Back-reaction effect in power-law inflation

We propose a general inverse formula for extracting inflationary parameters from the observed power spectrum of cosmological perturbations. Under the general slow-roll 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.

Recently there have been differing viewpoints on how to evaluate the curvature power spectrum generated during inflation. Since the primordial curvature power spectrum is the seed for structure formation and provides a link between observations and inflationary parameters, it is important to resolve any disagreements over the expression for the power spectrum. In this article we discuss these differing viewpoints and indicate issues that are relevant to both approaches. We th...

In a general single field inflationary model we consider the effects of long wavelength scalar fluctuations on the effective expansion rate and equation of state seen by a class of free falling observers, using a physical gauge invariant formulation. In a previous work we showed that for a free massive inflaton no backreaction is observed within some constraints. In this paper we extend the validity of our previous results to the case of an arbitrary self-interacting inflatio...

We develop a nonperturbative method through the Hartree factorization to examine the quantum fluctuation effects on the single-field inflationary models in a spatially flat FRW cosmological space-time. Apart from the background field equation as well as the Friedmann equation with the corrections of quantum field fluctuations, the modified Mukhanov-Sasaki equations for the mode functions of the quantum scalar field are also derived by introducing the nonzero $\Delta_B$ term. ...

It has recently been suggested that Planck scale physics may effect the evolution of cosmological fluctuations in the early stages of cosmological inflation in a non-trivial way, leading to an excited state for modes whose wavelength is super-Planck but sub-Hubble. In this case, the issue of how this excited state back-reacts on the background space-time arises. In fact, it has been suggested that such back-reaction effects may lead to tight constraints on the magnitude of po...

In this work we determine the power spectrum of the gravitational potential of the primordial fluctuations for an inflationary model whose \emph{inflaton} is a non-canonical scalar field of the tachyon-type. The respective background field equations for an inverse-square potential produce a power-law inflation, and it is explicitly shown that for such a potential the power spectrum tends to be scale-independent for highly accelerated regimes in the inflationary expansion.

This article provides an introductory review of inflation and cosmological perturbation theory. I begin by motivating the need for an epoch of inflation during the early stages of the radiation dominated era, and describe how inflation is typically achieved using scalar fields. Then, after an overview of linear cosmological perturbation theory, I derive the equations governing the perturbations, and outline the generation of the scalar and the tensor perturbations during infl...

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 correspondi...

The presence of cosmological fluctuations influences the background cosmology in which the perturbations evolve. This back-reaction arises as a second order effect in the cosmological perturbation expansion. The effect is cumulative in the sense that all fluctuation modes contribute to the change in the background geometry, and as a consequence the back-reaction effect can be large even if the amplitude of the fluctuation spectrum is small. We review two approaches used to qu...

Fundamental formulae representing the density perturbation spectrums generated in inflationary scenarios are rigorously proved. Quantum fluctuations as initial conditions for structure generation in some inflationary era can be calculated in general scale. Thus, we could avoid the matching of the large and the small scale results at the horizon crossing epoch. This is possible because the perturbed scalar field equation in a special gauge has some remarkable nice properties. ...