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

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

Unambiguous probabilities in an eternally inflating universe

``Constants of Nature'' and cosmological parameters may in fact be variables related to some slowly-varying fields. In models of eternal inflation, such fields will take different values in different parts of the universe. Here I show how one can assign probabilities to values of the ``constants'' measured by a typical observer. This method does not suffer from ambiguities previously discussed in the literature.Comment: 7 pages, Final version (minor changes), to appear in Phys. Rev. Let

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

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

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

Wave Function of a Brane-like Universe

Within the mini-superspace model, brane-like cosmology means performing the variation with respect to the embedding (Minkowski) time $\tau$ before fixing the cosmic (Einstein) time $t$. The departure from Einstein limit is parameterized by the 'energy' conjugate to $\tau$, and characterized by a classically disconnected Embryonic epoch. In contrast with canonical quantum gravity, the wave-function of the brane-like Universe is (i) $\tau$-dependent, and (ii) vanishes at the Big Bang. Hartle-Hawking and Linde proposals dictate discrete 'energy' levels, whereas Vilenkin proposal resembles $\alpha$-particle disintegration.Comment: Revtex, 4 twocolumn pages, 3 eps figures (accepted for publication in Class. Quan. Grav.

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

Coleman-Weinberg Potential In Good Agreement With WMAP

We briefly summarize and update a class of inflationary models from the early eighties based on a quartic (Coleman-Weinberg) potential for a gauge singlet scalar (inflaton) field. For vacuum energy scales comparable to the grand unification scale, the scalar spectral index n_s=0.94-0.97, in very good agreement with the WMAP three year results. The tensor to scalar ratio r<~0.14, while alpha=dn/dlnk is =~-10^-3. An SO(10) version naturally explains the observed baryon asymmetry via non-thermal leptogenesis.Comment: v1: 6 pages, 1 table. v2: minor corrections. v3: 8 pages, added some details, comments, references and 3 figures. v4: minor corrections, published versio

Pre-Big-Bang Requires the Universe to be Exponentially Large From the Very Beginning

We show that in a generic case of the pre-big-bang scenario, inflation will solve cosmological problems only if the universe at the onset of inflation is extremely large and homogeneous from the very beginning. The size of a homogeneous part of the universe at the beginning of the stage of pre-big-bang (PBB) inflation must be greater than $10^{19}$ $l_s$, where $l_s$ is the stringy length. The total mass of an inflationary domain must be greater than $10^{72} M_{s}$, where $M_{s} \sim l_s^{-1}$. If the universe is initially radiation dominated, then its total entropy at that time must be greater than $10^{68}$. If the universe is closed, then at the moment of its formation it must be uniform over $10^{24}$ causally disconnected domains. The natural duration of the PBB stage in this scenario is $M_p^{-1}$. We argue that the initial state of the open PBB universe could not be homogeneous because of quantum fluctuations. Independently of the issue of homogeneity, one must introduce two large dimensionless parameters, $g_0^{-2} > 10^{53}$, and $B > 10^{91}$, in order to solve the flatness problem in the PBB cosmology. A regime of eternal inflation does not occur in the PBB scenario. This should be compared with the simplest versions of the chaotic inflation scenario, where the regime of eternal inflation may begin in a universe of size $O(M_{p}^{-1})$ with vanishing initial radiation entropy, mass $O(M_p)$, and geometric entropy O(1). We conclude that the current version of the PBB scenario cannot replace usual inflation even if one solves the graceful exit problem in this scenario.Comment: 14 pages, a discussion of the flatness problem in the PBB cosmology is adde