320 research outputs found
Boundary Terms and Junction Conditions for the DGP Pi-Lagrangian and Galileon
In the decoupling limit of DGP, Pi describes the brane-bending degree of
freedom. It obeys second order equations of motion, yet it is governed by a
higher derivative Lagrangian. We show that, analogously to the Einstein-Hilbert
action for GR, the Pi-Lagrangian requires Gibbons-Hawking-York type boundary
terms to render the variational principle well-posed. These terms are important
if there are other boundaries present besides the DGP brane, such as in higher
dimensional cascading DGP models. We derive the necessary boundary terms in two
ways. First, we derive them directly from the brane-localized Pi-Lagrangian by
demanding well-posedness of the action. Second, we calculate them directly from
the bulk, taking into account the Gibbons-Hawking-York terms in the bulk
Einstein-Hilbert action. As an application, we use the new boundary terms to
derive Israel junction conditions for Pi across a sheet-like source. In
addition, we calculate boundary terms and junction conditions for the galileons
which generalize the DGP Pi-lagrangian, showing that the boundary term for the
n-th order galileon is the (n-1)-th order galileon.Comment: 23 pages, 1 figure. Extended the analysis to the general galileon
field. Version to appear in JHE
Smooth Initial Conditions from Weak Gravity
CMB measurements reveal an unnaturally smooth early universe. We propose a
mechanism to make this smoothness natural by weakening the strength of gravity
at early times, and therefore altering which initial conditions have low
entropy.Comment: 14 pages, 5 figures. Minor changes, version appearing in PL
Superluminality in DGP
We reconsider the issue of superluminal propagation in the DGP model of
infrared modified gravity. Superluminality was argued to exist in certain
otherwise physical backgrounds by using a particular, physically relevant
scaling limit of the theory. In this paper, we exhibit explicit
five-dimensional solutions of the full theory that are stable against small
fluctuations and that indeed support superluminal excitations. The scaling
limit is neither needed nor invoked in deriving the solutions or in the
analysis of its small fluctuations. To be certain that the superluminality
found here is physical, we analyze the retarded Green's function of the scalar
excitations, finding that it is causal and stable, but has support on a widened
light-cone. We propose to use absence of superluminal propagation as a method
to constrain the parameters of the DGP model. As a first application of the
method, we find that whenever the 4D energy density is a pure cosmological
constant and a hierarchy of scales exists between the 4D and 5D Planck masses,
superluminal propagation unavoidably occurs.Comment: 23 pages. Minor corrections. Version to appear in JHE
Generalizing Galileons
The Galileons are a set of terms within four-dimensional effective field
theories, obeying symmetries that can be derived from the dynamics of a
3+1-dimensional flat brane embedded in a 5-dimensional Minkowski Bulk. These
theories have some intriguing properties, including freedom from ghosts and a
non-renormalization theorem that hints at possible applications in both
particle physics and cosmology. In this brief review article, we will summarize
our attempts over the last year to extend the Galileon idea in two important
ways. We will discuss the effective field theory construction arising from
co-dimension greater than one flat branes embedded in a flat background - the
multiGalileons - and we will then describe symmetric covariant versions of the
Galileons, more suitable for general cosmological applications. While all these
Galileons can be thought of as interesting four-dimensional field theories in
their own rights, the work described here may also make it easier to embed them
into string theory, with its multiple extra dimensions and more general
gravitational backgrounds.Comment: 16 pages; invited brief review article for a special issue of
Classical and Quantum Gravity. Submitted to CQ
Conformal consistency relations for single-field inflation
We generalize the single-field consistency relations to capture not only the
leading term in the squeezed limit---going as 1/q^3, where q is the small
wavevector---but also the subleading one, going as 1/q^2. This term, for an
(n+1)-point function, is fixed in terms of the variation of the n-point
function under a special conformal transformation; this parallels the fact that
the 1/q^3 term is related with the scale dependence of the n-point function.
For the squeezed limit of the 3-point function, this conformal consistency
relation implies that there are no terms going as 1/q^2. We verify that the
squeezed limit of the 4-point function is related to the conformal variation of
the 3-point function both in the case of canonical slow-roll inflation and in
models with reduced speed of sound. In the second case the conformal
consistency conditions capture, at the level of observables, the relation among
operators induced by the non-linear realization of Lorentz invariance in the
Lagrangian. These results mean that, in any single-field model, primordial
correlation functions of \zeta are endowed with an SO(4,1) symmetry, with
dilations and special conformal transformations non-linearly realized by \zeta.
We also verify the conformal consistency relations for any n-point function in
models with a modulation of the inflaton potential, where the scale dependence
is not negligible. Finally, we generalize (some of) the consistency relations
involving tensors and soft internal momenta.Comment: 26 pages, 1 figure. v2. Corrected typos, notably a sign error in eq.
(54). Matches JCAP published versio
The Pseudo-Conformal Universe: Scale Invariance from Spontaneous Breaking of Conformal Symmetry
We present a novel theory of the very early universe which addresses the
traditional horizon and flatness problems of big bang cosmology and predicts a
scale invariant spectrum of perturbations. Unlike inflation, this scenario
requires no exponential accelerated expansion of space-time. Instead, the early
universe is described by a conformal field theory minimally coupled to gravity.
The conformal fields develop a time-dependent expectation value which breaks
the flat space so(4,2) conformal symmetry down to so(4,1), the symmetries of de
Sitter, giving perturbations a scale invariant spectrum. The solution is an
attractor, at least in the case of a single time-dependent field. Meanwhile,
the metric background remains approximately flat but slowly contracts, which
makes the universe increasingly flat, homogeneous and isotropic, akin to the
smoothing mechanism of ekpyrotic cosmology. Our scenario is very general,
requiring only a conformal field theory capable of developing the appropriate
time-dependent expectation values, and encompasses existing incarnations of
this idea, specifically the U(1) model of Rubakov and the Galileon Genesis
scenario. Its essential features depend only on the symmetry breaking pattern
and not on the details of the underlying lagrangian. It makes generic
observational predictions that make it potentially distinguishable from
standard inflation, in particular significant non-gaussianities and the absence
of primordial gravitational waves.Comment: 51 pages, 3 figures. v2 discussion and refs added, minus sign in
transformation laws fixed. Version appearing in JCA
On the (A)dS decoupling limits of massive gravity
We consider various decoupling limits of ghost-free massive gravity on (A)dS. The first is a decoupling limit on AdS space where the mass goes to zero while the AdS radius is held fixed. This results in an interacting massive Proca vector theory with a Λ2 ∼ (MPlm)1/2 strong coupling scale which is ghost-free by construction and yet can not be put in the form of the generalized Proca theories considered so far. We comment on the existence of a potential duality between this Proca theory and a CFT on the boundary. The second decoupling limit we consider is a new limit on dS, obtained by sending the mass towards the finite partially massless value. We do this by introducing the scalar Stückelberg field which restores the partially massless symmetry. For generic values of the parameters, only a finite number of operators enter the partially massless decoupling limit and take the form of dS Galileons. If the interactions are chosen to be precisely those of the ‘candidate’ non-linear partially massless theory, the resulting strong coupling scale has a higher value and the resulting decoupling limit includes an infinite number of interactions which we give in closed form. These interactions preserve both the linear partially massless symmetry and the dS version of the Galileon shift symmetry
Interacting spin-2 fields in three dimensions
Using the frame formulation of multi-gravity in three dimensions, we show
that demanding the presence of secondary constraints which remove the
Boulware-Deser ghosts restricts the possible interaction terms of the theory
and identifies invertible frame field combinations whose effective metric may
consistently couple to matter. The resulting ghost-free theories can be
represented by theory graphs which are trees. In the case of three frame
fields, we explicitly show that the requirement of positive masses and energies
for the bulk spin-2 modes in AdS is consistent with a positive central
charge for the putative dual CFT.Comment: 26 pages, 3 figures, v2: minor changes, matches published versio
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