1,208 research outputs found
Cosmological Imprint of an Energy Component with General Equation of State
We examine the possibility that a significant component of the energy density
of the universe has an equation-of-state different from that of matter,
radiation or cosmological constant (). An example is a cosmic scalar
field evolving in a potential, but our treatment is more general. Including
this component alters cosmic evolution in a way that fits current observations
well. Unlike , it evolves dynamically and develops fluctuations,
leaving a distinctive imprint on the microwave background anisotropy and mass
power spectrum.Comment: revised version, with added references, to appear in Phys. Rev. Lett.
(4 pages Latex, 2 postscript figures
Formal Verification of Neural Network Controlled Autonomous Systems
In this paper, we consider the problem of formally verifying the safety of an
autonomous robot equipped with a Neural Network (NN) controller that processes
LiDAR images to produce control actions. Given a workspace that is
characterized by a set of polytopic obstacles, our objective is to compute the
set of safe initial conditions such that a robot trajectory starting from these
initial conditions is guaranteed to avoid the obstacles. Our approach is to
construct a finite state abstraction of the system and use standard
reachability analysis over the finite state abstraction to compute the set of
the safe initial states. The first technical problem in computing the finite
state abstraction is to mathematically model the imaging function that maps the
robot position to the LiDAR image. To that end, we introduce the notion of
imaging-adapted sets as partitions of the workspace in which the imaging
function is guaranteed to be affine. We develop a polynomial-time algorithm to
partition the workspace into imaging-adapted sets along with computing the
corresponding affine imaging functions. Given this workspace partitioning, a
discrete-time linear dynamics of the robot, and a pre-trained NN controller
with Rectified Linear Unit (ReLU) nonlinearity, the second technical challenge
is to analyze the behavior of the neural network. To that end, we utilize a
Satisfiability Modulo Convex (SMC) encoding to enumerate all the possible
segments of different ReLUs. SMC solvers then use a Boolean satisfiability
solver and a convex programming solver and decompose the problem into smaller
subproblems. To accelerate this process, we develop a pre-processing algorithm
that could rapidly prune the space feasible ReLU segments. Finally, we
demonstrate the efficiency of the proposed algorithms using numerical
simulations with increasing complexity of the neural network controller
Holography and Variable Cosmological Constant
An effective local quantum field theory with UV and IR cutoffs correlated in
accordance with holographic entropy bounds is capable of rendering the
cosmological constant (CC) stable against quantum corrections. By setting an IR
cutoff to length scales relevant to cosmology, one easily obtains the currently
observed rho_Lambda ~ 10^{-47} GeV^4, thus alleviating the CC problem. It is
argued that scaling behavior of the CC in these scenarios implies an
interaction of the CC with matter sector or a time-dependent gravitational
constant, to accommodate the observational data.Comment: 7 pages, final version accepted by PR
Self interacting Brans Dicke cosmology and Quintessence
Recent cosmological observations reveal that we are living in a flat
accelerated expanding universe. In this work we have investigated the nature of
the potential compatible with the power law expansion of the universe in a self
interacting Brans Dicke cosmology with a perfect fluid background and have
analyzed whether this potential supports the accelerated expansion. It is found
that positive power law potential is relevant in this scenario and can drive
accelerated expansion for negative Brans Dicke coupling parameter . The
evolution of the density perturbation is also analyzed in this scenerio and is
seen that the model allows growing modes for negative .Comment: 8pages, 5 figures, PRD style, some changes are made, figures added,
reference added. To be published in Int. J. Mod. Phys.
A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration
Increasing evidence suggests that most of the energy density of the universe
consists of a dark energy component with negative pressure, a ``cosmological
constant" that causes the cosmic expansion to accelerate. In this paper, we
address the puzzle of why this component comes to dominate the universe only
recently rather than at some much earlier epoch. We present a class of theories
based on an evolving scalar field where the explanation is based entirely on
internal dynamical properties of the solutions. In the theories we consider,
the dynamics causes the scalar field to lock automatically into a negative
pressure state at the onset of matter-domination such that the present epoch is
the earliest possible time, consistent with nucleosynthesis restrictions, when
it can start to dominate.Comment: 5 pages, 3 figure
Rules for Computing Symmetry, Density and Stoichiometry in a Quasi-Unit-Cell Model of Quasicrystals
The quasi-unit cell picture describes the atomic structure of quasicrystals
in terms of a single, repeating cluster which overlaps neighbors according to
specific overlap rules. In this paper, we discuss the precise relationship
between a general atomic decoration in the quasi-unit cell picture atomic
decorations in the Penrose tiling and in related tiling pictures. Using these
relations, we obtain a simple, practical method for determining the density,
stoichiometry and symmetry of a quasicrystal based on the atomic decoration of
the quasi-unit cell taking proper account of the sharing of atoms between
clusters.Comment: 14 pages, 8 figure
Strong Brane Gravity and the Radion at Low Energies
For the 2-brane Randall-Sundrum model, we calculate the bulk geometry for
strong gravity, in the low matter density regime, for slowly varying matter
sources. This is relevant for astrophysical or cosmological applications. The
warped compactification means the radion can not be written as a homogeneous
mode in the orbifold coordinate, and we introduce it by extending the
coordinate patch approach of the linear theory to the non-linear case. The
negative tension brane is taken to be in vacuum. For conformally invariant
matter on the positive tension brane, we solve the bulk geometry as a
derivative expansion, formally summing the `Kaluza-Klein' contributions to all
orders. For general matter we compute the Einstein equations to leading order,
finding a scalar-tensor theory with ,
and geometrically interpret the radion. We comment that this radion scalar may
become large in the context of strong gravity with low density matter.
Equations of state allowing to be negative, can exhibit behavior
where the matter decreases the distance between the 2 branes, which we
illustrate numerically for static star solutions using an incompressible fluid.
For increasing stellar density, the branes become close before the upper mass
limit, but after violation of the dominant energy condition. This raises the
interesting question of whether astrophysically reasonable matter, and initial
data, could cause branes to collide at low energy, such as in dynamical
collapse.Comment: 24 pages, 3 figure
Metric Expansion from Microscopic Dynamics in an Inhomogeneous Universe
Theories with ingredients like the Higgs mechanism, gravitons, and inflaton
fields rejuvenate the idea that relativistic kinematics is dynamically
emergent. Eternal inflation treats the Hubble constant H as depending on
location. Microscopic dynamics implies that H is over much smaller lengths than
pocket universes to be understood as a local space reproduction rate. We
illustrate this via discussing that even exponential inflation in TeV-gravity
is slow on the relevant time scale. In our on small scales inhomogeneous
cosmos, a reproduction rate H depends on position. We therefore discuss
Einstein-Straus vacuoles and a Lindquist-Wheeler like lattice to connect the
local rate properly with the scaling of an expanding cosmos. Consistency allows
H to locally depend on Weyl curvature similar to vacuum polarization. We derive
a proportionality constant known from Kepler's third law and discuss the
implications for the finiteness of the cosmological constant.Comment: 23 pages, no figure
Dynamical dark energy: Current constraints and forecasts
We consider how well the dark energy equation of state as a function of
red shift will be measured using current and anticipated experiments. We
use a procedure which takes fair account of the uncertainties in the functional
dependence of on , as well as the parameter degeneracies, and avoids the
use of strong prior constraints. We apply the procedure to current data from
WMAP, SDSS, and the supernova searches, and obtain results that are consistent
with other analyses using different combinations of data sets. The effects of
systematic experimental errors and variations in the analysis technique are
discussed. Next, we use the same procedure to forecast the dark energy
constraints achieveable by the end of the decade, assuming 8 years of WMAP data
and realistic projections for ground-based measurements of supernovae and weak
lensing. We find the constraints on the current value of to be
, and on (between and ) to be
. Finally, we compare these limits to other
projections in the literature. Most show only a modest improvement; others show
a more substantial improvement, but there are serious concerns about
systematics. The remaining uncertainty still allows a significant span of
competing dark energy models. Most likely, new kinds of measurements, or
experiments more sophisticated than those currently planned, are needed to
reveal the true nature of dark energy.Comment: 24 pages, 20 figures. Added SN systematic uncertainties, extended
discussio
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