Slow-roll Inflationary Models Research Articles

Parametrizing the power spectrum: beyond the truncated Taylor expansion

The power spectrum is traditionally parametrized by a truncated Taylor series: . It is reasonable to truncate the Taylor series if , but it is not if . We argue that there is no good theoretical reason to prefer , and show that current observations are consistent with|n*′ln(k/k*)| ∼ |n* − 1| evenfor |ln(k/k*)| ∼ 1. Thus, there are regions of parameter space, which are both theoretically and observationallyrelevant, for which the traditional truncated Taylor series parametrization is inconsistent,and hence it can lead to incorrect parameter estimations. Motivated by this, we propose asimple extension of the traditional parametrization, which uses no extra parameters, butthat, unlike the traditional approach, covers well motivated inflationary spectra with|n*′| ∼ |n* − 1|. Our parametrization therefore covers not only standard slow-roll inflation models but alsoa much wider class of inflation models. We use this parametrization to perform a likelihoodanalysis for the cosmological parameters.

Nonlinear evolutions and non-Gaussianity in generalized gravity

We use the Hamilton-Jacobi theory to study the nonlinear evolutions of inhomogeneous spacetimes during inflation in generalized gravity. We find the exact solutions to the lowest order Hamilton-Jacobi equation for special scalar potentials and introduce an approximation method for general potentials. The conserved quantity invariant under a change of timelike hypersurfaces proves useful in dealing with gravitational perturbations. In the long-wavelength approximation, we find a conserved quantity related to the new canonical variable that makes the Hamiltonian density vanish, and calculate the non-Gaussianity in generalized gravity. The slow-roll inflation models with a single scalar field in generalized gravity predict too small non-Gaussianity to be detected by future CMB experiments.

Primordial non-Gaussianity from different cosmological scenarios

We review recent results about the level of non-Gaussianity in the primordial density perturbations generated in various cosmological scenarios, spanning from the standard single-field models of slow-roll inflation to new alternative scenarios. Through a full calculation at second order in perturbation theory we provide all the tools necessary to determine the level of the primordial non-Gaussianity in the large-scale Cosmic Microwave Background (CMB) temperature anisotropies in any model of cosmological perturbations. In light of present and future CMB observations we stress the importance of non-Gaussianity as a key discriminator among competing cosmological scenarios.

The Lyman-$\alpha$ forest as a probe of fundamental physics

We use LUQAS, a sample of 27 high resolution high signal-to-noise UVES quasar (QSO) spectra (Kim et al. 2004), and the Croft et al. (2002) sample together with a set of high resolution large box-size hydrodynamical simulations run with the code GADGET-II to recover the linear dark matter power spectrum at forest structures such as the difference between full hydro-dynamical simulations and a more simplified scheme based on the HPM (Hydro-Particle-Mesh) technique. We combine these data sets with the Cosmic Microwave Background (CMB) data of WMAP in order to get tighter constraints on cosmological parameters. We focus on the recovered values of the power spectrum amplitude, the primordial spectral index and the running of the primordial spectral index. By considering models of slow-roll inflation we give constraints on inflationary parameters. We explore the implications for the mass of a warm dark matter particle, including light gravitinos and sterile neutrinos, and from the perspective of constraining the neutrino mass.

Determination of cosmological parameters from cosmic shear data

We study how parameter error forecasts for tomographic cosmic shear observations are affected by sky coverage, density of source galaxies, inclusion of CMB experiments, simultaneou fitting of non--dark energy parameters, and the parametrization of the history of the dark energy equation-of-state parameter w(z). We find tomographic shear-shear power spectra on large angular scales (l<1000) inferred from all-sky observations, in combination with Planck, can achieve sigma(w0)=0.06 and sigma(wa)=0.09 assuming the equation-of-state parameter is given by w(z)=w0+wa(1-a(z)) and that nine other matter content and primordial power spectrum parameters are simultaneously fit. Taking parameters other than w0, wa and Omegam to be completely fixed by the CMB we find errors on w0 and wa that are only 10% and 30% better respectively, justifying this common simplifying assumption. We also study `dark energy tomography': reconstuction of w(z) assumed to be constant within each of five independent redshift bins. With smaller-scale information included by use of the Jain & Taylor ratio statistic we find sigma(wi)<0.1 for all five redshift bins and sigma(wi)<0.02 for both bins at z<0.8. Finally, addition of cosmic shear can also reduce errors on quantities already determined well by the CMB. We find the sum of neutrino masses can be determined to +-0.013eV and that the primordial power specrum power-law index, ns, as well as dns/dlnk, can be determined more than a factor of two better than by Planck alone. These improvements may be highly valuable since the lower bound on the sum of neutrino masses is 0.06eV as inferred from atmospheric neutrino oscillations, and slow-roll models of inflation predict non-zero dns/dlnk at the forecasted error levels when |n_S-1|>0.04.

Models of inflation liberated by the curvaton hypothesis

It is usually supposed that inflation is of the slow-roll variety, and that the inflaton generates the primordial curvature perturbation. According to the curvaton hypothesis, inflation need not be slow-roll, and if it is the inflaton generates a negligible curvature perturbation. We find that the construction of slow-roll inflation models becomes much easier under this hypothesis. Also, thermal inflation followed by fast-roll becomes viable, with no slow-roll inflation at all.

Constraining slow-roll inflation with WMAP and 2dF

We constrain slow-roll inflationary models using the recent Wilkinson Microwave Anisotropy Probe data combined with data from the VSA, CBI, ACBAR and 2dF experiments. We find the slow-roll parameters to be $0&lt;{\ensuremath{\epsilon}}_{1}&lt;0.032$ and ${\ensuremath{\epsilon}}_{2}+5.0{\ensuremath{\epsilon}}_{1}=0.036\ifmmode\pm\else\textpm\fi{}0.025.$ For inflation models $V\ensuremath{\propto}{\ensuremath{\varphi}}^{\ensuremath{\alpha}}$ we find that $\ensuremath{\alpha}&lt;3.9,4.3$ at the $2\ensuremath{\sigma}$ and $3\ensuremath{\sigma}$ levels, indicating that the $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ model is under very strong pressure from observations. We define a convergence criterion to judge the necessity of introducing further power spectrum parameters such as the spectral index and running of the spectral index. This criterion is typically violated by models with large negative running that fit the data, indicating that the running cannot be reliably measured with present data.

Next-generation test of cosmic inflation

The increasing precision of cosmological datasets is opening up new opportunities to test predictions from cosmic inflation. Here we study the impact of high precision constraints on the primordial power spectrum and show how a new generation of observations can provide impressive new tests of the slow-roll inflation paradigm, as well as produce significant discriminating power among different slow-roll models. In particular, we consider next-generation measurements of the Cosmic Microwave Background (CMB) temperature anisotropies and (especially) polarization, as well as new Lyman-$\alpha$ measurements that could become practical in the near future. We emphasize relationships between the slope of the power spectrum and its first derivative that are nearly universal among existing slow-roll inflationary models, and show how these relationships can be tested on several scales with new observations. Among other things, our results give additional motivation for an all-out effort to measure CMB polarization.

An inflation model with large variations in the spectral index

Recent fits of cosmological parameters by a Wilkinson Microwave Anisotropy Probe (WMAP) measurement favor a primordial scalar spectrum with a varying index. This result, if it stands, could severely constrain inflation model building. Most extant slow-roll inflation models allow for only a tiny amount of scale variations in the spectrum. We propose in this paper an extra-dimensional inflation model which is natural theoretically and can generate the required variations of the spectral index as implied by the WMAP for suitable choices of parameters.

Inflationary flow equations

I explore properties of the inflationary flow equations. I show that the flow equations do not correspond directly to inflationary dynamics. Nevertheless, they can be used as a rather complicated algorithm for generating inflationary models. I demonstrate that the flow equations can be solved analytically and give a closed form solution for the potentials to which flow equation solutions correspond. I end by considering some simpler algorithms for generating stochastic sets of slow-roll inflationary models for confrontation with observational data.

Microwave background constraints on inflationary parameters

We use a compilation of cosmic microwave anisotropy data (including the recent VSA, CBI and Archeops results), supplemented with an additional constraint on the expansion rate, to directly constrain the parameters of slow-roll inflation models. We find good agreement with other papers concerning the cosmological parameters, and display constraints on the power spectrum amplitude from inflation and the first two slow-roll parameters, finding in particular that � 1 < 0.057. The technique we use for parametrizing inflationary spectra may become essential once the data quality improves significantly.

Observational test of two-field inflation

We study adiabatic and isocurvature perturbation spectra produced by a period of cosmological inflation driven by two scalar fields. We show that there exists a model-independent consistency condition for all two-field models of slow-roll inflation, despite allowing for model-dependent linear processing of curvature and isocurvature perturbations during and after inflation on super-horizon scales. The scale dependence of all spectra are determined solely in terms of slow-roll parameters during inflation and the dimensionless cross-correlation between curvature and isocurvature perturbations. We present additional model-dependent consistency relations that may be derived in specific two-field models, such as the curvaton scenario.

Scale dependent spectral index in slow roll inflation

Recent observations suggest that the spectral index of the primordial perturbations is very close to unity, as expected in models of slow roll inflation. It is still possible for such models to produce spectra which are scale dependent. We present a formula for the spectrum produced by an arbitrary inflaton potential (within the context of slow roll models). This formula explicitly accounts for the possiblity of scale dependence agreeing with previous results when the running is small, but also giving accurate results (as opposed to previous formulas) in the more interesting case when running is non-negligible.

Constraints on inflation from cosmic microwave background and Lyman-α forest

We constrain the spectrum of primordial curvature perturbations by using recent cosmic microwave background (CMB) and large scale structure data. Specifically, we consider CMB data from the COBE, Boomerang and MAXIMA experiments, the real space galaxy power spectrum from the IRAS point source catalogue redshifts survey, and the linear matter power spectrum inferred from Lyman-α forest spectra, where we for simplicity assume the absence of appreciable covariances. We study the case of single field slow roll inflationary models, and we extract bounds on the scalar spectral index, n, the tensor to scalar ratio, r, and the running of the scalar spectral index, ∂ ln k , for various combinations of the observational data. We find that CMB data, when combined with data from Ly-α forest, place strong constraints on the inflationary parameters. Specifically, we obtain n≈0.9, r≲0.3 and ∂ ln k ≈0 , indicating that big n, big r models (often referred to as hybrid models) are ruled out.

Testing non-Gaussianity in cosmic microwave background maps by morphological statistics

The assumption of Gaussianity of the primordial perturbations plays an important role in modern cosmology. The most direct test of this hypothesis consists in testing Gaussianity of the CMB maps. Counting the pixels with the temperatures in given ranges and thus estimating the one point probability function of the field is the simplest of all the tests. Other usually more complex tests of Gaussianity generally use a great deal of the information already contained in the probability function. However, the most interesting outcome of such a test would be the signal of non-Gaussianity independent of the probability function. It is shown that the independent information has purely morphological character i.e. it depends on the geometry and topology of the level contours only. As an example we discuss in detail the quadratic model $v=u+\alpha (u^2-1)$ ($u$ is a Gaussian field with $\bar{u}=0$ and $<u^2>=1$, $\alpha$ is a parameter) which may arise in slow-roll or two-field inflation models. We show that in the limit of small amplitude $\alpha$ the full information about the non-Gaussianity is contained in the probability function. If other tests are performed on this model they simply recycle the same information. A simple procedure allowing to assess the sensitivity of any statistics to the morphological information is suggested. We provide an analytic estimate of the statistical limit for detecting the quadratic non-Gaussianity $\a_c$ as a function of the map size in the ideal situation when the scale of the field is resolved. This estimate is in a good agreement with the results of the Monte Carlo simulations of $256^2$ and $1024^2$ maps. The effect of resolution on the detection quadratic non-Gaussianity is also briefly discussed.

Probing the power spectrum bend with recent cosmic microwave background data

We constrain the spectrum of primordial curvature perturbations P(k) by using the new data on the cosmic microwave background from the Boomerang and MAXIMA experiments. Our study is based on slow-roll inflationary models, and we consider the possibility of a running spectral index. Specifically, we expand the power spectrum P(k) to second order in lnk, thus allowing the power spectrum to “bend” in k-space. We show that allowing the power spectrum to bend erases the ability of the present data to measure the tensor to scalar perturbation ratio. Moreover, if the primordial baryon density Ωbh2 is as low as found from big bang nucleosynthesis, the data favor a negative bending of the power spectrum, corresponding to a bump-like feature in the power spectrum around a scale of k=0.004 Mpc−1.

Direct detection of primordial gravitational waves in a BSI inflationary model

We investigate the possibility for a direct detection by future space interferometers of the stochastic gravitational wave (GW) background generated during the inflationary stage in a class of viable ΛCDM BSI models. At frequencies around 10 −3 Hz, maximal values Ω gw (ν)∼3×10 −15 are found, an improvement of about one order of magnitude compared to single-field, slow-roll inflationary models. This is presumably not sufficient in order to be probed in the near future.

Duality invariance of cosmological perturbation spectra

I show that cosmological perturbation spectra produced from quantum fluctuations in massless or self-interacting scalar fields during an inflationary era remain invariant under a two parameter family of transformations of the homogeneous background fields. This relates slow-roll inflation models to solutions which may be far from the usual slow-roll limit. For example, a scale-invariant spectrum of perturbations in a minimally coupled, massless field can be produced by an exponential expansion with $a\propto e^{Ht}$, or by a collapsing universe with $a\propto (-t)^{2/3}$.

Four-year COBE normalization of inflationary cosmologies.

We supply fitting formulas enabling the normalization of slow-roll inflation models to the four-year COBE data. We fully include the effect of the gravitational wave modes, including the predicted relation of the amplitude of these modes to that of the density perturbations. We provide the normalization of the matter power spectrum, which can be directly used for large-scale structure studies. The normalization for tilted spectra is a special case. We also provide fitting functions for the inflationary energy scale of COBE-normalized models and discuss the validity of approximating the spectra by power laws. In an Appendix, we extend our analysis to include models with a cosmological constant, both with and without gravitational waves.