Single-field Slow-roll Inflation Research Articles

Monte Carlo Markov chains analysis of WMAP3 and SDSS data points to broken symmetry inflaton potentials and provides a lower bound on the tensor to scalar ratio

background (CMB) and large scale structure (LSS) data (including the three years WMAP data) with single field slow-roll new inflation and chaotic inflation models. We do this within our approach to inflation as an effective field theory in the Ginsburg-Landau spirit with fourth degree trinomial potentials in the inflaton field � . We derive explicit formulae and study in detail the spectral index ns of the adiabatic fluctuations, the ratio r of tensor to scalar fluctuations, and the running index dns=d lnk. We use these analytic formulas as hard constraints on ns and r in the MCMC analysis. Our analysis differs in this crucial aspect from previous MCMC studies in the literature involving the WMAP3 data. Our results are as follows: (i) The data strongly indicate the breaking (whether spontaneous or explicit) of the � !� � symmetry of the inflaton potentials both for new and for chaotic inflation. (ii) Trinomial new inflation naturally satisfies this requirement and provides an excellent fit to the data. (iii) Trinomial chaotic inflation produces the best fit in a very narrow corner of the parameter space. (iv) The chaotic symmetric trinomial potential is almost certainly ruled out (at 95% C.L.). In trinomial chaotic inflation the MCMC runs go towards a potential in the boundary of the parameter space and which resembles a spontaneously symmetry broken potential of new inflation. (v) The above results and further physical analysis here lead us to conclude that new inflation gives the best description of the data. (vi) We find a lower bound for

Phenomenology of D-brane inflation with general speed of sound

A characteristic of D-brane inflation is that fluctuations in the inflaton field can propagate at a speed significantly less than the speed of light. This yields observable effects that are distinct from those of single-field slow-roll inflation, such as a modification of the inflationary consistency relation and a potentially large level of non-Gaussianities. We present a numerical algorithm that extends the inflationary flow formalism to models with general speed of sound. For an ensemble of D-brane-inflation models parametrized by the Hubble parameter and the speed of sound as polynomial functions of the inflaton field, we give qualitative predictions for the key inflationary observables. We discuss various consistency relations for D-brane inflation, and compare the qualitative shapes of the warp factors we derive from the numerical models with analytical warp factors considered in the literature. Finally, we derive and apply a generalized microphysical bound on the inflaton field variation during brane inflation. While a large number of models are consistent with current cosmological constraints, almost all of these models violate the compactification constraint on the field range in four-dimensional Planck units. If the field range bound is to hold, then models with a detectable level of non-Gaussianity predict a blue scalar spectral index, and a tensor component that is far below the detection limit of any future experiment.

Predictions of single field inflation for the tensor/scalar ratio and the running spectral index

We study the single field slow-roll inflation models that better agree with the available CMB and LSS data including the three years WMAP data: new inflation and hybrid inflation. We study these models as effective field theories in the Ginsburg-Landau context: a trinomial potential turns out to be a simple and well motivated model. The spectral index n{sub s} of the adiabatic fluctuations, the ratio r of tensor to scalar fluctuations and the running index dn{sub s}/dlnk are studied in detail. We derive explicit formulas for n{sub s}, r and dn{sub s}/dlnk and provide relevant plots. In new inflation, and for the chosen central value n{sub s}=0.95, we predict 0.03 1 behavior. Hybrid inflation for {mu}{sub 0}{sup 2}>{lambda}{sub 0}M{sub Pl}{sup 2}/192 fulfills all the present CMB+LSS data for a large enough initial inflaton amplitude. Even if chaotic inflation predicts n{sub s} values compatible with the data, chaotic inflation is disfavored since it predicts a too high value r{approx_equal}0.27 for the ratio of tensor to scalar fluctuations. The model which best agrees with the current data and which best prepares the way to the expected data r(less-or-similar sign)0.1, is the trinomial potential with negative mass term: new inflation.« less

Quantum corrections to slow roll inflation and new scaling of superhorizon fluctuations

Precise cosmological data from WMAP and forthcoming cosmic microwave background experiments motivate the study of the quantum corrections to the slow roll inflationary parameters. We find the quantum (loop) corrections to the equations of motion of the classical inflaton, to those for the fluctuations and to the Friedmann equation in general single field slow roll inflation. We implement a renormalized effective field theory (EFT) approach based on an expansion in ( H / M Pl ) 2 and slow roll parameters ϵ V , η V , σ V , ξ V . We find that the leading order quantum corrections to the inflaton effective potential and its equation of motion are determined by the power spectrum of scalar fluctuations. Its near scale invariance introduces a strong infrared behavior naturally regularized by the slow roll parameter Δ = η V − ϵ V = 1 2 ( n s − 1 ) + r / 8 . To leading order in the (EFT) and slow roll expansions we find V eff ( Φ 0 ) = V R ( Φ 0 ) [ 1 + Δ T 2 32 n s − 1 + 3 8 r n s − 1 + 1 4 r + higher orders ] where n s and r = Δ T 2 / Δ R 2 are the CMB observables that depend implicitly on Φ 0 and V R ( Φ 0 ) is the renormalized classical inflaton potential. This effective potential during slow roll inflation is strikingly different from the usual Minkowski space–time result. We also obtain the quantum corrections to the slow roll parameters in leading order. Superhorizon scalar field fluctuations grow for late times η → 0 − as | η | − 1 + Δ − d − where d − is a novel quantum correction to the scaling exponent related to the self-decay of superhorizon inflaton fluctuations φ → φ φ and η is the conformal time. We find to leading order − d − = Δ R 2 σ V ( η V − ϵ V ) + 6 ξ V 2 4 ( η V − ϵ V ) 2 in terms of the CMB observables. These results are generalized to the case of the inflaton interacting with a light scalar field σ and we obtain the decay rate Γ φ → σ σ . These quantum corrections arising from interactions will compete with higher order slow-roll corrections in the Gaussian approximation and must be taken into account for the precision determination of inflationary parameters extracted from CMB observations.

Primordial bispectrum information from CMB polarization

After the precise observations of the cosmic microwave background (CMB) anisotropy power spectrum, attention is now being focused on higher order statistics of the CMB anisotropies. Since linear evolution preserves the statistical properties of the initial conditions, observed non-Gaussianity of the CMB will mirror primordial non-Gaussianity. Single-field slow-roll inflation robustly predicts negligible non-Gaussianity so an indication of primordial non-Gaussianity will suggest alternative scenarios need to be considered. In this paper we calculate the information on primordial non-Gaussianity encoded in the polarization of the CMB. After deriving the optimal weights for a cubic estimator we evaluate the signal-to-noise ratio (S/N) of the estimator for Wilkinson Microwave Anisotropy Probe, Planck, and an ideal cosmic variance limited experiment. We find that when the experiment can observe CMB polarization with good sensitivity, the sensitivity to primordial non-Gaussianity increases by roughly a factor of 2. We also test the weakly non-Gaussian assumption used to derive the optimal weight factor by calculating the degradation factor produced by the gravitational lensing induced connected four-point function. The physical scales in the radiative transfer functions are largely irrelevant for the constraints on the primordial non-Gaussianity. We show that the total (S/N){sup 2} is simply proportional to the number ofmore » observed pixels on the sky.« less

Cosmic microwave background bispectrum and inflation

We derive an expression for the non-Gaussian cosmic-microwave-background (CMB) statistic $I_l^3$ defined recently by Ferreira, Magueijo, and G\'orski in terms of the slow-roll-inflation parameters $\epsilon$ and $\eta$. This result shows that a nonzero value of $I_l^3$ in COBE would rule out single-field slow-roll inflation. A sharp change in the slope of the inflaton potential could increase the predicted value of $I_l^3$, but not significantly. This further suggests that it will be difficult to account for such a detection in multiple-field models in which density perturbations are produced by quantum fluctuations in the scalar field driving inflation. An Appendix shows how to evaluate an integral that is needed in our calculation as well as in more general calculations of CMB bispectra.