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DOE OSTI2014

Quantum corrections in Higgs inflation: the real scalar case

We present a critical discussion of quantum corrections, renormalisation, and the computation of the beta functions and the effective potential in Higgs inflation. In contrast with claims in the literature, we find no evidence for a disagreement between the Jordan and Einstein frames, even at the quantum level. For clarity of discussion we concentrate on the case of a real scalar Higgs. We first review the classical calculation and then discuss the back reaction of gravity. We compute the beta functions for the Higgs quartic coupling and non-minimal coupling constant. Here, the mid-field regime is non-renormalisable, but we are able to give an upper bound on the 1-loop corrections to the effective potential. We show that, in computing the effective potential, the Jordan and Einstein frames are compatible if all mass scales are transformed between the two frames. As such, it is consistent to take a constant cutoff in either the Jordan or Einstein frame, and both prescriptions yield the same result for the effective potential. Our results are extended to the case of a complex scalar Higgs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Does Planck really rule out monomial inflation?

We consider the modifications of monomial chaotic inflation models due to radiative corrections induced by inflaton couplings to bosons and/or fermions necessary for reheating. To the lowest order, ignoring gravitational corrections and treating the inflaton as a classical background field, they are of the Coleman-Weinberg type and parametrized by the renormalization scale μ. In cosmology, there are not enough measurements to fix μ so that we end up with a family of models, each having a slightly different slope of the potential. We demonstrate by explicit calculation that within the family of chaotic φ{sup 2} models, some may be ruled out by Planck whereas some remain perfectly viable. In contrast, radiative corrections do not seem to help chaotic φ{sup 4} models to meet the Planck constraints.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Rescuing quadratic inflation

Inflationary models based on a single scalar field φ with a quadratic potential V = ½m{sup 2}φ{sup 2} are disfavoured by the recent Planck constraints on the scalar index, n{sub s}, and the tensor-to-scalar ratio for cosmological density perturbations, r{sub T}. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on n{sub s} and r{sub T}. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Linking Starobinsky-type inflation in no-scale supergravity to MSSM

A novel realization of the Starobinsky inflationary model within a moderate extension of the Minimal Supersymmetric Standard Model (MSSM) is presented. The proposed superpotential is uniquely determined by applying a continuous R and a Z{sub 2} discrete symmetry, whereas the Kähler potential is associated with a no-scale-type SU(54,1)/SU(54) × U(1){sub R} × Z{sub 2} Kähler manifold. The inflaton is identified with a Higgs-like modulus whose the vacuum expectation value controls the gravitational strength. Thanks to a strong enough coupling (with a parameter c{sub T} involved) between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton with c{sub T} ≥ 76 and the corresponding effective theory being valid up to the Planck scale. The inflationary observables turn out to be in agreement with the current data and the inflaton mass is predicted to be 3·10{sup 13}GeV. At the cost of a relatively small superpotential coupling constant, the model offers also a resolution of the μ problem of MSSM for c{sub T} ≤ 4500 and gravitino heavier than about 10{sup 4}GeV. Supplementing MSSM by three right-handed neutrinos we show that spontaneously arising couplings between the inflaton and the particle content of MSSM not only ensure a sufficiently low reheating temperature but also support a scenario of non-thermal leptogenesis consistently with the neutrino oscillation parameters.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Why does the effective field theory of inflation work?

The effective field theory (EFT) of inflation has become the preferred method for computing cosmological correlation functions of the curvature fluctuation, ζ. It makes explicit use of the soft breaking of time diffeomorphisms by the inflationary background to organize the operators expansion in the action of the Goldstone mode π associated with this breaking. Despite its ascendancy, there is another method for calculating ζ correlators, involving the direct calculation of the so-called Horndeski action order by order in powers of ζ and its derivatives. The question we address in this work is whether or not the ζ correlators calculated in these seemingly different ways are in fact the same. The answer is that the actions to cubic order in either set of variables do indeed give rise to the same ζ bispectra, but that to make this equivalence manifest requires a careful understanding of the non-linear transformations relating π to ζ and how boundary terms in the actions are affected by imposing this relation. As a by product of our study we find that the calculations in the π language can be simplified considerably in a way that allows us to use only the linear part of the π−ζ relation simply by changing the coefficients of some of the operators in the EFT. We also note that a proper accounting of the boundary terms will be of the greatest importance when computing the bispectrum for more general initial states than the Bunch-Davies one.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Power spectrum and non-Gaussianities in anisotropic inflation

We study the planar regime of curvature perturbations for single field inflationary models in an axially symmetric Bianchi I background. In a theory with standard scalar field action, the power spectrum for such modes has a pole as the planarity parameter goes to zero. We show that constraints from back reaction lead to a strong lower bound on the planarity parameter for high-momentum planar modes and use this bound to calculate the signal-to-noise ratio of the anisotropic power spectrum in the CMB, which in turn places an upper bound on the Hubble scale during inflation allowed in our model. We find that non-Gaussianities for these planar modes are enhanced for the flattened triangle and the squeezed triangle configurations, but show that the estimated values of the f{sub NL} parameters remain well below the experimental bounds from the CMB for generic planar modes (other, more promising signatures are also discussed). For a standard action, f{sub NL} from the squeezed configuration turns out to be larger compared to that from the flattened triangle configuration in the planar regime. However, in a theory with higher derivative operators, non-Gaussianities from the flattened triangle can become larger than the squeezed configuration in a certain limit of the planarity parameter.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Higgs dynamics during inflation

We investigate inflationary Higgs dynamics and constraints on the Standard Model parameters assuming the Higgs potential, computed to next-to-next leading order precision, is not significantly affected by new physics. For a high inflationary scale H ∼ 10{sup 14} GeV suggested by BICEP2, we show that the Higgs is a light field subject to fluctuations which affect its dynamics in a stochastic way. Starting from its inflationary value the Higgs must be able to relax to the Standard Model vacuum well before the electroweak scale. We find that this is consistent with the high inflationary scale only if the top mass m{sub t} is significantly below the best fit value. The region within 2σ errors of the measured m{sub t}, the Higgs mass m{sub h} and the strong coupling α{sub s} and consistent with inflation covers approximately the interval m{sub t}∼<171.8 GeV+0.538(m{sub h}−125.5 GeV) with 125.4 GeV∼<m{sub h}∼<126.3 GeV. If the low top mass region could be definitively ruled out, the observed high inflationary scale alone, if confirmed, would seem to imply new physics necessarily modifying the Standard Model Higgs potential below the inflationary scale.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

The TT, TB, EB and BB correlations in anisotropic inflation

The ongoing and future experiments will measure the B-mode from different sky coverage and frequency bands, with the potential to reveal non-trivial features in polarization map. In this work we study the TT, TB, EB and BB correlations associated with the B-mode polarization of CMB map in models of charged anisotropic inflation. The model contains a chaotic-type large field complex inflaton which is charged under the U(1) gauge field. We calculate the statistical anisotropies generated in the power spectra of the curvature perturbation, the tensor perturbation and their cross-correlation. It is shown that the asymmetry in tensor power spectrum is a very sensitive probe of the gauge coupling. While the level of statistical anisotropy in temperature power spectrum can be small and satisfy the observational bounds, the interactions from the gauge coupling can induce large directional dependence in tensor modes. This will leave interesting anisotropic fingerprints in various correlations involving the B-mode polarization such as the TB cross-correlation which may be detected in upcoming Planck polarization data. In addition, the TT correlation receives an anisotropic contribution from the tensor sector which naturally decays after l ∼> 100. We expect that the mechanism of using tensor sector to induce asymmetry at low l to be generic which can also be applied to address other low l CMB anomalies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Standard Model with a real singlet scalar and inflation

We study the post-inflationary dynamics of the Standard Model Higgs and a real singlet scalar s, coupled together through a renormalizable coupling λ{sub sh}h{sup 2}s{sup 2}, in a Z{sub 2} symmetric model that may explain the observed dark matter abundance and/or the origin of baryon asymmetry. The initial values for the Higgs and s condensates are given by inflationary fluctuations, and we follow their dissipation and relaxation to the low energy vacua. We find that both the lowest order perturbative and the non-perturbative decays are blocked by thermal effects and large background fields and that the condensates decay by two-loop thermal effects. Assuming instant reheating at T=10{sup 16} GeV, the characteristic temperature for the Higgs condensate thermalization is found to be T{sub h} ∼ 10{sup 14} GeV, whereas s thermalizes typically around T{sub s} ∼ 10{sup 6} GeV. By that time, the amplitude of the singlet is driven very close to the vacuum value by the expansion of the universe, unless the portal coupling takes a value λ{sub sh}∼< 10{sup -7} and the singlet s never thermalizes. With these values of the coupling, it is possible to slowly produce a sizeable fraction of the observed dark matter abundance via singlet condensate fragmentation and thermal Higgs scattering. Physics also below the electroweak scale can therefore be affected by the non-vacuum initial conditions generated by inflation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Dark matter chaotic inflation in light of BICEP2

We propose an economical model in which a singlet {sub 2}-odd scalar field accounts for the primordial inflation and the present dark matter abundance simultaneously in the light of recent BICEP2 result. Interestingly, the reheating temperature and the thermal dark matter abundance are closely connected by the same interaction between the singlet scalar and the standard model Higgs. In addition, the reheating temperature turns out to be quite high, T{sub R} ∼> 10{sup 12} GeV, and hence the thermal leptogenesis is compatible with this model. Therefore, it can be one of the simplest cosmological scenarios.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Curvaton in large field inflation

We comprehensively explore the quadratic curvaton models in the chaotic inflation. In the light of the BICEP2 result r ≈ 0.2, all model parameters and relevant observables are computed. It is found the curvaton field value is constrained into a narrow range, σ{sub *} = O(10{sup −2}–10{sup −1}) and the running of the spectral index is n{sub s}'∼>−10{sup −3}. We show that if the curvaton is added, the models are heavily degenerated on the n{sub s} - r plane. However, introducing a new plane, the degeneracy can be resolved. To distinguish the curvaton models, precise measurements of not only r but also n{sub s}' and the tensor tilt n{sub T} are required.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Inflation and dark energy from f(R) gravity

The standard Starobinsky inflation has been extended to the R + α R{sup n} - β R{sup 2-n} model to obtain a stable minimum of the Einstein frame scalar potential of the auxiliary field. As a result we have obtained obtain a scalar potential with non-zero value of residual vacuum energy, which may be a source of Dark Energy. Our results can be easily consistent with PLANCK or BICEP2 data for appropriate choices of the value of n.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Evolution of the spectral index after inflation

In this article we investigate the time evolution of the adiabatic (curvature) and isocurvature (entropy) spectral indices after inflation era for all cosmological scales with two different initial conditions. For this purpose, we first extract an explicit equation for the time evolution of the comoving curvature perturbation (which may be known as the generalized Mukhanov-Sasaki equation). It would be cleared that the evolution of adiabatic spectral index severely depends on the initial conditions moreover, as expected it is constant only for the super-Hubble scales and adiabatic initial conditions. Additionally, the adiabatic spectral index after recombination approaches a constant value for the isocurvature perturbations. Finally, we re-investigate the Sachs-Wolfe effect and show that the fudge factor 1/3 in the adiabatic ordinary Sachs-Wolfe formula must be replaced by 0.4.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Anisotropy in inflation with non-minimal coupling

We study a new anisotropic inflation model, with an inflaton field nonminimally coupled with the gravity and a vector field. We find that the anisotropic attractor solution exists not only in the weak curvature coupling limit, but more interestingly in the strong curvature coupling limit as well. We show that in the strong curvature coupling limit, the contribution from the anisotropy is greatly suppressed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Testing inflation and curvaton scenarios with CMB distortions

Prior to recombination, Silk damping causes the dissipation of energy from acoustic waves into the monopole of the Cosmic Microwave Background (CMB), resulting in spectral distortions. These can be used to probe the primordial scalar power spectrum on smaller scales than it is possible with CMB anisotropies. An enhancement of power on these scales is nevertheless required for the resulting distortions to be detectable by future experiments like PIXIE. In this paper, we examine all 49 single-field inflation models listed by Martin et al. in the Encyclopaedia Inflationaris [1] and find that only one of these may lead to a detectable level of distortions in a tuned region of its parameter space, namely the original hybrid model. Three effective multi-field scenarios are also studied: with softly and suddenly turning trajectories, and with a mild waterfall trajectory. Softly turning trajectories do not induce distortions at any detectable level, whereas a sudden turn in the field space or a mild waterfall trajectory predicts a peak (plus damped oscillations in the sudden turn case) in the scalar power spectrum, which can lead to an observable amount of CMB distortions. Finally, another scenario leading to potentially detectable distortions involves a curvaton whose blue spectrum is subdominant on CMB angular scales and overtakes the inflaton spectrum on smaller scales. In this case however, we show that the bounds from ultra compact minihaloes are not satisfied. Expectations for an ultimate PRISM-class experiment characterized by an improvement in sensitivity by a factor of ten are discussed for some models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Non-Abelian dynamics in the resonant decay of the Higgs after inflation

We study the resonant decay of the Higgs condensate into weak gauge bosons after inflation and estimate the corrections arising from the non-Abelian self-interactions of the gauge fields. We find that non-Abelian interaction terms induce an effective mass which tends to shut down the resonance. For the broad resonance relevant for the Standard Model Higgs the produced gauge particles backreact on the dynamics of the Higgs condensate before the non-Abelian terms grow large. The non-Abelian terms can however significantly affect the final stages of the resonance after the backreaction. In the narrow resonance regime, which may be important for extensions of the Standard Model, the non-Abelian terms affect already the linear stage and terminate the resonance before the Higgs condensate is affected by the backreaction of decay products.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Combined features in the primordial spectra induced by a sudden turn in two-field DBI inflation

We investigate the features generated by a sharp turn along the inflationary trajectory in a two-field model of Dirac-Born-Infeld inflation, where one of the fields is heavy. Distinct features are generated by two different effects: the mixing of the light and heavy modes during the turn, on the one hand, and the resonance between the oscillations along the heavy direction after the turn, on the other hand. Contrary to models with standard kinetic terms, the resonance effect is not strongly suppressed because the action contains derivative interactions. Working in the potential basis, we study the oscillations after the turn and compute the amplitude of the mixing and resonance features in the power spectrum, as well as in the bispectrum for the latter effect. We find that the amplitudes and positions of these combined features obey specific consistency relations, which could be confronted with cosmological data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Scale-dependent hemispherical asymmetry from general initial state during inflation

We consider a general initial state for inflation as the mechanism for generating scale-dependent hemispherical asymmetry. An observable scale-dependent non-Gaussianity is generated that leads to observable hemispherical asymmetry from the super-horizon long mode modulation. We show that the amplitude of dipole asymmetry falls off exponentially on small angular scales which can address the absence of dipole asymmetry at these scales. In addition, depending on the nature of non-vaccum initial state, the amplitude of the dipole asymmetry has oscillatory features which can be detected in a careful CMB map analysis. Furthermore, we show that the non-vacuum initial state provides a natural mechanism for enhancing the super horizon long mode perturbation as required to generate the dipole asymmetry.

79 ASTRONOMY AND ASTROPHYSICS↗