Observational test of two-field inflation (original) (raw)

Adiabatic and isocurvature perturbations from inflation: Power spectra and consistency relations

Physical Review D, 2001

We study adiabatic and isocurvature perturbations produced during a period of cosmological inflation. We compute the power spectra and cross spectra of the curvature and isocurvature modes, as well as the tensor perturbation spectrum in terms of the slow-roll parameters. We provide two consistency relations for the amplitudes and spectral indices of the corresponding power spectra. These relations represent a definite prediction and a test of inflationary models which should be adopted when studying cosmological perturbations through the Cosmic Microwave Background in forthcoming satellite experiments.

Density perturbations from two-field inflation

1996

We discuss metric perturbations produced during a period of inflation in the early universe where two scalar fields evolve. The final scalar perturbation spectrum can be calculated in terms of the perturbed expansion along neighbouring trajectories in field-space. In the usual single field case this is fixed by the values of the fields at horizon-crossing, but in the presence of more than one field there is no longer a unique slow-roll trajectory. The presence of entropy as well as adiabatic fluctuations means that the super-horizon-sized metric perturbation ζ may no longer be conserved and the evolution must be integrated along the whole of the subsequent trajectory. In general there is an inequality between the ratio of tensor to scalar perturbations and the tilt of the gravitational wave spectrum, which becomes an equality when only adiabatic perturbations are possible and ζ is conserved.

Correlation-consistency cartography of the double-inflation landscape

Physical Review D, 2003

We show explicitly some exciting features of double-inflation: (i) it can often lead to strongly correlated adiabatic and entropy (isocurvature) power spectra. (ii) The two-field slow-roll consistency relations can be violated when the correlation is large at Hubble crossing. (iii) The spectra of adiabatic and entropy perturbations can be strongly scale-dependent and tilted toward either the red or blue. These effects are typically due to a light or time-dependent entropy mass and a nonnegligible angular velocity in field space during inflation. They are illustrated via a multi-parameter numerical search for correlations in two concrete models. The correlation is found to be particularly strong in a supersymmetric scenario due to rapid growth of entropy perturbations in the tachyonic region separating the two inflationary stages. Our analysis suggests that realistic double-inflation models will provide a rich and fruitful arena for the application of future cosmic data sets and new approximation schemes which go beyond slow-roll.

Isocurvature perturbations in multiple inflationary models

Physical review D: Particles and fields, 1994

Dynamics of long-wave isocurvature perturbations during an inflationary stage in multiple (multi-component) inflationary models is calculated analytically for the case where scalar fields producing this stage interact between themselves through gravity only. This enables to determine correct amplitudes of such perturbations produced by vacuum quantum fluctuations of the scalar fields during the multiple inflationary stage. Exact matching to a post-inflationary evolution that gives the amplitude of isocurvature perturbations in the cold dark matter model with radiation is performed in the case where a massive inflaton field remains uncoupled from usual matter up to the present time. For this model, isocurvature perturbations are smaller than adiabatic ones in the region of the break in the perturbation spectrum which arises due to a transition between the two phases of inflation, but they may be much bigger and have a maximum at much shorter scales. The case of an inflaton with a quartic coupling which remains uncoupled after inflation is considered, too.

Metric perturbations in two-field inflation

Physical Review D, 1996

We study the metric perturbations produced during inflation in models with two scalar fields evolving simultaneously. In particular, we emphasize how the large-scale curvature perturbation ζ on fixed energy density hypersurfaces may not be conserved in general for multiple field inflation due to the presence of entropy as well as adiabatic fluctuations. We show that the usual method of solving the linearized perturbation equations is equivalent to the recently proposed analysis of Sasaki and Stewart in terms of the perturbed expansion along neighboring trajectories in field-space. In the case of a separable potential it is possible to compute in the slow-roll approximation the spectrum of density perturbations and gravitational waves at the end of inflation. In general there is an inequality between the ratio of tensor to scalar perturbations and the tilt of the gravitational wave spectrum, which becomes an equality when only adiabatic perturbations are possible and ζ is conserved.

Confrontation of a double inflationary cosmological model with observations

The Astrophysical Journal, 1994

CDM models with non-scale-free step-like spectra of adiabatic perturbations produced in a realistic double inflationary model are compared with recent observational data. The model contains two additional free parameters relatively to the standard CDM model with the flat (n = 1) initial spectrum. Results of the COBE experiment are used for the determination of a free overall spectrum normalization. Then predictions for the galaxy biasing parameter, the variance for "counts in cells", the galaxy angular correlation function, bulk flow peculiar velocities and the Mach number test are obtained. Also considered are conditions for galaxy and quasar formation. Observational data strongly restricts allowed values for the two remaining model parameters. However, a non-empty region for them satisfying all considered tests is found.

Inflationary signatures of single-field models beyond slow-roll

If the expansion of the early Universe was not purely de Sitter, the statistical imprints of the primordial density perturbation on the cosmic microwave background can be quite different from those following slow-roll inflation. In this paper we study the inflationary signatures of all single-field models not plagued by ghost-like instabilities. We assume small deviations from exact scale-invariance, as supported by current cosmological constraints, allow for a rapid change of the Hubble parameter and the phase speed of scalar fluctuations. We obtain the propagator of scalar fluctuations and compute the bispectrum, keeping next-order corrections proportional to the deviation of the spectral index from unity. These theories offer an explicit example where the shape and scale dependences of the bispectrum are highly non-trivial for reasonable breaking of slow-roll.

Inflation models and observation

Journal of Cosmology and Astroparticle Physics, 2006

We consider small-field models which invoke the usual framework for the effective field theory, and large-field models which go beyond that. Present and future possibilities for discriminating between the models are assessed, on the assumption that the primordial curvature perturbation is generated during inflation. With PLANCK data, the theoretical and observational uncertainties on the spectral index will be comparable, providing useful discrimination between small-field models. Further discrimination between models may come later through the tensor fraction, the running of the spectral index and non-gaussianity. The prediction for the trispectrum in a generic multi-field inflation model is given for the first time.

Oscillations during inflation and the cosmological density perturbations

Physical Review D, 2001

Adiabatic (curvature) perturbations are produced during a period of cosmological inflation that is driven by a single scalar field, the inflaton. On particle physics grounds -though -it is natural to expect that this scalar field is coupled to other scalar degrees of freedom. This gives rise to oscillations between the perturbation of the inflaton field and the perturbations of the other scalar degrees of freedom, similar to the phenomenon of neutrino oscillations. Since the degree of the mixing is governed by the squared mass matrix of the scalar fields, the oscillations can occur even if the energy density of the extra scalar fields is much smaller than the energy density of the inflaton field. The probability of oscillation is resonantly amplified when perturbations cross the horizon and the perturbations in the inflaton field may disappear at horizon crossing giving rise to perturbations in scalar fields other than the inflaton. Adiabatic and isocurvature perturbations are inevitably correlated at the end of inflation and we provide a simple expression for the cross-correlation in terms of the slow-roll parameters.

The importance of slow-roll corrections during multi-field inflation

Journal of Cosmology and Astroparticle Physics, 2012

We re-examine the importance of slow-roll corrections during the evolution of cosmological perturbations in models of multi-field inflation. We find that in many instances the presence of light degrees of freedom leads to situations in which next to leading order slow-roll corrections become significant. Examples where we expect such corrections to be crucial include models in which modes exit the Hubble radius while the inflationary trajectory undergoes an abrupt turn in field space, or during a phase transition. We illustrate this with two examples -hybrid inflation and double quadratic inflation. Utilizing both analytic estimates and full numerical results, we find that corrections can be as large as 20%. Our results have implications for many existing models in the literature, as these corrections must be included to obtain accurate observational predictions -particularly given the level of accuracy expected from CMB experiments such as Planck.