8,764 research outputs found
FRCAMB: An Code for Anisotropies in the Microwave Background
An gravity model is proposed to realize a late time accelerated
expansion of our Universe. To test the viability of an gravity model
through cosmic observations, the background evolution and the
Einstein-Boltzmann equation should be solved for studying the effects on the
cosmic microwave background power spectrum and on the matter power spectrum. In
the market, we already have the modified versions of {\bf CAMB} code, for
instance {\bf EFTCAMB} and {\bf MGCAMB}. However, in these publicly available
Einstein-Boltzmann codes, a specific background cosmology, for example the
CDM or CDM, is assumed. This assumption would be non-proper for a
specific model where the background evolution may be different from a
CDM cosmology. Therefore the main task for this paper is to present a
code to calculate the anisotropies in the microwave background for any
gravity model based on {\bf CAMB} code, i.e. {\bf FRCAMB}, where the background
and perturbation evolutions are included consistently. As results, one can
treat {\bf FRCAMB} as a blackbox to output the CMB power spectrum and matter
power spectrum, once an function, its first two derivative with respect
to , i.e. , and the reasonable
values of the model parameters are inputted properly. As by-products, one can
also output the effective equation of state of model, the evolution of
the dimensionless energy densities and other interesting cosmological
quantities.Comment: 8 pages, 7 figure
Deep Epitome for Unravelling Generalized Hamming Network: A Fuzzy Logic Interpretation of Deep Learning
This paper gives a rigorous analysis of trained Generalized Hamming
Networks(GHN) proposed by Fan (2017) and discloses an interesting finding about
GHNs, i.e., stacked convolution layers in a GHN is equivalent to a single yet
wide convolution layer. The revealed equivalence, on the theoretical side, can
be regarded as a constructive manifestation of the universal approximation
theorem Cybenko(1989); Hornik (1991). In practice, it has profound and
multi-fold implications. For network visualization, the constructed deep
epitomes at each layer provide a visualization of network internal
representation that does not rely on the input data. Moreover, deep epitomes
allows the direct extraction of features in just one step, without resorting to
regularized optimizations used in existing visualization tools.Comment: 25 pages, 14 figure
A New Unified Dark Fluid Model and Its Cosmic Constraint
In this paper, we propose a new unified dark fluid (UDF) model with equation
of state (EoS) , which includes the generalized
Chaplygin gas model (gGg) as its special case, where , and
are three positive numbers. It is clear that this model reduces to the gCg
model with EoS , when ,
and . By combination the cold dark matter
and the cosmological constant, one can coin a EoS of unified dark fluid in the
form of . With this
observations, our proposed EoS provides a possible deviation from CDM
model when the model parameters and deviate from 1 and 3
respectively. By using the currently available cosmic observations from type Ia
supernovae (SN Ia) Union2.1, baryon acoustic oscillation (BAO) and cosmic
microwave background radiation (CMB), we test the viability of this model and
detect the possible devotion from the CDM model. The results show that
the new UDF model fits the cosmic observation as well as that of the
CDM model and no deviation is found from the CDM model in
confidence level. However, our new UDF model can give a non-zero
sound speed, as a contrast, which is zero for the CDM model. We expect
the large structure formation information can distinct the new UDF model from
the CDM model.Comment: 7 pages, 3 figures. arXiv admin note: substantial text overlap with
arXiv:1204.5571, arXiv:1204.479
CVA and FVA to Derivatives Trades Collateralized by Cash
In this article, we combine replication pricing with expectation pricing for
derivative trades that are partially collateralized by cash. The derivatives
are replicated by underlying assets and cash, using repurchasing agreement
(repo) and margining, which incur funding costs. We derive a partial
differential equation (PDE) for the derivatives price, obtain and decompose its
solution into the risk-free value of the derivative plus credit valuation
adjustment (CVA) and funding valuation adjustment (FVA). For most derivatives,
as we shall show, CVAs can be evaluated analytically or semi-analytically,
while FVAs, as well as the derivatives values, will have to be solved
recursively through numerical procedures due to their interdependence. In
numerical demonstrations, continuous and discrete margin revisions are
considered, respectively, for an equity call option and a vanilla interest-rate
swaps.Comment: 29 pages, 4 figure
Constraints on the Holographic Dark Energy Model from Type Ia Supernovae, WMAP7, Baryon Acoustic Oscillation and Redshift-Space Distortion
In this paper, we use the joint measurement of geometry and growth rate from
matter density perturbations to constrain the holographic dark energy model.
The geometry measurement includes type Ia supernovae (SN Ia) Union2.1, full
information of cosmic microwave background (CMB) from WMAP-7yr and baryon
acoustic oscillation (BAO). For the growth rate of matter density
perturbations, the results measured from the redshift-space
distortion (RSD) in the galaxy power spectrum are employed. Via the Markov
Chain Monte Carlo method, we try to constrain the model parameters space. The
jointed constraint shows that and with regions. After marginalizing the other irrelevant
model parameters, we show the evolution of the equation of state of HDE with
respect to the redshift . Though the current cosmic data points favor a
phantom like HDE Universe for the mean values of the model parameters in the
future, it can behave like quintessence in regions.Comment: 10 pages, 4 figures, to appear in Phys. Rev.
Unified Dark Fluid with Constant Adiabatic Sound Speed: Including Entropic Perturbations
In this paper, we continue to study a unified dark fluid model with a
constant adiabatic sound speed but with the entropic perturbations. When the
entropic perturbations are included, an effective sound speed, which reduces to
the adiabatic sound speed when the entropic perturbations are zero, has to be
specified as an additional free model parameter. Due to the relations between
the adiabatic sound speed and equations of state (EoS)
, the equation of state can be
determined up to an integration constant in principle when an adiabatic sound
speed is given. Then there are two degrees of freedom to describe the linear
perturbations for a fluid. Its micro-scale properties are characterized by its
EoS or adiabatic sound speed and an effective sound speed. We take the
effective sound speed and adiabatic sound speed as free model parameters and
then use the currently available cosmic observational data sets, which include
type Ia supernova Union 2.1, baryon acoustic oscillation and WMAP 7-year data
of cosmic background radiation, to constrain the possible entropic
perturbations and the adiabatic sound speed via the Markov Chain Monte Carlo
method. The results show that the cosmic observations favor a small effective
sound speed in region.Comment: 7 pages, 5 figures, to appear in Phys. Rev.
Probing the Neutrino Mass through the Cross Correlation between the Rees-Sciama Effect and Weak Lensing
Cosmology plays a fundamental role to determine the neutrino mass, therefore
also to determine its mass hierarchy, since the massive neutrino contributes to
the total matter density in the Universe at the background and perturbation
levels, once it becomes non-relativistic. After the non-relativistic transition
the fluctuations are smashed out at the scales . Therefore, the
missing fluctuation in the total matter is imprinted on the large scale
structure, say the suppression of the matter power spectrum at the scales . In this paper, instead of considering
the linear perturbation theory, which is well understood in the presence of
neutrino, we propose to use the cross correlation between the Rees-Sciama
effect and weak lensing to probe the neutrino mass. At the small scales, the
density contrast grows faster than the background scale factor ,
that makes a sign flipping on , which happens only in the non-linear regime. We show that
the flipping scale in the cross power spectrum between the Rees-Sciama effect
and weak lensing depends on the neutrino mass by assuming the shallow and deep
weak lensing surveys. Our analysis shows that the Deep survey has larger
signal-to-noise ratio . Finally, we use the Fisher information
matrix to forecast constraint on the neutrino mass.Comment: 7 pages, 5 figures, to appear in JCA
Inflation-rate Derivatives: From Market Model to Foreign Currency Analogy
In this paper, we establish a market model for the term structure of forward
inflation rates based on the risk-neutral dynamics of nominal and real
zero-coupon bonds. Under the market model, we can price inflation caplets as
well as inflation swaptions with a formula similar to the Black's formula, thus
justify the current market practice. We demonstrate how to further extend the
market model to cope with volatility smiles. Moreover, we establish a
consistency condition on the volatility of real zero-coupon bonds using
arbitrage arguments, and with that re-derive the model of Jarrow and Yildirim
(2003) with real forward rates based on "foreign currency analogy", and thus
interconnect the two modeling paradigms.Comment: 36 pages, 8 figure
Confronting DGP Braneworld Gravity with Cosmic Observations after Planck Data
The normal branch of Dvali-Gabadadze-Porrati braneworld gravity with brane
tension is confronted by the currently available cosmic observations from the
geometrical and dynamical perspectives. On the geometrical side, the type Ia
supernova as standard candle, the baryon acoustic oscillation as standard ruler
and the cosmic microwave background measurement from the first released 15.5
months data were used to fix the background evolutions. On the dynamical side,
the redshift space distortion data will be used to determine the evolution of
the matter perturbation. Through a Markov chain Monte Carlo analysis, we found
the dimensionless crossover scale
in a spatially
flat normal branch of Dvali-Gabadadze-Porrati braneworld. This result suggests
that the crossover scale should be around which is
consistent with the previous result and greater. It also
implies that the five-dimensional gravity effect is weak to be observed in
scale.Comment: 6 pages, 3 figures, match the published versio
Detecting Primordial Gravitational Waves Signal from BICEP2 and {\it Planck} HFI GHz Dust Polarization
The dust polarization is parameterized as a power law form of the multipole
: ( denotes or
), where is its amplitude with the ratio and . Extrapolating to GHz from
GHz yields a value of
(and an additional uncertainty ) over the
range . Based on these data, we report the tensor-to-scalar ratio
defined at by joining the
BICEP2+{\it Planck}2013+WMAP9+BAO+HST and {\it Planck} HFI GHz dust
polarization and its implication to the detection of the primordial
gravitational waves. Considering the CDM+ model, we found
at confidence level with and at
confidence level with . The results imply no
significant evidence for the primordial gravitational waves in
regions. However the post probability distribution of peaks at a small
positive value. And moves to larger positive values when the extrapolation
error bars are included. This might imply a very weak signal of the primordial
gravitational waves. It also implies the crucial fact in calibrating the
amplitude of the dust polarizations in detecting the primordial gravitational
waves in the future. When the running of the scalar spectral tilt is included,
we found at confidence level with and
at confidence level with
. The later one implies the detection of the
primordial gravitational waves in regions at the cost of decreasing
the value of to .Comment: 5 pages, 4 figures, title changed, n_{run} was include
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