2,220 research outputs found
Reconstructing the Local Potential of Inflation with BICEP2 data
We locally reconstruct the inflationary potential by using the current
constraints on and from BICEP2 data. Assuming small and
negligible , the inflationary potential is approximately linear
in range but becomes non-linear in range. However if we vary the value of within
the range given by constraints from {\it Planck} measurement, the local
reconstruction is only valid in the range of ,
which challenges the inflationary background from the point of view of
effective field theory. We show that, within the range of , the inflation potential can be precisely reconstructed. With the
current reconstruction, we show that and are
consistent, while model is ruled out by confidence level of the
reconstructed range of potential. This sets up a strong limit of large-field
inflation models.Comment: 11 pages, 10 figure
Non-parametric reconstruction of an inflaton potential from Einstein-Cartan-Sciama-Kibble gravity with particle production
The coupling between spin and torsion in the Einstein-Cartan-Sciama-Kibble
theory of gravity generates gravitational repulsion at very high densities,
which prevents a singularity in a black hole and may create there a new
universe. We show that quantum particle production in such a universe near the
last bounce, which represents the Big Bang gives the dynamics that solves the
horizon, flatness, and homogeneity problems in cosmology. For a particular
range of the particle production coefficient, we obtain a nearly constant
Hubble parameter that gives an exponential expansion of the universe with more
than 60 -folds, which lasts about s. This scenario can thus
explain cosmic inflation without requiring a fundamental scalar field and
reheating. From the obtained time dependence of the scale factor, we follow the
prescription of Ellis and Madsen to reconstruct in a non-parametric way a
scalar field potential which gives the same dynamics of the early universe.
This potential gives the slow-roll parameters of cosmic inflation, from which
we calculate the tensor-to-scalar ratio, the scalar spectral index of density
perturbations, and its running as functions of the production coefficient. We
find that these quantities do not significantly depend on the scale factor at
the Big Bounce. Our predictions for these quantities are consistent with the
Planck 2015 observations.Comment: 9 pages, 11 figure
Planck 2013 results. XXII. Constraints on inflation
We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to be ns = 0:9603 _ 0:0073, ruling out exact scale invariance at over 5_: Planck establishes an upper bound on the tensor-to-scalar ratio of r < 0:11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V00 < 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n _ 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining dns=dln k = 0:0134 _ 0:0090. We verify these conclusions through a numerical analysis, which makes no slowroll approximation, and carry out a Bayesian parameter estimation and model-selection analysis for a number of inflationary models including monomial, natural, and hilltop potentials. For each model, we present the Planck constraints on the parameters of the potential and explore several possibilities for the post-inflationary entropy generation epoch, thus obtaining nontrivial data-driven constraints. We also present a direct reconstruction of the observable range of the inflaton potential. Unless a quartic term is allowed in the potential, we find results consistent with second-order slow-roll predictions. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit by __2 e_ _ 10; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with Planck bounds on fNL. Planck constrains with unprecedented accuracy the amplitude and possible correlation (with the adiabatic mode) of non-decaying isocurvature fluctuations. The fractional primordial contributions of cold dark matter (CDM) isocurvature modes of the types expected in the curvaton and axion scenarios have upper bounds of 0.25% and 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelated isocurvature component can improve the _2 e_ by approximately 4 as a result of slightly lowering the theoretical prediction for the ` <_ 40 multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions
Planck 2013 results. XXII. Constraints on inflation
We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to be ns = 0:9603 _ 0:0073, ruling out exact scale invariance at over 5_: Planck establishes an upper bound on the tensor-to-scalar ratio of r < 0:11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V00 < 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n _ 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining dns=dln k = 0:0134 _ 0:0090. We verify these conclusions through a numerical analysis, which makes no slowroll approximation, and carry out a Bayesian parameter estimation and model-selection analysis for a number of inflationary models including monomial, natural, and hilltop potentials. For each model, we present the Planck constraints on the parameters of the potential and explore several possibilities for the post-inflationary entropy generation epoch, thus obtaining nontrivial data-driven constraints. We also present a direct reconstruction of the observable range of the inflaton potential. Unless a quartic term is allowed in the potential, we find results consistent with second-order slow-roll predictions. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit by __2 e_ _ 10; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with Planck bounds on fNL. Planck constrains with unprecedented accuracy the amplitude and possible correlation (with the adiabatic mode) of non-decaying isocurvature fluctuations. The fractional primordial contributions of cold dark matter (CDM) isocurvature modes of the types expected in the curvaton and axion scenarios have upper bounds of 0.25% and 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelated isocurvature component can improve the _2 e_ by approximately 4 as a result of slightly lowering the theoretical prediction for the ` <_ 40 multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions
Scale-Based Monotonicity Analysis in Qualitative Modelling with Flat Segments
Qualitative models are often more suitable than classical quantitative models in tasks such as Model-based Diagnosis (MBD), explaining system behavior, and designing novel devices from first principles. Monotonicity is an important feature to leverage when constructing qualitative models. Detecting monotonic pieces robustly and efficiently from sensor or simulation data remains an open problem. This paper presents scale-based monotonicity: the notion that monotonicity can be defined relative to a scale. Real-valued functions defined on a finite set of reals e.g. sensor data or simulation results, can be partitioned into quasi-monotonic segments, i.e. segments monotonic with respect to a scale, in linear time. A novel segmentation algorithm is introduced along with a scale-based definition of "flatness"
Reconstructing the Inflaton Potential---in Principle and in Practice
Generalizing the original work by Hodges and Blumenthal, we outline a
formalism which allows one, in principle, to reconstruct the potential of the
inflaton field from knowledge of the tensor gravitational wave spectrum or the
scalar density fluctuation spectrum, with special emphasis on the importance of
the tensor spectrum. We provide some illustrative examples of such
reconstruction. We then discuss in some detail the question of whether one can
use real observations to carry out this procedure. We conclude that in
practice, a full reconstruction of the functional form of the potential will
not be possible within the foreseeable future. However, with a knowledge of the
dark matter components, it should soon be possible to combine
intermediate-scale data with measurements of large-scale cosmic microwave
background anisotropies to yield useful information regarding the potential.Comment: 39 pages plus 2 figures (upon request:[email protected]), LaTeX,
FNAL--PUB--93/029-A; SUSSEX-AST 93/3-
The WiggleZ Dark Energy Survey: improved distance measurements to z = 1 with reconstruction of the baryonic acoustic feature
We present significant improvements in cosmic distance measurements from the WiggleZ Dark Energy Survey, achieved by applying the reconstruction of the baryonic acoustic feature technique. We show using both data and simulations that the reconstruction technique can often be effective despite patchiness of the survey, significant edge effects and shot-noise. We investigate three redshift bins in the redshift range 0.2 < z < 1, and in all three find improvement after reconstruction in the detection of the baryonic acoustic feature and its usage as a standard ruler. We measure model-independent distance measures DV(rsfid/rs) of 1716 ± 83, 2221 ± 101, 2516 ± 86 Mpc (68 per cent CL) at effective redshifts z = 0.44, 0.6, 0.73, respectively, where DV is the volume-averaged distance, and rs is the sound horizon at the end of the baryon drag epoch. These significantly improved 4.8, 4.5 and 3.4 per cent accuracy measurements are equivalent to those expected from surveys with up to 2.5 times the volume of WiggleZ without reconstruction applied. These measurements are fully consistent with cosmologies allowed by the analyses of the Planck Collaboration and the Sloan Digital Sky Survey. We provide the DV(rsfid/rs) posterior probability distributions and their covariances. When combining these measurements with temperature fluctuations measurements of Planck, the polarization of Wilkinson Microwave Anisotropy Probe 9, and the 6dF Galaxy Survey baryonic acoustic feature, we do not detect deviations from a flat Λ cold dark matter (ΛCDM) model. Assuming this model, we constrain the current expansion rate to H₀ = 67.15 ± 0.98 km s⁻¹Mpc⁻¹. Allowing the equation of state of dark energy to vary, we obtain wDE = −1.080 ± 0.135. When assuming a curved ΛCDM model we obtain a curvature value of ΩK = −0.0043 ± 0.0047
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