924 research outputs found
Hierarchy of the Selberg zeta functions
We introduce a Selberg type zeta function of two variables which interpolates
several higher Selberg zeta functions. The analytic continuation, the
functional equation and the determinant expression of this function via the
Laplacian on a Riemann surface are obtained.Comment: 14 page
String-inspired cosmology
I discuss cosmological models either derived from, or inspired by, string
theory or M-theory. In particular I discuss solutions in the low-energy
effective theory and the role of the dilaton, moduli and antisymmetric form
fields in the dimensionally reduced effective action. The pre big bang model is
an attempt to use cosmological solutions to make observational predictions. I
then discuss the effective theory of gravity found in recent brane-world models
where we live on a 3-brane embedded in a five-dimensional spacetime and how the
study of cosmological perturbations may enable us to test these ideas.Comment: 15 pages, 5 figures, latex with iopart, invited talk at `The Early
Universe and Cosmological Observations: a Critical Review', Cape Town, July
200
From simplicial Chern-Simons theory to the shadow invariant II
This is the second of a series of papers in which we introduce and study a
rigorous "simplicial" realization of the non-Abelian Chern-Simons path integral
for manifolds M of the form M = Sigma x S1 and arbitrary simply-connected
compact structure groups G. More precisely, we introduce, for general links L
in M, a rigorous simplicial version WLO_{rig}(L) of the corresponding Wilson
loop observable WLO(L) in the so-called "torus gauge" by Blau and Thompson
(Nucl. Phys. B408(2):345-390, 1993). For a simple class of links L we then
evaluate WLO_{rig}(L) explicitly in a non-perturbative way, finding agreement
with Turaev's shadow invariant |L|.Comment: 53 pages, 1 figure. Some minor changes and corrections have been mad
Integrals Over Polytopes, Multiple Zeta Values and Polylogarithms, and Euler's Constant
Let be the triangle with vertices (1,0), (0,1), (1,1). We study certain
integrals over , one of which was computed by Euler. We give expressions for
them both as a linear combination of multiple zeta values, and as a polynomial
in single zeta values. We obtain asymptotic expansions of the integrals, and of
sums of certain multiple zeta values with constant weight. We also give related
expressions for Euler's constant. In the final section, we evaluate more
general integrals -- one is a Chen (Drinfeld-Kontsevich) iterated integral --
over some polytopes that are higher-dimensional analogs of . This leads to a
relation between certain multiple polylogarithm values and multiple zeta
values.Comment: 19 pages, to appear in Mat Zametki. Ver 2.: Added Remark 3 on a Chen
(Drinfeld-Kontsevich) iterated integral; simplified Proposition 2; gave
reference for (19); corrected [16]; fixed typ
A Solution to the Graceful Exit Problem in Pre-Big Bang Cosmology
We examine the string cosmology equations with a dilaton potential in the
context of the Pre-Big Bang Scenario with the desired scale factor duality, and
give a generic algorithm for obtaining solutions with appropriate evolutionary
properties. This enables us to find pre-big bang type solutions with suitable
dilaton behaviour that are regular at , thereby solving the graceful exit
problem. However to avoid fine tuning of initial data, an `exotic' equation of
state is needed that relates the fluid properties to the dilaton field. We
discuss why such an equation of state should be required for reliable dilaton
behaviour at late times.Comment: 16 pages LaTeX, 5 figures. To appear in Physical Review
Early observations of the nearby type Ia supernova SN 2015F
We present photometry and time-series spectroscopy of the nearby type Ia supernova (SN Ia) SN 2015F over days to days relative to maximum light, obtained as part of the Public ESO Spectroscopic Survey of Transient Objects (PESSTO). SN 2015F is a slightly sub-luminous SN Ia with a decline rate of mag, placing it in the region between normal and SN 1991bg-like events. Our densely-sampled photometric data place tight constraints on the epoch of first light and form of the early-time light curve. The spectra exhibit photospheric C II absorption until days, and high-velocity Ca II is particularly strong at km s, suggesting mixing in the outermost layers of the SN ejecta. Although unusual in SN Ia spectra, including V II in the modelling significantly improves the spectral fits. Intriguingly, we detect an absorption feature at 6800 \AA\ that persists until maximum light. Our favoured explanation for this line is photospheric Al II, which has never been claimed before in SNe Ia, although detached high-velocity C II material could also be responsible. In both cases the absorbing material seems to be confined to a relatively narrow region in velocity space. The nucleosynthesis of detectable amounts of Al II would argue against a low-metallicity white dwarf progenitor. We also show that this 6800 \AA\ feature is weakly present in other normal SN Ia events, and common in the SN 1991bg-like sub-class
Adiabatic perturbations in pre big bang models: matching conditions and scale invariance
At low energy, the four-dimensional effective action of the ekpyrotic model
of the universe is equivalent to a slightly modified version of the pre big
bang model. We discuss cosmological perturbations in these models. In
particular we address the issue of matching the perturbations from a collapsing
to an expanding phase in full generality. We show that, generically, one
obtains for the spectrum of scalar perturbations in the original pre big
model (with vanishing potential). When an exponential potential for the dilaton
is included, a scale invariant spectrum () of adiabatic scalar
perturbations is produced under very generic matching conditions, both in a
modified pre big bang and ekpyrotic scenario. We also derive general results
valid for power law scale factors matched to a radiation dominated era.Comment: 11 pages, 1 figure, revised version with small corrections to match
version in print. Results and conclusions unchange
Square lattice Ising model susceptibility: Series expansion method and differential equation for
In a previous paper (J. Phys. A {\bf 37} (2004) 9651-9668) we have given the
Fuchsian linear differential equation satisfied by , the
``three-particle'' contribution to the susceptibility of the isotropic square
lattice Ising model. This paper gives the details of the calculations (with
some useful tricks and tools) allowing one to obtain long series in polynomial
time. The method is based on series expansion in the variables that appear in
the -dimensional integrals representing the -particle contribution to
the isotropic square lattice Ising model susceptibility . The
integration rules are straightforward due to remarkable formulas we derived for
these variables. We obtain without any numerical approximation as
a fully integrated series in the variable , where , with the conventional Ising model coupling constant. We also
give some perspectives and comments on these results.Comment: 28 pages, no figur
Construction of nonsingular cosmological solutions in string theories
We study nonsingular cosmological scenarios in a general -dimensional
string effective action of the dilaton-modulus-axion system in the presence of
the matter source. In the standard dilatonic Brans-Dicke parameter
() with radiation, we analytically obtain singularity-free bouncing
solutions where the universe starts out in a state with a finite curvature and
evolves toward the weakly coupled regime. We apply this analytic method to the
string-gas cosmology including the massive state in addition to the leading
massless state (radiation), with and without the axion. We numerically find
bouncing solutions which asymptotically approach an almost radiation-dominant
universe with a decreasing curvature irrespective of the presence of the axion,
implying that inclusion of the matter source is crucial for the existence of
such solutions for . In the theories with , it is
possible to obtain complete regular bouncing solutions with a finite dilaton
and curvature in both past and future asymptotics for the general dimension,
. We also discuss the case where dilatonic higher-order corrections are
involved to the tree-level effective action and demonstrate that the presence
of axion/modulus fields and the matter source does not significantly affect the
dynamics of the dilaton-driven inflation and the subsequent graceful exit.Comment: 27 pages, 6 eps figure
Using late-time optical and near-infrared spectra to constrain Type Ia supernova explosion properties
The late-time spectra of Type Ia supernovae (SNe Ia) are powerful probes of
the underlying physics of their explosions. We investigate the late-time
optical and near-infrared spectra of seven SNe Ia obtained at the VLT with
XShooter at 200 d after explosion. At these epochs, the inner Fe-rich ejecta
can be studied. We use a line-fitting analysis to determine the relative line
fluxes, velocity shifts, and line widths of prominent features contributing to
the spectra ([Fe II], [Ni II], and [Co III]). By focussing on [Fe II] and [Ni
II] emission lines in the ~7000-7500 \AA\ region of the spectrum, we find that
the ratio of stable [Ni II] to mainly radioactively-produced [Fe II] for most
SNe Ia in the sample is consistent with Chandrasekhar-mass delayed-detonation
explosion models, as well as sub-Chandrasekhar mass explosions that have
metallicity values above solar. The mean measured Ni/Fe abundance of our sample
is consistent with the solar value. The more highly ionised [Co III] emission
lines are found to be more centrally located in the ejecta and have broader
lines than the [Fe II] and [Ni II] features. Our analysis also strengthens
previous results that SNe Ia with higher Si II velocities at maximum light
preferentially display blueshifted [Fe II] 7155 \AA\ lines at late times. Our
combined results lead us to speculate that the majority of normal SN Ia
explosions produce ejecta distributions that deviate significantly from
spherical symmetry.Comment: 17 pages, 12 figure, accepted for publication in MNRA
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