52 research outputs found
Scale-Invariant Curvature Fluctuations from an Extended Semiclassical Gravity
We present an extension of the semiclassical Einstein equations which couples
n-point correlation functions of a stochastic Einstein tensor to the n-point
functions of the quantum stress-energy tensor. We apply this extension to
calculate the quantum fluctuations during an inflationary period, where we take
as a model a massive conformally coupled scalar field on a perturbed de Sitter
space and describe how a renormalization independent, almost-scale-invariant
power spectrum of the scalar metric perturbation is produced. Furthermore, we
discuss how this model yields a natural basis for the calculation of
non-Gaussianities of the considered metric fluctuations.Comment: 16 pages, 2 figures; final versio
Thermal nature of de Sitter spacetime and spontaneous excitation of atoms
We consider, in de Sitter spacetime, both freely falling and static two-level
atoms in interaction with a conformally coupled massless scalar field in the de
Sitter-invariant vacuum, and separately calculate the contributions of vacuum
fluctuations and radiation reaction to the atom's spontaneous excitation rate.
We find that spontaneous excitations occur even for the freely falling atom as
if there is a thermal bath of radiation at the Gibbons-Hawking temperature and
we thus recover, in a different physical context, the results of Gibbons and
Hawking that reveals the thermal nature of de Sitter spacetime. Similarly, for
the case of the static atom, our results show that the atom also perceives a
thermal bath which now arises as a result of the intrinsic thermal nature of de
Sitter spacetime and the Unruh effect associated with the inherent acceleration
of the atom.Comment: 11 page
Dispersive fields in de Sitter space and event horizon thermodynamics
When Lorentz invariance is violated at high energy, the laws of black hole
thermodynamics are apparently no longer satisfied. To shed light on this
observation, we study dispersive fields in de Sitter space. We show that the
Bunch-Davies vacuum state restricted to the static patch is no longer thermal,
and that the Tolman law is violated. However we also show that, for free fields
at least, this vacuum is the only stationary stable state, as if it were in
equilibrium. We then present a precise correspondence between dispersive
effects found in de Sitter and in black hole metrics. This indicates that the
consequences of dispersion on thermodynamical laws could also be similar.Comment: 19 pages. Black and White version on Phys.Rev.D serve
Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property
In a recent paper, we proved that a large class of spacetimes, not
necessarily homogeneous or isotropous and relevant at a cosmological level,
possesses a preferred codimension one submanifold, i.e., the past cosmological
horizon, on which it is possible to encode the information of a scalar field
theory living in the bulk. Such bulk-to-boundary reconstruction procedure
entails the identification of a preferred quasifree algebraic state for the
bulk theory, enjoying remarkable properties concerning invariance under
isometries (if any) of the bulk and energy positivity, and reducing to
well-known vacua in standard situations. In this paper, specialising to open
FRW models, we extend previously obtained results and we prove that the
preferred state is of Hadamard form, hence the backreaction on the metric is
finite and the state can be used as a starting point for renormalisation
procedures. That state could play a distinguished role in the discussion of the
evolution of scalar fluctuations of the metric, an analysis often performed in
the development of any model describing the dynamic of an early Universe which
undergoes an inflationary phase of rapid expansion in the past.Comment: 41 page
Naturalness in Cosmological Initial Conditions
We propose a novel approach to the problem of constraining cosmological
initial conditions. Within the framework of effective field theory, we classify
initial conditions in terms of boundary terms added to the effective action
describing the cosmological evolution below Planckian energies. These boundary
terms can be thought of as spacelike branes which may support extra
instantaneous degrees of freedom and extra operators. Interactions and
renormalization of these boundary terms allow us to apply to the boundary terms
the field-theoretical requirement of naturalness, i.e. stability under
radiative corrections. We apply this requirement to slow-roll inflation with
non-adiabatic initial conditions, and to cyclic cosmology. This allows us to
define in a precise sense when some of these models are fine-tuned. We also
describe how to parametrize in a model-independent way non-Gaussian initial
conditions; we show that in some cases they are both potentially observable and
pass our naturalness requirement.Comment: 35 pages, 8 figure
On the scalar sector of the covariant graviton two-point function in de Sitter spacetime
We examine the scalar sector of the covariant graviton two-point function in
de Sitter spacetime. This sector consists of the pure-trace part and another
part described by a scalar field. We show that it does not contribute to
two-point functions of gauge-invariant quantities. We also demonstrate that the
long-distance growth present in some gauges is absent in this sector for a wide
range of gauge parameters.Comment: 15 pages, no figures, LaTeX, considerably shortene
On the Decoherence of Primordial Fluctuations During Inflation
We study the process whereby quantum cosmological perturbations become
classical within inflationary cosmology. By setting up a master-equation
formulation we show how quantum coherence for super-Hubble modes can be
destroyed by their coupling to the environment provided by sub-Hubble modes. We
identify what features the sub-Hubble environment must have in order to
decohere the longer wavelengths, and identify how the onset of decoherence (and
how long it takes) depends on the properties of the sub-Hubble physics which
forms the environment. Our results show that the decoherence process is largely
insensitive to the details of the coupling between the sub- and super-Hubble
scales. They also show how locality implies, quite generally, that the
decohered density matrix at late times is diagonal in the field representation
(as is implicitly assumed by extant calculations of inflationary density
perturbations). Our calculations also imply that decoherence can arise even for
couplings which are as weak as gravitational in strength.Comment: 31 pages, 1 figur
Results on the Wess-Zumino consistency condition for arbitrary Lie algebras
The so-called covariant Poincare lemma on the induced cohomology of the
spacetime exterior derivative in the cohomology of the gauge part of the BRST
differential is extended to cover the case of arbitrary, non reductive Lie
algebras. As a consequence, the general solution of the Wess-Zumino consistency
condition with a non trivial descent can, for arbitrary (super) Lie algebras,
be computed in the small algebra of the 1 form potentials, the ghosts and their
exterior derivatives. For particular Lie algebras that are the semidirect sum
of a semisimple Lie subalgebra with an ideal, a theorem by Hochschild and Serre
is used to characterize more precisely the cohomology of the gauge part of the
BRST differential in the small algebra. In the case of an abelian ideal, this
leads to a complete solution of the Wess-Zumino consistency condition in this
space. As an application, the consistent deformations of 2+1 dimensional
Chern-Simons theory based on iso(2,1) are rediscussed.Comment: 39 pages Latex file, 1 eps figure, typos and proof of lemma 5
correcte
Cosmological horizons and reconstruction of quantum field theories
As a starting point, we state some relevant geometrical properties enjoyed by
the cosmological horizon of a certain class of Friedmann-Robertson-Walker
backgrounds. Those properties are generalised to a larger class of expanding
spacetimes admitting a geodesically complete cosmological horizon \scrim
common to all co-moving observers. This structure is later exploited in order
to recast, in a cosmological background, some recent results for a linear
scalar quantum field theory in spacetimes asymptotically flat at null infinity.
Under suitable hypotheses on , encompassing both the cosmological de Sitter
background and a large class of other FRW spacetimes, the algebra of
observables for a Klein-Gordon field is mapped into a subalgebra of the algebra
of observables \cW(\scrim) constructed on the cosmological horizon. There is
exactly one pure quasifree state on \cW(\scrim) which fulfils a
suitable energy-positivity condition with respect to a generator related with
the cosmological time displacements. Furthermore induces a preferred
physically meaningful quantum state for the quantum theory in the
bulk. If admits a timelike Killing generator preserving \scrim, then the
associated self-adjoint generator in the GNS representation of has
positive spectrum (i.e. energy). Moreover turns out to be invariant
under every symmetry of the bulk metric which preserves the cosmological
horizon. In the case of an expanding de Sitter spacetime, coincides
with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this
case. Remarks on the validity of the Hadamard property for in more
general spacetimes are presented.Comment: 32 pages, 1 figure, to appear on Comm. Math. Phys., dedicated to
Professor Klaus Fredenhagen on the occasion of his 60th birthda
Group theoretical approach to quantum fields in de Sitter space I. The principal series
Using unitary irreducible representations of the de Sitter group, we
construct the Fock space of a massive free scalar field.
In this approach, the vacuum is the unique dS invariant state. The quantum
field is a posteriori defined by an operator subject to covariant
transformations under the dS isometry group. This insures that it obeys
canonical commutation relations, up to an overall factor which should not
vanish as it fixes the value of hbar. However, contrary to what is obtained for
the Poincare group, the covariance condition leaves an arbitrariness in the
definition of the field. This arbitrariness allows to recover the amplitudes
governing spontaneous pair creation processes, as well as the class of alpha
vacua obtained in the usual field theoretical approach. The two approaches can
be formally related by introducing a squeezing operator which acts on the state
in the field theoretical description and on the operator in the present
treatment. The choice of the different dS invariant schemes (different alpha
vacua) is here posed in very simple terms: it is related to a first order
differential equation which is singular on the horizon and whose general
solution is therefore characterized by the amplitude on either side of the
horizon. Our algebraic approach offers a new method to define quantum field
theory on some deformations of dS space.Comment: 35 pages, 2 figures ; Corrected typo, Changed referenc
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