13 research outputs found
Cosmological Dark Energy: Prospects for a Dynamical Theory
We present an approach to the problem of vacuum energy in cosmology, based on
dynamical screening of Lambda on the horizon scale. We review first the
physical basis of vacuum energy as a phenomenon connected with macroscopic
boundary conditions, and the origin of the idea of its screening by particle
creation and vacuum polarization effects. We discuss next the relevance of the
quantum trace anomaly to this issue. The trace anomaly implies additional terms
in the low energy effective theory of gravity, which amounts to a non-trivial
modification of the classical Einstein theory, fully consistent with the
Equivalence Principle. We show that the new dynamical degrees of freedom the
anomaly contains provide a natural mechanism for relaxing Lambda to zero on
cosmological scales. We consider possible signatures of the restoration of
conformal invariance predicted by the fluctuations of these new scalar degrees
of freedom on the spectrum and statistics of the CMB, in light of the latest
bounds from WMAP. Finally we assess the prospects for a new cosmological model
in which the dark energy adjusts itself dynamically to the cosmological horizon
boundary, and therefore remains naturally of order H^2 at all times without
fine tuning.Comment: 50 pages, Invited Contribution to New Journal of Physics Focus Issue
on Dark Energ
Quantum Diffeomorphisms and Conformal Symmetry
We analyze the constraints of general coordinate invariance for quantum
theories possessing conformal symmetry in four dimensions. The character of
these constraints simplifies enormously on the Einstein universe . The global conformal symmetry algebra of this space determines
uniquely a finite shift in the Hamiltonian constraint from its classical value.
In other words, the global Wheeler-De Witt equation is {\it modified} at the
quantum level in a well-defined way in this case. We argue that the higher
moments of should not be imposed on the physical states {\it a priori}
either, but only the weaker condition . We
present an explicit example of the quantization and diffeomorphism constraints
on for a free conformal scalar field.Comment: PlainTeX File, 37 page
Conformal Invariance and Cosmic Background Radiation
The spectrum and statistics of the cosmic microwave background radiation
(CMBR) are investigated under the hypothesis that scale invariance of the
primordial density fluctuations should be promoted to full conformal
invariance. As in the theory of critical phenomena, this hypothesis leads in
general to deviations from naive scaling. The spectral index of the two-point
function of density fluctuations is given in terms of the quantum trace anomaly
and is greater than one, leading to less power at large distance scales than a
strict Harrison-Zel'dovich spectrum. Conformal invariance also implies
non-gaussian statistics for the higher point correlations and in particular, it
completely determines the large angular dependence of the three-point
correlations of the CMBR.Comment: 4 pages, Revtex file, uuencoded with one figur
On Infrared Effects in de~Sitter Background
We have estimated higher order quantum gravity corrections to de~Sitter
spacetime. Our results suggest that, while the classical spacetime metric may
be distorted by the graviton self-interactions, the corrections are relatively
weaker than previously thought, possibly growing like a power rather than
exponentially in time.Comment: 17, UM-TH-94-11, (1 postscript fig. at end
Conformal Invariance, Dark Energy, and CMB Non-Gaussianity
In addition to simple scale invariance, a universe dominated by dark energy
naturally gives rise to correlation functions possessing full conformal
invariance. This is due to the mathematical isomorphism between the conformal
group of certain 3 dimensional slices of de Sitter space and the de Sitter
isometry group SO(4,1). In the standard homogeneous isotropic cosmological
model in which primordial density perturbations are generated during a long
vacuum energy dominated de Sitter phase, the embedding of flat spatial sections
in de Sitter space induces a conformal invariant perturbation spectrum and
definite prediction for the shape of the non-Gaussian CMB bispectrum. In the
case in which the density fluctuations are generated instead on the de Sitter
horizon, conformal invariance of the horizon embedding implies a different but
also quite definite prediction for the angular correlations of CMB
non-Gaussianity on the sky. Each of these forms for the bispectrum is intrinsic
to the symmetries of de Sitter space and in that sense, independent of specific
model assumptions. Each is different from the predictions of single field slow
roll inflation models which rely on the breaking of de Sitter invariance. We
propose a quantum origin for the CMB fluctuations in the scalar gravitational
sector from the conformal anomaly that could give rise to these
non-Gaussianities without a slow roll inflaton field, and argue that conformal
invariance also leads to the expectation for the relation n_S-1=n_T between the
spectral indices of the scalar and tensor power spectrum. Confirmation of this
prediction or detection of non-Gaussian correlations in the CMB of one of the
bispectral shape functions predicted by conformal invariance can be used both
to establish the physical origins of primordial density fluctuations and
distinguish between different dynamical models of cosmological vacuum dark
energy.Comment: 73 pages, 9 figures. Final Version published in JCAP. New Section 4
added on linearized scalar gravitational potentials; New Section 8 added on
gravitational wave tensor perturbations and relation of spectral indices n_T
= n_S -1; Table of Contents added; Eqs. (3.14) and (3.15) added to clarify
relationship of bispectrum plotted to CMB measurements; Some other minor
modification
Weyl Cohomology and the Effective Action for Conformal Anomalies
We present a general method of deriving the effective action for conformal
anomalies in any even dimension, which satisfies the Wess-Zumino consistency
condition by construction. The method relies on defining the coboundary
operator of the local Weyl group, and giving a cohomological interpretation to
counterterms in the effective action in dimensional regularization with respect
to this group. Non-trivial cocycles of the Weyl group arise from local
functionals that are Weyl invariant in and only in the physical even integer
dimension. In the physical dimension the non-trivial cocycles generate
covariant non-local action functionals characterized by sensitivity to global
Weyl rescalings. The non-local action so obtained is unique up to the addition
of trivial cocycles and Weyl invariant terms, both of which are insensitive to
global Weyl rescalings. These distinct behaviors under rigid dilations can be
used to distinguish between infrared relevant and irrelevant operators in a
generally covariant manner. Variation of the non-local effective action
yields two new conserved geometric stress tensors with local traces. The method
may be extended to any even dimension by making use of the general construction
of conformal invariants given by Fefferman and Graham. As a corollary,
conformal field theory behavior of correlators at the asymptotic infinity of
either anti-de Sitter or de Sitter spacetimes follows, i.e. AdS or
deS/CFT correspondence. The same construction naturally selects all
infrared relevant terms (and only those terms) in the low energy effective
action of gravity in any even integer dimension. The infrared relevant terms
arising from the known anomalies in d=4 imply that the classical Einstein
theory is modified at large distances.Comment: 32 pages. LateX file. LateX twic
Attractor states and infrared scaling in de Sitter space
The renormalized expectation value of the energy-momentum tensor for a scalar
field with any mass m and curvature coupling xi is studied for an arbitrary
homogeneous and isotropic physical initial state in de Sitter spacetime. We
prove quite generally that has a fixed point attractor behavior at
late times, which depends only on m and xi, for any fourth order adiabatic
state that is infrared finite. Specifically, when m^2 + xi R > 0,
approaches the Bunch-Davies de Sitter invariant value at late times,
independently of the initial state. When m = xi = 0, it approaches instead the
de Sitter invariant Allen-Folacci value. When m = 0 and xi \ge 0 we show that
this state independent asymptotic value of the energy-momentum tensor is
proportional to the conserved geometrical tensor (3)H_{ab}, which is related to
the behavior of the quantum effective action of the scalar field under global
Weyl rescaling. This relationship serves to generalize the definition of the
trace anomaly in the infrared for massless, non-conformal fields. In the case
m^2 + xi R = 0, but m and xi separately different from zero, grows
linearly with cosmic time at late times. For most values of m and xi in the
tachyonic cases, m^2 + xi R grows exponentially at late cosmic
times for all physically admissable initial states.Comment: 30 pages, 6 figures, 46 kB tar.gz fil
Characteristic angular scales in cosmic microwave background radiation
We investigate the stochasticity in temperature fluctuations in the cosmic microwave background (CMB) radiation data from the Wilkinson Microwave Anisotropy Probe. We show that the angular fluctuation of the temperature is a Markov process with a Markov angular scale, ΘMarkov = 1.01-0.07+0.09. We characterize the complexity of the CMB fluctuations by means of a Fokker–Planck or Langevin equation and measure the associated Kramers–Moyal coefficients for the fluctuating temperature field T(\hat n) and its increment, \Delta T=T(\hat n_1)-T(\hat n_2) . Through this method we show that temperature fluctuations in the CMB have fat tails compared to a Gaussian distribution