerge as a global average if low mass star formation is suppressed in
galaxies experiencing rapid starbursts. Such an IMF is consistent with
observations of star-forming regions, and would help to reconcile the fossil
record of star formation with the directly observed SFH.Comment: 21 pages, 7 figures, 3 tables; submitted to Monthly Notice
Quantum Wall Crossing in N=2 Gauge Theories
We study refined and motivic wall-crossing formulas in N=2 supersymmetric
gauge theories with SU(2) gauge group and N_f < 4 matter hypermultiplets in the
fundamental representation. Such gauge theories provide an excellent testing
ground for the conjecture that "refined = motivic."Comment: 24 pages, 4 figure
Hadron Masses and Screening from AdS Wilson Loops
We show that in strongly coupled N=4 SYM the binding energy of a heavy and a
light quark is independent of the strength of the coupling constant. As a
consequence we are able to show that in the presence of light quarks the analog
of the QCD string can snap and color charges are screened. The resulting
neutral mesons interact with each other only via pion exchange and we estimate
the massesComment: 4 pages, revte
Black holes, cuspy atmospheres, and galaxy formation
In cuspy atmospheres, jets driven by supermassive black holes (BHs) offset
radiative cooling. The jets fire episodically, but often enough that the cuspy
atmosphere does not move very far towards a cooling catastrophe in the
intervals of jet inactivity. The ability of energy released on the sub-parsec
scale of the BH to balance cooling on scales of several tens of kiloparsecs
arises through a combination of the temperature sensitivity of the accretion
rate and the way in which the radius of jet disruption varies with ambient
density. Accretion of hot gas does not significantly increase BH masses, which
are determined by periods of rapid BH growth and star formation when cold gas
is briefly abundant at the galactic centre. Hot gas does not accumulate in
shallow potential wells. As the Universe ages, deeper wells form, and
eventually hot gas accumulates. This gas soon prevents the formation of further
stars, since jets powered by the BH prevent it from cooling, and it mops up
most cold infalling gas before many stars can form. Thus BHs set the upper
limit to the masses of galaxies. The formation of low-mass galaxies is
inhibited by a combination of photo-heating and supernova-driven galactic
winds. Working in tandem these mechanisms can probably explain the profound
difference between the galaxy luminosity function and the mass function of dark
halos expected in the cold dark matter cosmology.Comment: To appear in Phil Trans Roy So
Shifted convolution and the Titchmarsh divisor problem over F_q[t]
In this paper we solve a function field analogue of classical problems in
analytic number theory, concerning the auto-correlations of divisor functions,
in the limit of a large finite field.Comment: 22 pages, updated versio
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