The Numerical Treatment of Inflationary Models

Ringeval, Christophe

doi:10.1007/978-3-540-74353-8_7

Cited by 58 publications

(67 citation statements)

References 74 publications

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“…We also need parameters describing the reheating phase, θ reh , such as the reheating temperature and the equation of state. In fact, one can show that only one parameter is sufficient, the so-called rescaled reheating parameter R [115][116][117][118][119]. In the present paper, following Ref.…”

Section: Fast Evidence Computationmentioning

confidence: 64%

Compatibility of Planck and BICEP2 results in light of inflation

et al. 2014

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We investigate the implications for inflation of the detection of B-modes polarization in the Cosmic Microwave Background (CMB) by BICEP2. We show that the hypothesis of primordial origin of the measurement is favored only by the first four bandpowers, while the others would prefer unreasonably large values of the tensor-to-scalar ratio. Using only those four bandpowers, we carry out a complete analysis in the cosmological and inflationary slow-roll parameter space using the BICEP2 polarization measurements alone and extract the Bayesian evidences and complexities for all the Encyclopaedia Inflationaris models. This allows us to determine the most probable and simplest BICEP2 inflationary scenarios. Although this list contains the simplest monomial potentials, it also includes many other scenarios, suggesting that focusing model building efforts on large field models only is unjustified at this stage. We demonstrate that the sets of inflationary models preferred by Planck alone and BICEP2 alone are almost disjoint, indicating a clear tension between the two data sets. We address this tension with a Bayesian measure of compatibility between BICEP2 and Planck. We find that for models favored by Planck the two data sets tend to be incompatible, whereas there is a moderate evidence of compatibility for the BICEP2 preferred models. As a result, it would be premature to draw any conclusion on the best Planck models, such as Starobinsky and/or Kähler moduli inflation. For the subset of scenarios not exhibiting data sets incompatibility, we update the evidences and complexities using both data sets together.

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Section: Fast Evidence Computationmentioning

confidence: 64%

Compatibility of Planck and BICEP2 results in light of inflation

et al. 2014

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“…For this purpose, we have used the method of [84], similarly to what was done in [40] in the case of a long waterfall phase. As a cross-check, we have used the δN formalism [85][86][87] that allows one to derive good analytical approximations for the power spectrum of curvature perturbations.…”

Section: Background Classical Dynamicsmentioning

confidence: 99%

Massive primordial black holes from hybrid inflation as dark matter and the seeds of galaxies

2015

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In this paper we present a new scenario where massive primordial black holes (PBHs) are produced from the collapse of large curvature perturbations generated during a mild-waterfall phase of hybrid inflation. We determine the values of the inflaton potential parameters leading to a PBH mass spectrum peaking on planetarylike masses at matter-radiation equality and producing abundances comparable to those of dark matter today, while the matter power spectrum on scales probed by cosmic microwave background (CMB) anisotropies agrees with Planck data. These PBHs could have acquired large stellar masses today, via merging, and the model passes both the constraints from CMB distortions and microlensing. This scenario is supported by Chandra observations of numerous BH candidates in the central region of Andromeda. Moreover, the tail of the PBH mass distribution could be responsible for the seeds of supermassive black holes at the center of galaxies, as well as for ultraluminous x-ray sources. We find that our effective hybrid potential can originate e.g. from D-term inflation with a Fayet-Iliopoulos term of the order of the Planck scale but sub-Planckian values of the inflaton field. Finally, we discuss the implications of quantum diffusion at the instability point of the potential, able to generate a Swiss-cheese-like structure of the Universe, eventually leading to apparent accelerated cosmic expansion.

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“…The multipole moments are in fact computed at any scale (i.e. for any value of ) by means of numerical calculations (since, in the most general case, they are solution of more involved differential equations) [103]. Moreover, their shape is not only determined by the spectral index but is also affected by the other cosmological parameters.…”

Section: E Inflationary Predictionsmentioning

confidence: 99%

Cosmological inflation and the quantum measurement problem

2012

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According to cosmological inflation, the inhomogeneities in our universe are of quantum mechanical origin. This scenario is phenomenologically very appealing as it solves the puzzles of the standard hot big bang model and naturally explains why the spectrum of cosmological perturbations is almost scale invariant. It is also an ideal playground to discuss deep questions among which is the quantum measurement problem in a cosmological context. Although the large squeezing of the quantum state of the perturbations and the phenomenon of decoherence explain many aspects of the quantum to classical transition, it remains to understand how a specific outcome can be produced in the early universe, in the absence of any observer. The Continuous Spontaneous Localization (CSL) approach to quantum mechanics attempts to solve the quantum measurement question in a general context. In this framework, the wavefunction collapse is caused by adding new non linear and stochastic terms to the Schrödinger equation. In this paper, we apply this theory to inflation, which amounts to solving the CSL parametric oscillator case. We choose the wavefunction collapse to occur on an eigenstate of the Mukhanov-Sasaki variable and discuss the corresponding modified Schrödinger equation. Then, we compute the power spectrum of the perturbations and show that it acquires a universal shape with two branches, one which remains scale invariant and one with n S = 4, a spectral index in obvious contradiction with the Cosmic Microwave Background (CMB) anisotropy observations. The requirement that the non-scale invariant part be outside the observational window puts stringent constraints on the parameter controlling the deviations from ordinary quantum mechanics. Due to the absence of a CSL amplification mechanism in field theory, this has also for consequence that the collapse mechanism of the inflationary fluctuations is not efficient. Then, we determine the collapse time. On small scales the collapse is almost instantaneous, and we recover exactly the behavior of the CSL harmonic oscillator (a case for which we present new results), whereas, on large scales, we find that the collapse is delayed and can take several e-folds to happen. We conclude that recovering the observational successes of inflation and, at the same time, reaching a satisfactory resolution of the inflationary "macro-objectification" issue seems problematic in the framework considered here. This work also provides a complete solution to the CSL parametric oscillator system, a topic we suggest could play a very important rôle to further constrain the CSL parameters. Our results illustrate the remarkable power of inflation and cosmology to constrain new physics.

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The Numerical Treatment of Inflationary Models

Cited by 58 publications

References 74 publications

Compatibility of Planck and BICEP2 results in light of inflation

Compatibility of Planck and BICEP2 results in light of inflation

Massive primordial black holes from hybrid inflation as dark matter and the seeds of galaxies

Cosmological inflation and the quantum measurement problem

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