Cosmological parameter estimation and the inflationary cosmology (original) (raw)
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Cosmological parameter estimation and the spectral index from inflation
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.
Inflationary perturbations and precision cosmology
Physical Review D, 2005
Inflationary cosmology provides a natural mechanism for the generation of primordial perturbations which seed the formation of observed cosmic structure and lead to specific signals of anisotropy in the cosmic microwave background radiation. In order to test the broad inflationary paradigm as well as particular models against precision observations, it is crucial to be able to make accurate predictions for the power spectrum of both scalar and tensor fluctuations. We present detailed calculations of these quantities utilizing direct numerical approaches as well as error-controlled uniform approximations, comparing with the (uncontrolled) traditional slow-roll approach. A simple extension of the leading-order uniform approximation yields results for the power spectra amplitudes, the spectral indices, and the running of spectral indices, with accuracy of the order of 0.1%-approximately the same level at which the transfer functions are known. Several representative examples are used to demonstrate these results.
On the correspondence between theory and observations in inflationary cosmology
Physics Letters B, 1993
We study the dynamical correspondence between the scalar fluctuation spectrum and the inflationary potential V(O) and consider a power law spectrum with index fl as an example We show that for the range offl relevant to the interpretation of COBE observations, this correspondence is fragile, in the sense that small changes in fl could produce dramatic changes in the correspondmg V(¢) This is of potential significance for the reconstruction of V(O) from such observations and also in the wider context of inflationary models in which V(¢) is specially chosen to produce a desired spectrum and dynamics
Bayesian analysis of inflation: Parameter estimation for single field models
Phys Rev D, 2011
Future astrophysical data sets promise to strengthen constraints on models of inflation, and extracting these constraints requires methods and tools commensurate with the quality of the data. In this paper we describe ModeCode, a new, publicly available code that computes the primordial scalar and tensor power spectra for single-field inflationary models. ModeCode solves the inflationary mode equations numerically, avoiding the slow roll approximation. It is interfaced with CAMB and CosmoMC to compute cosmic microwave background angular power spectra and perform likelihood analysis and parameter estimation. ModeCode is easily extendable to additional models of inflation, and future updates will include Bayesian model comparison. Errors from ModeCode contribute negligibly to the error budget for analyses of data from Planck or other next generation experiments. We constrain representative single-field models (ϕn with n=2/3, 1, 2, and 4, natural inflation, and “hilltop” inflation) using current data, and provide forecasts for Planck. From current data, we obtain weak but nontrivial limits on the post-inflationary physics, which is a significant source of uncertainty in the predictions of inflationary models, while we find that Planck will dramatically improve these constraints. In particular, Planck will link the inflationary dynamics with the post-inflationary growth of the horizon, and thus begin to probe the “primordial dark ages” between TeV and grand unified theory scale energies.
Inflationary cosmology: from theory to observations
Revista Mexicana de Física E, 2020
The main aim of this paper is to provide a qualitative introduction to the cosmological inflation theory and its relationship with current cosmological observations. The inflationary model solves many of the fundamental problemsthat challenge the Standard Big Bang cosmology such as the Flatness, Horizon and the magnetic Monopole problems. Additionally it provides an explanation for the initial conditions observed throughout the Large-Scale Structure of the Universe, such as galaxies. In this review we describe general solutions to the problems in the Big Bang cosmology carry out by a single scalar eld. Then, with the use of current surveys, we show the constraints imposed on the inflationary parameters (ns; r) which allow us to make the connection between theoretical and observational cosmology. In this way, with the latest results, it is possible to select or at least to constrain the right inflationary model, parameterized by a single scalar eld potential V (\phi).
Cosmological parameter estimation with free-form primordial power spectrum
Physical Review D, 2013
Constraints on the main cosmological parameters using cosmic microwave background (CMB) or large scale structure data are usually based on the power-law assumption of the primordial power spectrum (PPS). However, in the absence of a preferred model for the early Universe, this raises a concern that current cosmological parameter estimates are strongly prejudiced by the assumed power-law form of PPS. In this paper, for the first time, we perform cosmological parameter estimation allowing the free form of the primordial spectrum. This is in fact the most general approach to estimate cosmological parameters without assuming any particular form for the primordial spectrum. We use a direct reconstruction of the PPS for any point in the cosmological parameter space using the recently modified Richardson-Lucy algorithm; however, other alternative reconstruction methods could be used for this purpose as well. We use WMAP 9 year data in our analysis considering the CMB lensing effect, and we report, for the first time, that the flat spatial universe with no cosmological constant is ruled out by more than a 4 confidence limit without assuming any particular form of the primordial spectrum. This would be probably the most robust indication for dark energy using CMB data alone. Our results on the estimated cosmological parameters show that higher values of the baryonic and matter density and a lower value of the Hubble parameter (in comparison to the estimated values by assuming power-law PPS) is preferred by the data. However, the estimated cosmological parameters by assuming a free form of the PPS have an overlap at 1 confidence level with the estimated values assuming the power-law form of PPS.
Accurate determination of inflationary perturbations
Physical Review D, 1996
We use a numerical code for accurate computation of the amplitude of linear density perturbations and gravitational waves generated by single-field inflation models to study the accuracy of existing analytic results based on the slow-roll approximation. We use our code to calculate the coefficient of an expansion about the exact analytic result for power-law inflation; this generates a fitting function which can be applied to all inflationary models to obtain extremely accurate results. In the appropriate limit our results confirm the Stewart-Lyth analytic second-order calculation, and we find that their results are very accurate for inflationary models favoured by current observational constraints.
Exact Cosmology and Specification of an Inflationary Scenario
Gravitation & Cosmology - GRAVIT COSMOL, 2005
We propose a revision of the most important results from the slow-roll approximation using an exact inflationary approach. The most important quantities which may be derived theoretically from slow-roll inflation and may then be compared with observational data, such as the curvature perturbation; the spectral index n(k ), a nd the derivative of the spectral index n with respect to ln k , are presented in an explicit form. We study these quantities in the case when a scalar field has a logarithmic evolution with time and for power-law inflation. tONAQ KOSMOLOGIESKAQ MODELX I SPECIFIKACIQ INFLQCIONNOGO SCENARIQ s.w. ˜ERWON, m. nOWELLO, r. tRIJE
Journal of Cosmology and Astroparticle Physics, 2006
We present the constraints on inflationary parameters in a flat ΛCDM universe obtained by WMAP three year data release, plus smaller scale CMB and two LSS data sets, 2dF and SDSS (treated separately). We use a Markov Chain Monte Carlo (MCMC) technique combined with an analytic description of the inflationary spectra in terms of the horizon flow functions (HFF). By imposing a consistency condition for the tensor-to-scalar ratio, we study the constraints both on single field standard inflation and on inflation with the violation of the null energy condition, which leads to a blue spectrum for gravitational waves. For standard inflation, the constraint on the tensor-to-scalar ratio we obtain from CMB data and 2dF05 is: r 0.01 < 0.26 at 2 σ cl. Without the consistency condition between the tensor-to-scalar ratio and the tensor slope, the constraints on the tensor amplitude is not significantly changed, but the constraints on the HFFs are significantly relaxed. We then show that when the third HFF ǫ 3 is allowed to be non-zero and to be of order unity, a large negative (at 2σ) value for the running of the scalar spectral index in standard inflation is found in any set of data we consider.
Reconciliation of High Energy Scale Models of Inflation with Planck
2014
The inflationary cosmology paradigm is very successful in explaining the CMB anisotropy to the percent level. Besides the dependence on the inflationary model, the power spectra, spectral tilt and non-Gaussianity of the CMB temperature fluctuations also depend on the initial state of inflation. Here, we examine to what extent these observables are affected by our ignorance in the initial condition for inflationary perturbations, due to unknown new physics at a high scale M. For initial states that satisfy constraints from backreaction, we find that the amplitude of the power spectra could still be significantly altered, while the modification in bispectrum remains small. For such initial states, M has an upper bound of a few tens of H, with H being the Hubble parameter during inflation. We show that for M∼ 20 H, such initial states always (substantially) suppress the tensor to scalar ratio. In particular we show that a general choice of initial conditions can satisfactorily reconcil...