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DOE OSTI2014

Inflation physics from the cosmic microwave background and large scale structure

Here, fluctuations in the intensity and polarization of the cosmic microwave background (CMB) and the large-scale distribution of matter in the universe each contain clues about the nature of the earliest moments of time. The next generation of CMB and large-scale structure (LSS) experiments are poised to test the leading paradigm for these earliest moments—the theory of cosmic inflation—and to detect the imprints of the inflationary epoch, thereby dramatically increasing our understanding of fundamental physics and the early universe. A future CMB experiment with sufficient angular resolution and frequency coverage that surveys at least 1% of the sky to a depth of 1 uK-arcmin can deliver a constraint on the tensor-to-scalar ratio that will either result in a 5σ measurement of the energy scale of inflation or rule out all large-field inflation models, even in the presence of foregrounds and the gravitational lensing B -mode signal. LSS experiments, particularly spectroscopic surveys such as the Dark Energy Spectroscopic Instrument, will complement the CMB effort by improving current constraints on running of the spectral index by up to a factor of four, improving constraints on curvature by a factor of ten, and providing non-Gaussianity constraints that are competitive with the current CMB bounds.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Planck 2015 results: XX. Constraints on inflation

In this paper, we present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey, which includes more than twice the integration time of the nominal survey used for the 2013 release papers. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be n s = 0.968 ± 0.006 and tightly constrain its scale dependence to dn s / dlnk = -0.003 ± 0.007 when combined with the Planck lensing likelihood. When the Planck high-ℓ polarization data are included, the results are consistent and uncertainties are further reduced. The upper bound on the tensor-to-scalar ratio is r 0.002 < 0.11 (95% CL). This upper limit is consistent with the B-mode polarization constraint r< 0.12 (95% CL) obtained from a joint analysis of the BICEP2/Keck Array and Planck data. These results imply that V(φ) ∝ φ 2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R 2 inflation. We search for several physically motivated deviations from a simple power-law spectrum of curvature perturbations, including those motivated by a reconstruction of the inflaton potential not relying on the slow-roll approximation. We find that such models are not preferred, either according to a Bayesian model comparison or according to a frequentist simulation-based analysis. Three independent methods reconstructing the primordial power spectrum consistently recover a featureless and smooth P R (k)over the range of scales 0.008 Mpc -1 ≲ k ≲ 0.1 Mpc -1 . At large scales, each method finds deviations from a power law, connected to a deficit at multipoles ℓ ≈ 20-40 in the temperature power spectrum, but at an uncompelling statistical significance owing to the large cosmic variance present at these multipoles. By combining power spectrum and non-Gaussianity bounds, we constrain models with generalized Lagrangians, including Galileon models and axion monodromy models. The Planck data are consistent with adiabatic primordial perturbations, and the estimated values for the parameters of the base Λ cold dark matter (ΛCDM) model are not significantly altered when more general initial conditions are admitted. In correlated mixed adiabatic and isocurvature models, the 95% CL upper bound for the non-adiabatic contribution to the observed CMB temperature variance is | α non - adi | < 1.9%, 4.0%, and 2.9% for CDM, neutrino density, and neutrino velocity isocurvature modes, respectively. We have tested inflationary models producing an anisotropic modulation of the primordial curvature power spectrum finding that the dipolar modulation in the CMB temperature field induced by a CDM isocurvature perturbation is not preferred at a statistically significant level. We also establish tight constraints on a possible quadrupolar modulation of the curvature perturbation. Lastly, these results are consistent with the Planck 2013 analysis based on the nominal mission data and further constrain slow-roll single-field inflationary models, as expected from the increased precision of Planck data using the full set of observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

A new algorithm for calculating the curvature perturbations in stochastic inflation

We propose a new approach for calculating the curvature perturbations produced during inflation in the stochastic formalism. In our formalism, the fluctuations of the e-foldings are directly calculated without perturbatively expanding the inflaton field and they are connected to the curvature perturbations by the δN formalism. The result automatically includes the contributions of the higher order perturbations because we solve the equation of motion non-perturbatively. In this paper, we analytically prove that our result (the power spectrum and the nonlinearity parameter) is consistent with the standard result in single field slow-roll inflation. We also describe the algorithm for numerical calculations of the curvature perturbations in more general inflation models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Symmetron inflation

We define a new inflationary scenario in which inflation starts naturally after the Big Bang when the energy density drops below some critical value. As a model, we use recently proposed symmetron field whose effective potential depends on the energy density of the environment. At high densities, right after the Big Bang, the potential for the symmetron is trivial, and the field sits in equilibrium at the bottom of the potential. When the density drops below some critical value, the potential changes its shape into a symmetry breaking potential, and the field starts rolling down. This scenario does not require any special initial conditions for inflation to start. We also construct a concrete model with two fields, i.e. with symmetron as an inflaton and an additional scalar field which describes the matter content in the early universe. For the simplest coupling, the amplitude and shape of the power spectrum are the same as in the single field slow-roll inflation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Predictions in multifield models of inflation

This paper presents a method for obtaining an analytic expression for the density function of observables in multifield models of inflation with sum-separable potentials. The most striking result is that the density function in general possesses a sharp peak and the location of this peak is only mildly sensitive to the distribution of initial conditions. A simple argument is given for why this result holds for a more general class of models than just those with sum-separable potentials and why for such models, it is possible to obtain robust predictions for observable quantities. As an example, the joint density function of the spectral index and running in double quadratic inflation is computed. For scales leaving the horizon 55 e-folds before the end of inflation, the density function peaks at n{sub s} = 0.967 and α = 0.0006 for the spectral index and running respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Exploring two-field inflation in the Wess-Zumino model

We explore inflation via the effective potential of the minimal Wess-Zumino model, considering both the real and imaginary components of the complex field. Using transport techniques, we calculate the full allowed range of n{sub s}, r and f{sub NL} for different choices of the single free parameter, v, and present the probability distribution of these signatures given a simple choice for the prior distribution of initial conditions. Our work provides a case study of multi-field inflation in a simple but realistic setting, with important lessons that are likely to apply more generally. For example, we find that there are initial conditions consistent with observations of n{sub s} and r for values of v that would be excluded if only evolutions in the real field direction were to be considered, and that these may yield enhanced values of f{sub NL}. Moreover, we find that initial conditions fixed at high energy density, where the potential is close to quartic in form, can still lead to evolutions in a concave region of the potential during the observable number of e-folds, as preferred by present data. The Wess-Zumino model therefore provides an illustration that multi-field dynamics must be taken into account when seeking to understand fully the phenomenology of such models of inflation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

BICEP2 implications for single-field slow-roll inflation revisited

It is generally believed that in single-field slow-roll inflation, a large tensor-to-scalar ratio r > 0.1 requires inflaton field values close to or above the Planck scale. Recently, it has been claimed that r > 0.15 can be achieved with much smaller inflaton field values Δφ < M{sub Pl}/10. We show that in single-field slow-roll inflation, it is impossible to reconcile r > 0.1 with such small field values, independently of the form of the potential, and that the recent claim to the contrary is based on an invalid approximation. We conclude that the result of the BICEP2 measurement of r > 0.1, if confirmed, truly has the potential to rule out small-field models of single-field slow-roll inflation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Resurrecting quadratic inflation in no-scale supergravity in light of BICEP2

The magnitude of primordial tensor perturbations reported by the BICEP2 experiment is consistent with simple models of chaotic inflation driven by a single scalar field with a power-law potential ∝ φ{sup n} : n ≅ 2, in contrast to the WMAP and Planck results, which favored models resembling the Starobinsky R+R{sup 2} model if running of the scalar spectral index could be neglected. While models of inflation with a quadratic potential may be constructed in simple N = 1 supergravity, these constructions are more challenging in no-scale supergravity. We discuss here how quadratic inflation can be accommodated within supergravity, focusing primarily on the no-scale case. We also argue that the quadratic inflaton may be identified with the supersymmetric partner of a singlet (right-handed) neutrino, whose subsequent decay could have generated the baryon asymmetry via leptogenesis.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Higgs gravitational interaction, weak boson scattering, and Higgs inflation in Jordan and Einstein frames

We study gravitational interaction of Higgs boson through the unique dimension-4 operator ξH{sup †}HR, with H the Higgs doublet and R the Ricci scalar curvature. We analyze the effect of this dimensionless nonminimal coupling ξ on weak gauge boson scattering in both Jordan and Einstein frames. We explicitly establish the longitudinal-Goldstone equivalence theorem with nonzero ξ coupling in both frames, and analyze the unitarity constraints. We study the ξ-induced weak boson scattering cross sections at O(1−30) TeV scales, and propose to probe the Higgs-gravity coupling via weak boson scattering experiments at the LHC (14 TeV) and the next generation pp colliders (50-100 TeV). We further extend our study to Higgs inflation, and quantitatively derive the perturbative unitarity bounds via coupled channel analysis, under large field background at the inflation scale. We analyze the unitarity constraints on the parameter space in both the conventional Higgs inflation and the improved models in light of the recent BICEP2 data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

The problem with false vacuum Higgs inflation

We investigate the possibility of using the only known fundamental scalar, the Higgs, as an inflaton with minimal coupling to gravity. The peculiar appearance of a plateau or a false vacuum in the renormalised effective scalar potential suggests that the Higgs might drive inflation. For the case of a false vacuum we use an additional singlet scalar field, motivated by the strong CP problem, and its coupling to the Higgs to lift the barrier allowing for a graceful exit from inflation by mimicking hybrid inflation. We find that this scenario is incompatible with current measurements of the Higgs mass and the QCD coupling constant and conclude that the Higgs can only be the inflaton in more complicated scenarios.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

New sources of gravitational waves during inflation

We point out that detectable inflationary tensor modes can be generated by particle or string sources produced during inflation, consistently with the requirements for inflation and constraints from scalar fluctuations. We show via examples that this effect can dominate over the contribution from quantum fluctuations of the metric, occurring even when the inflationary potential energy is too low to produce a comparable signal. Thus a detection of tensor modes from inflation does not automatically constitute a determination of the inflationary Hubble scale.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Wiggly whipped inflation

Motivated by BICEP2 results on the CMB polarization B-mode which imply primordial gravitational waves are produced when the Universe has the expansion rate of about H ≈ 10{sup 14} GeV, and by deviations from a smooth power-law behavior for multipoles ℓ <50 in the CMB temperature anisotropy power spectrum found in the WMAP and Planck experiments, we have expanded our class of large field inflationary models that fit both the BICEP2 and Planck CMB observations consistently. These best-fitted large field models are found to have a transition from a faster roll to the slow roll V(φ)=m{sup 2} φ{sup 2}/2 inflation at a field value around 14.6 M{sub Pl} and thus a potential energy of V(φ) ∼ (10{sup 16} GeV){sup 4}. In general this transition with sharp features in the inflaton potential produces not only suppression of scalars relative to tensor modes at small k but also introduces wiggles in the primordial perturbation spectrum. These wiggles are shown to be useful to explain some localized features in the CMB angular power spectrum and can also have other observational consequences. Thus, primordial GW can be used now to make a tomography of inflation determining its fine structure. The resulting Wiggly Whipped Inflation scenario is described in details and the anticipated perturbation power spectra, CMB power spectra, non-Gaussianity and other observational consequences are calculated and compared to existing and forthcoming observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Statistical anisotropies in gravitational waves in solid inflation

Solid inflation can support a long period of anisotropic inflation. We calculate the statistical anisotropies in the scalar and tensor power spectra and their cross-correlation in anisotropic solid inflation. The tensor-scalar cross-correlation can either be positive or negative, which impacts the statistical anisotropies of the TT and TB spectra in CMB map more significantly compared with the tensor self-correlation. The tensor power spectrum contains potentially comparable contributions from quadrupole and octopole angular patterns, which is different from the power spectra of scalar, the cross-correlation or the scalar bispectrum, where the quadrupole type statistical anisotropy dominates over octopole.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Quantum cosmological consistency condition for inflation

We investigate the quantum cosmological tunneling scenario for inflationary models. Within a path-integral approach, we derive the corresponding tunneling probability distribution. A sharp peak in this distribution can be interpreted as the initial condition for inflation and therefore as a quantum cosmological prediction for its energy scale. This energy scale is also a genuine prediction of any inflationary model by itself, as the primordial gravitons generated during inflation leave their imprint in the B-polarization of the cosmic microwave background. In this way, one can derive a consistency condition for inflationary models that guarantees compatibility with a tunneling origin and can lead to a testable quantum cosmological prediction. The general method is demonstrated explicitly for the model of natural inflation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Just enough inflation: power spectrum modifications at large scales

We show that models of 'just enough' inflation, where the slow-roll evolution lasted only 50- 60 e-foldings, feature modifications of the CMB power spectrum at large angular scales. We perform a systematic analytic analysis in the limit of a sudden transition between any possible non-slow-roll background evolution and the final stage of slow-roll inflation. We find a high degree of universality since most common backgrounds like fast-roll evolution, matter or radiation-dominance give rise to a power loss at large angular scales and a peak together with an oscillatory behaviour at scales around the value of the Hubble parameter at the beginning of slow-roll inflation. Depending on the value of the equation of state parameter, different pre-inflationary epochs lead instead to an enhancement of power at low ℓ, and so seem disfavoured by recent observational hints for a lack of CMB power at ℓ∼< 40. We also comment on the importance of initial conditions and the possibility to have multiple pre-inflationary stages.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Inflation and uplifting with nilpotent superfields

Recently it was found that a broad class of existing inflationary models based on supergravity can be significantly simplified if some of the standard, unconstrained chiral superfields are replaced by nilpotent superfields, associated with Volkov-Akulov supersymmetry. The same method allows to simplify the existing models of uplifting of AdS vacua in string theory. In this paper we will show that one can go well beyond simplifying the models that already exist. We will propose a broad class of new models of chaotic inflation based on supergravity with nilpotent superfields, which simultaneously incorporate both inflation and uplifting. They provide a simple unified description of inflation and the present acceleration of the universe in the supergravity context.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

First test of high frequency Gravity Waves from inflation using Advanced LIGO

Inflation models ending in a first order phase transition produce gravitational waves (GW) via bubble collisions of the true vacuum phase. We demonstrate that these bubble collisions can leave an observable signature in Advanced LIGO, an upcoming ground-based GW experiment. These GW are dependent on two parameters of the inflationary model: ε represents the energy difference between the false vacuum and the true vacuum of the inflaton potential, and χ measures how fast the phase transition ends (χ ∼ the number of e-folds during the actual phase transition). Advanced LIGO will be able to test the validity of single-phase transition models within the parameter space 10{sup 7} GeV∼< ε{sup 1/4} ∼< 10{sup 10} GeV and 0.19 ∼< χ ∼< 1. If inflation occurred through a first order phase transition, then Advanced LIGO could be the first to discover high frequency GW from inflation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Estimation of inflation parameters for Perturbed Power Law model using recent CMB measurements

Cosmic Microwave Background (CMB) is an important probe for understanding the inflationary era of the Universe. We consider the Perturbed Power Law (PPL) model of inflation which is a soft deviation from Power Law (PL) inflationary model. This model captures the effect of higher order derivative of Hubble parameter during inflation, which in turn leads to a non-zero effective mass m{sub eff} for the inflaton field. The higher order derivatives of Hubble parameter at leading order sources constant difference in the spectral index for scalar and tensor perturbation going beyond PL model of inflation. PPL model have two observable independent parameters, namely spectral index for tensor perturbation ν{sub t} and change in spectral index for scalar perturbation ν{sub st} to explain the observed features in the scalar and tensor power spectrum of perturbation. From the recent measurements of CMB power spectra by WMAP, Planck and BICEP-2 for temperature and polarization, we estimate the feasibility of PPL model with standard ΛCDM model. Although BICEP-2 claimed a detection of r=0.2, estimates of dust contamination provided by Planck have left open the possibility that only upper bound on r will be expected in a joint analysis. As a result we consider different upper bounds on the value of r and show that PPL model can explain a lower value of tensor to scalar ratio (r<0.1 or r<0.01) for a scalar spectral index of n{sub s}=0.96 by having a non-zero value of effective mass of the inflaton field m{sup 2}{sub eff}/H{sup 2}. The analysis with WP + Planck likelihood shows a non-zero detection of m{sup 2}{sub eff}/H{sup 2} with 5.7 σ and 8.1 σ respectively for r<0.1 and r<0.01. Whereas, with BICEP-2 likelihood m{sup 2}{sub eff}/H{sup 2} = −0.0237 ± 0.0135 which is consistent with zero.

79 ASTRONOMY AND ASTROPHYSICS↗