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

Testing Multi-Field Inflation: A Geometric Approach

We develop an approach for linking the power spectra, bispectrum, and trispectrum to the geometric and kinematical features of multifield inflationary Lagrangians. Our geometric approach can also be useful in determining when a complicated multifield model can be well approximated by a model with one, two, or a handful of fields. To arrive at these results, we focus on the mode interactions in the kinematical basis, starting with the case of no sourcing and showing that there is a series of mode conservation laws analogous to the conservation law for the adiabatic mode in single-field inflation. We then treat the special case of a quadratic potential with canonical kinetic terms, showing that it produces a series of mode sourcing relations identical in form to that for the adiabatic mode. We build on this result to show that the mode sourcing relations for general multifield inflation are extension of this special case but contain higher-order covariant derivatives of the potential and corrections from the field metric. In parallel, we show how these interactions depend on the geometry of the inflationary Lagrangian and on the kinematics of the associated field trajectory. Finally, we consider how the mode interactions and effective number of fields active during inflation are reflected in the spectra and introduce a multifield consistency relation, as well as a multifield observable that can potentially distinguish two-field scenarios from scenarios involving three or more effective fields.Comment: 21 pages, 4 figures + tables. Revised to clarify several points and reorganized Section III for pedagogical reasons. Error in one equation and typos were corrected, as well as additional references adde

Enhancing the tensor-to-scalar ratio in simple inflation

We show that in theories with a nontrivial kinetic term the contribution of the gravitational waves to the CMB fluctuations can be substantially larger than that is naively expected in simple inflationary models. This increase of the tensor-to-scalar perturbation ratio leads to a larger B-component of the CMB polarization, thus making the prospects for future detection much more promising. The other important consequence of the considered model is a higher energy scale of inflation and hence higher reheating temperature compared to a simple inflation.Comment: 9 pages, 1 figure and references are added, discussion is slightly extended, published versio

Back-reaction of Cosmological Fluctuations during Power-Law Inflation

We study the renormalized energy-momentum tensor of cosmological scalar fluctuations during the slow-rollover regime for power-law inflation and find that it is characterized by a negative energy density at the leading order, with the same time behaviour as the background energy. The average expansion rate appears decreased by the back-reaction of the effective energy of cosmological fluctuations, but this value is comparable with the energy of background only if inflation starts at a Planckian energy. We also find that, for this particular model, the first and second order inflaton fluctuations are decoupled and satisfy the same equation of motion. To conclude, the fourth order adiabatic expansion for the inflaton scalar field is evaluated for a general potential V(\phi).Comment: 9 pages, no figures, revtex. Some changes made, comments and references added, conclusions unchanged, version accepted for pubblication in Phys. Rev.

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

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

Inflation without Slow Roll

We draw attention to the possibility that inflation (i.e. accelerated expansion) might continue after the end of slow roll, during a period of fast oscillations of the inflaton field \phi . This phenomenon takes place when a mild non-convexity inequality is satisfied by the potential V(\phi). The presence of such a period of \phi-oscillation-driven inflation can substantially modify reheating scenarios. In some models the effect of these fast oscillations might be imprinted on the primordial perturbation spectrum at cosmological scales.Comment: 9 pages, Revtex, psfig, 1 figure, minor modifications, references adde

Second Order Gauge-Invariant Perturbations during Inflation

The evolution of gauge invariant second-order scalar perturbations in a general single field inflationary scenario are presented. Different second order gauge invariant expressions for the curvature are considered. We evaluate perturbatively one of these second order curvature fluctuations and a second order gauge invariant scalar field fluctuation during the slow-roll stage of a massive chaotic inflationary scenario, taking into account the deviation from a pure de Sitter evolution and considering only the contribution of super-Hubble perturbations in mode-mode coupling. The spectra resulting from their contribution to the second order quantum correlation function are nearly scale-invariant, with additional logarithmic corrections to the first order spectrum. For all scales of interest the amplitude of these spectra depend on the total number of e-folds. We find, on comparing first and second order perturbation results, an upper limit to the total number of e-folds beyond which the two orders are comparable.Comment: 17 pages, 6 figures. Final version to appear in Phys. Rev.

Sub-eV scalar dark matter through the super-renormalizable Higgs portal

The Higgs portal of the Standard Model provides the opportunity for coupling to a very light scalar field $\phi$ via the super-renormalizable operator $\phi(H^\dagger H)$. This allows for the existence of a very light scalar dark matter that has coherent interaction with the Standard Model particles and yet has its mass protected against radiative corrections. We analyze ensuing constraints from the fifth-force measurements, along with the cosmological requirements. We find that the detectable level of the fifth-force can be achieved in models with low inflationary scales, and certain amount of fine-tuning in the initial deviation of $\phi$ from its minimum.Comment: 6 pages, 3 figures. References added in the revised version

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