Reconstructing the inflaton potential—an overview

We obtain observational constraints on Randall-Sundrum type II braneworld inflation using a compilation of data including WMAP, the 2dF and latest SDSS galaxy redshift surveys. We place constraints on three classes of inflation models (large-field, small-field and hybrid models) in the high-energy regime, which exhibit different behaviour compared to the low-energy case. The quartic potential is outside the 2σ observational contour bound for a number of e-folds less than 60, and steep inflation driven by an exponential potential is excluded because of its high tensor-to-scalar ratio. It is more difficult to strongly constrain small-field and hybrid models due to additional freedoms associated with the potentials, but we obtain upper bounds for the energy scale of inflation and the model parameters in certain cases. We also discuss possible ways to break the degeneracy of consistency relations and inflationary observables.

Section: Constraints On Braneworld Inflationmentioning

confidence: 99%

Constraints on braneworld inflation from CMB anisotropies

Tsujikawa¹,

Liddle²

2004

“…For single field inflationary models, Hubble parameter H(k) and its evolution during inflation can be translated into the inflationary potential using Hamilton-Jacobi formulation [17,18] as,…”

Section: Background Of Perturbed Power Law (Ppl) Model Of Inflationmentioning

confidence: 99%

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

Mukherjee

Das

Joy³

et al. 2015

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 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 t and change in spectral index for scalar perturbation ν 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 s = 0.96 by having a non-zero value of effective mass of the inflaton field m 2 eff H 2 . The analysis with WP+ Planck likelihood shows a non-zero detection of m 2 eff H 2 with 5.7 σ and 8.1 σ respectively for r < 0.1 and r < 0.01. Whereas, with BICEP-2 likelihood m 2 eff H 2 = −0.0237 ± 0.0135 which is consistent with zero.

“…Most earlier studies regarding the form of an inflationary potential relied on a prior choice of the potential V (φ), or on slow-roll approximations in the calculation of power spectra and their relation to the mass of the field φ during inflation (see [14] for a review). The latter approach can at best produce the tail of an inflationary potential, but not its full shape [15].…”

Section: Constructing Inflationary Cosmologymentioning

confidence: 99%

“…Instead of specifying the fluctuation amplitude directly as a function of k, it is convenient to specify it as a function of the number of e-folds N e of expansion between the epoch when the horizon scale modes left the horizon and the end of inflation. To leading order in slow roll parameters, n s is given by [14] …”

Section: Constructing Inflationary Cosmologymentioning

confidence: 99%

Inflation and quintessence: theoretical approach of cosmological reconstruction

Neupane

Scherer

2008

In the first part of this paper, we outline the construction of an inflationary cosmology in the framework where inflation is described by a universally evolving scalar field φ with potential V (φ). By considering a generic situation that inflaton attains a nearly constant velocity, during inflation, m −1 P |dφ/dN | ≡ α + β exp(βN ) (where N ≡ ln a is the e-folding time), we reconstruct a scalar potential and find the conditions that have to satisfied by the (reconstructed) potential to be consistent with the WMAP inflationary data. The consistency of our model with WMAP result (such as n s = 0.951 +0.015 −0.019 and r < 0.3) would require 0.16 < α < 0.26 and β < 0. The running of spectral index, α ≡ dn s /d ln k, is found to be small for a wide range of α.In the second part of this paper, we introduce a novel approach of constructing dark energy within the context of the standard scalar-tensor theory. The assumption that a scalar field might roll with a nearly constant velocity, during inflation, can also be applied to quintessence or dark energy models. For the minimally coupled quintessence, α Q ≡ dA(Q)/d(κQ) = 0 (where A(Q) is the standard matter-quintessence coupling), the dark energy equation of state in the range −1 ≤ w DE < −0.82 can be obtained for 0 ≤ α < 0.63. For α < 0.1, the model allows for only modest evolution of dark energy density with redshift. We also show, under certain conditions, that the α Q > 0 solution decreases the dark energy equation of state w Q with decreasing redshift as compared to the α Q = 0 solution. This effect can be opposite in the α Q < 0 case. The effect of the matterquintessence coupling can be significant only if |α Q | 0.1, while a small coupling |α Q | < 0.1 will have almost no effect on cosmological parameters, including Ω Q , w Q and H(z). The best fit value of α Q in our model is found to be α Q ≃ 0.06, but it may contain significant numerical errors, viz α Q = 0.06 ± 0.35, which thereby implies the consistency of our model with general relativity (for which α Q = 0) at 1σ level.