640 research outputs found

### Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials

We investigate the construction of diffusions consisting of infinitely
numerous Brownian particles moving in $\mathbb{R}^d$ and interacting via
logarithmic functions (two-dimensional Coulomb potentials). These potentials
are very strong and act over a long range in nature. The associated equilibrium
states are no longer Gibbs measures. We present general results for the
construction of such diffusions and, as applications thereof, construct two
typical interacting Brownian motions with logarithmic interaction potentials,
namely the Dyson model in infinite dimensions and Ginibre interacting Brownian
motions. The former is a particle system in $\mathbb{R}$, while the latter is
in $\mathbb{R}^2$. Both models are translation and rotation invariant in space,
and as such, are prototypes of dimensions $d=1,2$, respectively. The
equilibrium states of the former diffusion model are determinantal or Pfaffian
random point fields with sine kernels. They appear in the thermodynamical
limits of the spectrum of the ensembles of Gaussian random matrices such as
GOE, GUE and GSE. The equilibrium states of the latter diffusion model are the
thermodynamical limits of the spectrum of the ensemble of complex non-Hermitian
Gaussian random matrices known as the Ginibre ensemble.Comment: Published in at http://dx.doi.org/10.1214/11-AOP736 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org

### The CMB and the measure of the multiverse

In the context of eternal inflation, cosmological predictions depend on the
choice of measure to regulate the diverging spacetime volume. The spectrum of
inflationary perturbations is no exception, as we demonstrate by comparing the
predictions of the fat geodesic and causal patch measures. To highlight the
effect of the measure---as opposed to any effects related to a possible
landscape of vacua---we take the cosmological model, including the model of
inflation, to be fixed. We also condition on the average CMB temperature
accompanying the measurement. Both measures predict a 1-point expectation value
for the gauge-invariant Newtonian potential, which takes the form of a
(scale-dependent) monopole, in addition to a related contribution to the
3-point correlation function, with the detailed form of these quantities
differing between the measures. However, for both measures both effects are
well within cosmic variance. Our results make clear the theoretical relevance
of the measure, and at the same time validate the standard inflationary
predictions in the context of eternal inflation.Comment: 28 pages; v2: reference added, some clarification

### Is Our Universe Natural?

It goes without saying that we are stuck with the universe we have.
Nevertheless, we would like to go beyond simply describing our observed
universe, and try to understand why it is that way rather than some other way.
Physicists and cosmologists have been exploring increasingly ambitious ideas
that attempt to explain why certain features of our universe aren't as
surprising as they might first appear.Comment: Invited review for Nature, 11 page

### Universality of the Volume Bound in Slow-Roll Eternal Inflation

It has recently been shown that in single field slow-roll inflation the total
volume cannot grow by a factor larger than e^(S_dS/2) without becoming
infinite. The bound is saturated exactly at the phase transition to eternal
inflation where the probability to produce infinite volume becomes non zero. We
show that the bound holds sharply also in any space-time dimensions, when
arbitrary higher-dimensional operators are included and in the multi-field
inflationary case. The relation with the entropy of de Sitter and the
universality of the bound strengthen the case for a deeper holographic
interpretation. As a spin-off we provide the formalism to compute the
probability distribution of the volume after inflation for generic multi-field
models, which might help to address questions about the population of vacua of
the landscape during slow-roll inflation.Comment: 24 pages, 5 figure

### A geometric bound on F-term inflation

We discuss a general bound on the possibility to realise inflation in any
minimal supergravity with F-terms. The derivation crucially depends on the
sGoldstini, the scalar field directions that are singled out by spontaneous
supersymmetry breaking. The resulting bound involves both slow-roll parameters
and the geometry of the K\"ahler manifold of the chiral scalars. We analyse the
inflationary implications of this bound, and in particular discuss to what
extent the requirements of single field and slow-roll can both be met in F-term
inflation.Comment: 14 pages, improved analysis, references added, matches published
versio

### On Inflation with Non-minimal Coupling

A simple realization of inflation consists of adding the following operators
to the Einstein-Hilbert action: (partial phi)^2, lambda phi^4, and xi phi^2 R,
with xi a large non-minimal coupling. Recently there has been much discussion
as to whether such theories make sense quantum mechanically and if the inflaton
phi can also be the Standard Model Higgs. In this note we answer these
questions. Firstly, for a single scalar phi, we show that the quantum field
theory is well behaved in the pure gravity and kinetic sectors, since the
quantum generated corrections are small. However, the theory likely breaks down
at ~ m_pl / xi due to scattering provided by the self-interacting potential
lambda phi^4. Secondly, we show that the theory changes for multiple scalars
phi with non-minimal coupling xi phi dot phi R, since this introduces
qualitatively new interactions which manifestly generate large quantum
corrections even in the gravity and kinetic sectors, spoiling the theory for
energies > m_pl / xi. Since the Higgs doublet of the Standard Model includes
the Higgs boson and 3 Goldstone bosons, it falls into the latter category and
therefore its validity is manifestly spoiled. We show that these conclusions
hold in both the Jordan and Einstein frames and describe an intuitive analogy
in the form of the pion Lagrangian. We also examine the recent claim that
curvature-squared inflation models fail quantum mechanically. Our work appears
to go beyond the recent discussions.Comment: 14 pages, 2 figures. Version 2: Clarified findings and improved
wording. Elaborated important sections and removed an unnecessary section.
Added references. Version 3: Updated towards JHEP version. Version 4: Final
JHEP versio

### Inflation on the Brane with Vanishing Gravity

Many existing models of brane inflation suffer from a steep irreducible
gravitational potential between the branes that causes inflation to end too
early. Inspired by the fact that point masses in 2+1 D exert no gravitational
force, we propose a novel unwarped and non-supersymmetric setup for inflation,
consisting of 3-branes in two extra dimensions compactified on a sphere. The
size of the sphere is stabilized by a combination of a bulk cosmological
constant and a magnetic flux. Computing the 4D effective potential between
probe branes in this background, we find a non-zero contribution only from
exchange of level-1 KK modes of the graviton and radion. Identifying antipodal
points on the 2-sphere projects out these modes, eliminating entirely the
troublesome gravitational contribution to the inflationary potential.Comment: 19 pages, 11 figures, JHEP forma

### Scalar Three-point Functions in a CDL Background

Motivated by the FRW-CFT proposal by Freivogel, Sekino, Susskind and Yeh, we
compute the three-point function of a scalar field in a Coleman-De Luccia
instanton background. We first compute the three-point function of the scalar
field making only very mild assumptions about the scalar potential and the
instanton background. We obtain the three-point function for points in the FRW
patch of the CDL instanton and take two interesting limits; the limit where the
three points are near the boundary of the hyperbolic slices of the FRW patch,
and the limit where the three points lie on the past lightcone of the FRW
patch. We expand the past lightcone three-point function in spherical
harmonics. We show that the near boundary limit expansion of the three-point
function of a massless scalar field exhibits conformal structure compatible
with FRW-CFT when the FRW patch is flat. We also compute the three-point
function when the scalar is massive, and explain the obstacles to generalizing
the conjectured field-operator correspondence of massless fields to massive
fields.Comment: 42 pages + appendices, 10 figures; v2, v3: minor correction

### Spinning Conformal Correlators

We develop the embedding formalism for conformal field theories, aimed at
doing computations with symmetric traceless operators of arbitrary spin. We use
an index-free notation where tensors are encoded by polynomials in auxiliary
polarization vectors. The efficiency of the formalism is demonstrated by
computing the tensor structures allowed in n-point conformal correlation
functions of tensors operators. Constraints due to tensor conservation also
take a simple form in this formalism. Finally, we obtain a perfect match
between the number of independent tensor structures of conformal correlators in
d dimensions and the number of independent structures in scattering amplitudes
of spinning particles in (d+1)-dimensional Minkowski space.Comment: 46 pages, 3 figures; V2: references added; V3: tiny misprint
corrected in (A.9

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