Running of the scalar spectral index from inflationary models

Monthly Notices of the Royal Astronomical Society, 1998

Accurate estimation of cosmological parameters from microwave background anisotropies requires high-accuracy understanding of the cosmological model. Normally, a power-law spectrum of density perturbations is assumed, in which case the spectral index n can be measured to around ±0.004 using microwave anisotropy satellites such as MAP and Planck. However, inflationary models generically predict that the spectral index n of the density perturbation spectrum will be scale-dependent. We carry out a detailed investigation of the measurability of this scale dependence by Planck, including the influence of polarization on the parameter estimation. We also estimate the increase in the uncertainty in all other parameters if the scale dependence has to be included. This increase applies even if the scale dependence is too small to be measured unless it is assumed absent, but is shown to be a small effect. We study the implications for inflation models, beginning with a brief examination of the generic slow-roll inflation situation, and then move to a detailed examination of a recentlydevised hybrid inflation model for which the scale dependence of n may be observable.

Physical Review Letters, 2002

Motivated by the prospect of testing inflation from precision cosmic microwave background observations, we present analytic results for scalar and tensor perturbations in single-field inflation models based on the application of uniform approximations. This technique is systematically improvable, possesses controlled error bounds, and does not rely on assuming the slow-roll parameters to be constant. We provide closed-form expressions for the power spectra and the corresponding scalar and tensor spectral indices.

Physical Review D, 2008

A model is developed in which the inflaton potential experiences a sudden small change in its second derivative (the effective mass of the inflaton). An exact treatment demonstrates that the resulting density perturbation has a quasi-flat power spectrum with a break in its slope (a step in ns). The step in the spectral index is modulated by characteristic oscillations and results in large running of the spectral index localised over a few e-folds of scales. A field-theoretic model giving rise to such behaviour of the inflationary potential is based on a fast phase transition experienced by a second scalar field weakly coupled to the inflaton. Such a transition is similar to that which terminates inflation in the hybrid inflationary scenario. This scenario suggests that the observed running of the spectral index in the WMAP data may be caused by a fast second order phase transition which occurred during inflation.

Physical Review D, 2007

We revisit the problem of constraining steps in the inflationary potential with cosmological data. We argue that a step in the inflationary potential produces qualitatively similar oscillations in the primordial power spectrum, independently of the details of the inflationary model. We propose a phenomenological description of these oscillations and constrain these features using a selection of cosmological data including the baryonic peak data from the correlation function of luminous red galaxies in the Sloan Digital Sky Survey. Our results show that degeneracies of the oscillation with standard cosmological parameters are virtually non-existent. The inclusion of new data severely tightens the constraints on the parameter space of oscillation parameters with respect to older work. This confirms that extensions to the simplest inflationary models can be successfully constrained using cosmological data.

Physical Review D, 1993

We investigate models of 'intermediate' inflation, where the scale factor a(t) grows as a(t) = exp(At f), 0 < f < 1, A constant. These solutions arise as exact analytic solutions for a given class of potentials for the inflaton φ. For a simpler class of potentials falling off as a power of φ they arise as slow-roll solutions, and in particular they include, for f = 2/3, the class of potentials which give the Harrison-Zel'dovich spectrum. The perturbation spectral index n can be greater than unity on astrophysical scales. It is also possible to generate substantial gravitational waves while keeping the scalar spectrum close to scale-invariance; this latter possibility performs well when confronted with most observational data.

2000

Next-to-leading order expressions related to Stewart-Lyth inverse problem are used to determine the inflationary models with a tensorial power spectrum described by a scale-invariant spectral index. Beyond power-law inflation, solutions are characterized by scale-dependent scalar indices. These models can be used as assumption on the generation of primordial perturbations to test for scale dependence of scalar index at large angular

2021

The primordial power spectrum informs the possible inflationary histories of our universe. Given a power spectrum, the ensuing cosmic microwave background is calculated and compared to the observed one. Thus, one focus of modern cosmology is building wellmotivated inflationary models that predict the primordial power spectrum observables. The common practice uses analytic terms for the scalar spectral index ns and the index running α, forgoing the effort required to evaluate the model numerically. However, the validity of these terms has never been rigorously probed and relies on perturbative methods, which may lose their efficacy for large perturbations. The requirement for more accurate theoretical predictions becomes crucial with the advent of highly sensitive measuring instruments. This paper probes the limits of the perturbative treatment that connects inflationary potential parameters to primordial power spectrum observables. We show that the validity of analytic approximation...

k-inflation represents the most general single-field inflation, in which the perturbations usually obey an equation of motion with a time-dependent sound speed. In this paper, we study the observational predictions of the k-inflation by using the high-order uniform asymptotic approximation method. We calculate explicitly the slow-roll expressions of the power spectra, spectral indices, and running of the spectral indices for both the scalar and tensor perturbations. These expressions are all written in terms of the Hubble and sound speed flow parameters. It is shown that the previous results obtained by using the first-order uniform asymptotic approximation have been significantly improved by the high-order corrections of the uniform asymptotic approximations. Furthermore, we also check our results by comparing them with the ones obtained by other approximation methods, including the Green's function method, WKB approximation, and improved WKB approximation, and find the relative errors.

Physical Review Letters, 2014

2021

We study small field models of inflation, which, against previous expectations, yield significant Gravitational Wave (GW) signal while reproducing other measured observable quantities in the Cosmic Microwave Background (CMB). We numerically study these, using previously published analytic works as general guidelines. We first discuss the framework necessary to understand model building, and some of its motivations. We review the slow-roll paradigm, derive the slow-roll parameters, and discuss different formulations thereof. We review the Lyth bound and its theoretical descendants, we outline the small/large field taxonomy and their characterization in the current nomenclature. We then present our models and the methods employed in their building and examination. We employ MCMC simulations to evaluate model likelihood and by process of marginalization extract the most probable coefficients for these inflationary potentials. An additional method employed is a multinomial fit, where we...

2019

We propose a new approach to investigate inflation in a model-independent way, and in particular to elaborate the involved observables, through the introduction of the “scale factor potential”. Through its use one can immediately determine the inflation end, which corresponds to its first (and global) minimum. Additionally, we express the inflationary observables in terms of its logarithm, using as independent variable the e-folding number. As an example, we construct a new class of scalar potentials that can lead to the desired spectral index and tensor-to-scalar ratio, namely $$n_s \approx 0.965$$ n s ≈ 0.965 and $$r \sim 10^{-4}$$ r ∼ 10 - 4 for 60 e -folds, in agreement with observations.

Physical Review D, 2004

We present a numerical integration of the cosmological scalar perturbation equations in warm inflation. The initial conditions are provided by a discussion of the thermal fluctuations of an inflaton field and thermal radiation using a combination of thermal field theory and thermodynamics. The perturbation equations include the effects of a damping coefficient Γ and a thermodynamic potential V . We give an analytic expression for the spectral index of scalar fluctuations in terms of a new slow-roll parameter constructed from Γ. A series of toy models, inspired by spontaneous symmetry breaking and a known form of the damping coefficient, lead to a spectrum with ns > 1 on large scales and ns < 1 on small scales.

The Tenth Marcel Grossmann Meeting, 2006

In the framework of a flat FLRW model we derive an inflationary regime in which the scalar field, laying on the plateau of its potential, admits a linear time dependence and remains close to a constant value. The behaviour of inhomogeneous perturbations is determined on the background metric in agreement to the "slow-rolling" approximation. We show that the inhomogeneous scales which before inflation were not much greater then the physical horizon, conserve their spectrum (almost) unaltered after the de Sitter phase.

Journal of Cosmology and Astroparticle Physics, 2005

We propose a general inverse formula for extracting inflationary parameters from the observed power spectrum of cosmological perturbations. Under the general slowroll scheme, which helps to probe the properties of inflation in a model independent way, we invert the leading order, single field, power spectrum formula. We also give some physically interesting examples to demonstrate its wide applicability and illuminate its properties.

Physical Review D, 2000

We evaluate the observational constraints on the spectral index n, in the context of the ΛCDM hypothesis which represents the simplest viable cosmology. We first take n to be practically scaleindependent. Ignoring reionization, we find at a nominal 2-σ level n ≃ 1.0 ± 0.1. If we make the more realisitic assumption that reionization occurs when a fraction f ∼ 10 −5 to 1 of the matter has collapsed, the 2-σ lower bound is unchanged while the 1-σ bound rises slightly. These constraints are compared with the prediction of various inflation models. Then we investigate the two-parameter scale-dependent spectral index, predicted by running-mass inflation models, and find that present data allow significant scale-dependence of n, which occurs in a physically reasonable regime of parameter space.