Hunting Down the Best Model of Inflation with Bayesian Evidence

We present the first calculation of the Bayesian evidence for different prototypical single field inflationary scenarios, including representative classes of small field and large field models. This approach allows us to compare inflationary models in a well-defined statistical way and to determine the current "best model of inflation". The calculation is performed numerically by interfacing the inflationary code FieldInf with MultiNest. We find that small field models are currently preferred, while large field models having a self-interacting potential of power p>4 are strongly disfavoured. The class of small field models as a whole has posterior odds of approximately 3:1 when compared with the large field class. The methodology and results presented in this article are an additional step toward the construction of a full numerical pipeline to constrain the physics of the early Universe with astrophysical observations. More accurate data (such as the Planck data) and the techniques introduced here should allow us to identify conclusively the best inflationary model.Comment: 12 pages, 2 figures, uses RevTeX. Misprint corrected, references added. Matches published versio

Testing Two-Field Inflation

We derive semi-analytic formulae for the power spectra of two-field inflation assuming an arbitrary potential and non-canonical kinetic terms, and we use them both to build phenomenological intuition and to constrain classes of two-field models using WMAP data. Using covariant formalism, we first develop a framework for understanding the background field kinematics and introduce a "slow-turn" approximation. Next, we find covariant expressions for the evolution of the adiabatic/curvature and entropy/isocurvature modes, and we discuss how the mode evolution can be inferred directly from the background kinematics and the geometry of the field manifold. From these expressions, we derive semi-analytic formulae for the curvature, isocurvature, and cross spectra, and the spectral observables, all to second-order in the slow-roll and slow-turn approximations. In tandem, we show how our covariant formalism provides useful intuition into how the characteristics of the inflationary Lagrangian translate into distinct features in the power spectra. In particular, we find that key features of the power spectra can be directly read off of the nature of the roll path, the curve the field vector rolls along with respect to the field manifold. For example, models whose roll path makes a sharp turn 60 e-folds before inflation ends tend to be ruled out because they produce strong departures from scale invariance. Finally, we apply our formalism to confront four classes of two-field models with WMAP data, including doubly quadratic and quartic potentials and non-standard kinetic terms, showing how whether a model is ruled out depends not only on certain features of the inflationary Lagrangian, but also on the initial conditions. Ultimately, models must possess the right balance of kinematical and dynamical behaviors, which we capture in a set of functions that can be reconstructed from spectral observables.Comment: Revised to match accepted PRD version: Improved discussion of background kinematics and multi-field effects, added tables summarizing key quantities and their links to observables, more detailed figures, fixed typos in former equations (103) and (117). 49 PRD pages, 11 figure

Chaotic inflation, radiative corrections and precision cosmology

We employ chaotic (phi^2 and phi^4) inflation to illustrate the important role radiative corrections can play during the inflationary phase. Yukawa interactions of phi, in particular, lead to corrections of the form -kappa phi^4 ln(phi/mu), where kappa>0 and mu is a renormalization scale. For instance, phi^4 chaotic inflation with radiative corrections looks compatible with the most recent WMAP (5 year) analysis, in sharp contrast to the tree level case. We obtain the 95% confidence limits 2.4x10^-14<~kappa<~5.7x10^-14, 0.931<~n_s<~0.958 and 0.038<~r<~0.205, where n_s and r respectively denote the scalar spectral index and scalar to tensor ratio. The limits for phi^2 inflation are kappa<~7.7x10^-15, 0.929<~n_s<~0.966 and 0.023<~r<~0.135. The next round of precision experiments should provide a more stringent test of realistic chaotic phi^2 and phi^4 inflation.Comment: 5 pages, 4 figures, 2 tables. v2: added comments and references. v3: changed title, published versio

A Toy Model for Open Inflation

The open inflation scenario based on the theory of bubble formation in the models of a single scalar field suffered from a fatal defect. In all the versions of this scenario known so far, the Coleman-De Luccia instantons describing the creation of an open universe did not exist. We propose a simple one-field model where the CDL instanton does exist and the open inflation scenario can be realized.Comment: 7 pages, 4 figures, revtex, a discussion of density perturbations is extende

Analysis of inflationary cosmological models in gauge theories of gravitation

Inflationary homogeneous isotropic cosmological models filled by scalar fields and ultrarelativistic matter are examined in the framework of gauge theories of gravitation. By using quadratic scalar field potential numerical analysis of flat, open and closed models is curried out. Properties of cosmological models are investigated in dependence on indefinite parameter of cosmological equations and initial conditions at a bounce. Fulfilled analysis demonstrates regular character of all cosmological models.Comment: LaTeX2e, iopart class file, 12 pages, 19 figure

The Triple-Alpha Process and the Anthropically Allowed Values of the Weak Scale

In multiple-universe models, the constants of nature may have different values in different universes. Agrawal, Barr, Donoghue and Seckel have pointed out that the Higgs mass parameter, as the only dimensionful parameter of the standard model, is of particular interest. By considering a range of values of this parameter, they showed that the Higgs vacuum expectation value must have a magnitude less than 5.0 times its observed value, in order for complex elements, and thus life, to form. In this report, we look at the effects of the Higgs mass parameter on the triple-alpha process in stars. This process, which is greatly enhanced by a resonance in Carbon-12, is responsible for virtually all of the carbon production in the universe. We find that the Higgs vacuum expectation value must have a magnitude greater than 0.90 times its observed value in order for an appreciable amount of carbon to form, thus significantly narrowing the allowed region of Agrawal et al.Comment: 9 pages, 1 figur

Thermal background can solve the cosmological moduli problem

It is shown that the coherent field oscillation of moduli fields with weak or TeV scale masses can dissipate its energy efficiently if they have a derivative coupling to standard bosonic fields in a thermal state. This mechanism may provide a new solution to the cosmological moduli problem in some special situations.Comment: 4 pages. revised versio

First CMB Constraints on the Inflationary Reheating Temperature

We present the first Bayesian constraints on the single field inflationary reheating era obtained from Cosmic Microwave Background (CMB) data. After demonstrating that this epoch can be fully characterized by the so-called reheating parameter, we show that it is constrained by the seven years Wilkinson Microwave Anisotropies Probe (WMAP7) data for all large and small field models. An interesting feature of our approach is that it yields lower bounds on the reheating temperature which can be combined with the upper bounds associated with gravitinos production. For large field models, we find the energy scale of reheating to be higher than those probed at the Large Hadron Collider, Ereh > 17.3 TeV at 95% of confidence. For small field models, we obtain the two-sigma lower limits Ereh > 890 TeV for a mean equation of state during reheating = -0.3 and Ereh > 390 GeV for = -0.2. The physical origin of these constraints is pedagogically explained by means of the slow-roll approximation. Finally, when marginalizing over all possible reheating history, the WMAP7 data push massive inflation under pressure (p < 2.2 at 95% of confidence where p is the power index of the large field potentials) while they slightly favor super-Planckian field expectation values in the small field models.Comment: 18 pages, 15 figures, uses RevTeX. References added, matches published versio

Observational tests of inflation with a field derivative coupling to gravity

A field kinetic coupling with the Einstein tensor leads to a gravitationally enhanced friction during inflation, by which even steep potentials with theoretically natural model parameters can drive cosmic acceleration. In the presence of this non-minimal derivative coupling we place observational constraints on a number of representative inflationary models such as chaotic inflation, inflation with exponential potentials, natural inflation, and hybrid inflation. We show that most of the models can be made compatible with the current observational data mainly due to the suppressed tensor-to-scalar ratio.Comment: 11 pages, 5 figure

Quintessence and phantom cosmology with non-minimal derivative coupling

We investigate cosmological scenarios with a non-minimal derivative coupling between the scalar field and the curvature, examining both the quintessence and the phantom cases in zero and constant potentials. In general, we find that the universe transits from one de Sitter solution to another, determined by the coupling parameter. Furthermore, according to the parameter choices and without the need for matter, we can obtain a Big Bang, an expanding universe with no beginning, a cosmological turnaround, an eternally contracting universe, a Big Crunch, a Big Rip avoidance and a cosmological bounce. This variety of behaviors reveals the capabilities of the present scenario.Comment: 8 pages, 8 figure