16 research outputs found
Momentum transforms, Laplacians and quantum mechanics in fractional spaces (Former Title)
We define an infinite class of unitary transformations between configuration and momentum fractional spaces, thus generalizing the Fourier transform to a special class of fractal geometries. Each transform diagonalizes a unique Laplacian operator. We also introduce a new version of fractional spaces, where coordinates and momenta span the whole real line. In one topological dimension, these results are extended to more general measures
Nonlocal gravity and the diffusion equation
We propose a nonlocal scalar-tensor model of gravity with pseudodifferential
operators inspired by the effective action of p-adic string and string field
theory on flat spacetime. An infinite number of derivatives act both on the
metric and scalar field sector. The system is localized via the diffusion
equation approach and its cosmology is studied. We find several exact dynamical
solutions, also in the presence of a barotropic fluid, which are stationary in
the diffusion flow. In particular, and contrary to standard general relativity,
there exist solutions with exponential and power-law scale factor also in an
open universe, as well as solutions with sudden future singularities or a
bounce. Also, from the point of view of quantum field theory, spontaneous
symmetry breaking can be naturally realized in the class of actions we
consider.Comment: 18 pages, 5 figures. v2: typos corrected, references added. Major
changes are an expansion of the discussion of homogeneous perturbations and
the inclusion of cosmological fluids in the dynamic
Non-perturbative spectrum of non-local gravity
We investigate the non-perturbative degrees of freedom of a class of weakly non-local gravitational theories that have been proposed as an ultraviolet completion of general relativity. At the perturbative level, it is known that the degrees of freedom of non-local gravity are the same of the Einstein\u2013Hilbert theory around any maximally symmetric spacetime. We prove that, at the non-perturbative level, the degrees of freedom are actually eight in four dimensions, contrary to what one might guess on the basis of the \u201cinfinite number of derivatives\u201d present in the action. It is shown that six of these degrees of freedom do not propagate on Minkowski spacetime, but they might play a role at large scales on curved backgrounds. We also propose a criterion to select the form factor almost uniquely
A solution to the 4-tachyon off-shell amplitude in cubic string field theory
We derive an analytic series solution of the elliptic equations providing the
4-tachyon off-shell amplitude in cubic string field theory (CSFT). From such a
solution we compute the exact coefficient of the quartic effective action
relevant for time dependent solutions and we derive the exact coefficient of
the quartic tachyon coupling. The rolling tachyon solution expressed as a
series of exponentials is studied both using level-truncation
computations and the exact 4-tachyon amplitude. The results for the level
truncated coefficients are shown to converge to those derived using the exact
string amplitude. The agreement with previous work on the subject, both on the
quartic tachyon coupling and on the CSFT rolling tachyon, is an excellent test
for the accuracy of our off-shell solution.Comment: 26 pages, 5 figure
Large Nongaussianity from Nonlocal Inflation
We study the possibility of obtaining large nongaussian signatures in the
Cosmic Microwave Background in a general class of single-field nonlocal
hill-top inflation models. We estimate the nonlinearity parameter f_{NL} which
characterizes nongaussianity in such models and show that large nongaussianity
is possible. For the recently proposed p-adic inflation model we find that
f_{NL} ~ 120 when the string coupling is order unity. We show that large
nongaussianity is also possible in a toy model with an action similar to those
which arise in string field theory.Comment: 27 pages, no figures. Added references and some clarifying remark
Predictions for Nongaussianity from Nonlocal Inflation
In our previous work the nonlinearity parameter f_NL, which characterizes
nongaussianity in the cosmic microwave background, was estimated for a class of
inflationary models based on nonlocal field theory. These models include p-adic
inflation and generically have the remarkable property that slow roll inflation
can proceed even with an extremely steep potential. Previous calculations found
that large nongaussianity is possible; however, the technical complications
associated with studying perturbations in theories with infinitely many
derivatives forced us to provide only an order of magnitude estimate for f_NL.
We reconsider the problem of computing f_NL in nonlocal inflation models,
showing that a particular choice of field basis and recent progress in
cosmological perturbation theory makes an exact computation possible. We
provide the first quantitatively accurate computation of the bispectrum in
nonlocal inflation, confirming our previous claim that it can be observably
large. We show that the shape of the bispectrum in this class of models makes
it observationally distinguishable from Dirac-Born-Infeld inflation models.Comment: 26 pages, 5 figures; references added, sign convention for f_NL
clarified, minor correction
Non-perturbative spectrum of non-local gravity
4 pags., 1 tab. -- Open Access funded by Creative Commons Atribution Licence 4.0We investigate the non-perturbative degrees of freedom of a class of weakly non-local gravitational theories that have been proposed as an ultraviolet completion of general relativity. At the perturbative level, it is known that the degrees of freedom of non-local gravity are the same of the Einstein–Hilbert theory around any maximally symmetric spacetime. We prove that, at the non-perturbative level, the degrees of freedom are actually eight in four dimensions, contrary to what one might guess on the basis of the “infinite number of derivatives” present in the action. It is shown that six of these degrees of freedom do not propagate on Minkowski spacetime, but they might play a role at large scales on curved backgrounds. We also propose a criterion to select the form factor almost uniquely.G.C. and L.M. are supported by the I+D grant FIS2017-86497-C2-2-P of the Spanish Ministry of Science, Innovation and Universities
Erratum to: Initial conditions and degrees of freedom of non-local gravity (Journal of High Energy Physics, (2018), 2018, 5, (87), 10.1007/JHEP05(2018)087)
The authors did not realize that some of the initial conditions indicated to solve the Cauchy problem in nonlocal systems are not independent, so that the number of initial conditions is reduced from 4 to 2 in the case of the scalar field