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Register a new userTesting Inflation with Large Scale Structure: Connecting Hopes with Reality
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The statistics of primordial curvature fluctuations are our window into the period of inflation, where these fluctuations were generated. To date, the cosmic microwave background has been the dominant source of information about these perturbations. Large scale structure is however from where drastic improvements should originate. In this paper, we explain the theoretical motivations for pursuing such measurements and the challenges that lie ahead. In particular, we discuss and identify theoretical targets regarding the measurement of primordial non-Gaussianity. We argue that when quantified in terms of the local (equilateral) template amplitude $f_{rm NL}^{rm loc}$ ($f_{rm NL}^{rm eq}$), natural target levels of sensitivity are $Delta f_{rm NL}^{rm loc, eq.} simeq 1$. We highlight that such levels are within reach of future surveys by measuring 2-, 3- and 4-point statistics of the galaxy spatial distribution. This paper summarizes a workshop held at CITA (University of Toronto) on October 23-24, 2014.
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We examine the cosmological implications of measurements of the void-galaxy cross-correlation at redshift $z=0.57$ combined with baryon acoustic oscillation (BAO) data at $0.1<z<2.4$. We find direct evidence of the late-time acceleration due to dark energy at $>10sigma$ significance from these data alone, independent of the cosmic microwave background and supernovae. Using a nucleosynthesis prior on $Omega_bh^2$, we measure the Hubble constant to be $H_0=72.3pm1.9;{rm km,s}^{-1}{rm Mpc}^{-1}$ from BAO+voids at $z<2$, and $H_0=69.0pm1.2;{rm km,s}^{-1}{rm Mpc}^{-1}$ when adding Lyman-$alpha$ BAO at $z=2.34$, both independent of the CMB. Adding voids to CMB, BAO and supernova data greatly improves measurement of the dark energy equation of state, increasing the figure of merit by >40%, but remaining consistent with flat flat $Lambda$ cold dark matter.
We estimate large-scale curvature perturbations from isocurvature fluctuations in the waterfall field during hybrid inflation, in addition to the usual inflaton field perturbations. The tachyonic instability at the end of inflation leads to an explosive growth of super-Hubble scale perturbations, but they retain the steep blue spectrum characteristic of vacuum fluctuations in a massive field during inflation. The power spectrum thus peaks around the Hubble-horizon scale at the end of inflation. We extend the usual delta-N formalism to include the essential role of these small fluctuations when estimating the large-scale curvature perturbation. The resulting curvature perturbation due to fluctuations in the waterfall field is second-order and the spectrum is expected to be of order 10^{-54} on cosmological scales.
This is the second in a series of papers on preheating in inflationary models comprised of multiple scalar fields coupled nonminimally to gravity. In this paper, we work in the rigid-spacetime approximation and consider field trajectories within the single-field attractor, which is a generic feature of these models. We construct the Floquet charts to find regions of parameter space in which particle production is efficient for both the adiabatic and isocurvature modes, and analyze the resonance structure using analytic and semi-analytic techniques. Particle production in the adiabatic direction is characterized by the existence of an asymptotic scaling solution at large values of the nonminimal couplings, $xi_I gg 1$, in which the dominant instability band arises in the long-wavelength limit, for comoving wavenumbers $k rightarrow 0$. However, the large-$xi_I$ regime is not reached until $xi_I geq {cal O} (100)$. In the intermediate regime, with $xi_I sim {cal O}(1 - 10)$, the resonance structure depends strongly on wavenumber and couplings. The resonance structure for isocurvature perturbations is distinct and more complicated than its adiabatic counterpart. An intermediate regime, for $xi_I sim {cal O} (1 - 10)$, is again evident. For large values of $xi_I$, the Floquet chart consists of densely spaced, nearly parallel instability bands, suggesting a very efficient preheating behavior. The increased efficiency arises from features of the nontrivial field-space manifold in the Einstein frame, which itself arises from the fields nonminimal couplings in the Jordan frame, and has no analogue in models with minimal couplings. Quantitatively, the approach to the large-$xi_I$ asymptotic solution for isocurvature modes is slower than in the case of the adiabatic modes.
We study soft limits of correlation functions for the density and velocity fields in the theory of structure formation. First, we re-derive the (resummed) consistency conditions at unequal times using the eikonal approximation. These are solely based on symmetry arguments and are therefore universal. Then, we explore the existence of equal-time relations in the soft limit which, on the other hand, depend on the interplay between soft and hard modes. We scrutinize two approaches in the literature: The time-flow formalism, and a background method where the soft mode is absorbed into a locally curved cosmology. The latter has been recently used to set up (angular averaged) `equal-time consistency relations. We explicitly demonstrate that the time-flow relations and `equal-time consistency conditions are only fulfilled at the linear level, and fail at next-to-leading order for an Einstein de-Sitter universe. While applied to the velocities both proposals break down beyond leading order, we find that the `equal-time consistency conditions quantitatively approximates the perturbative results for the density contrast. Thus, we generalize the background method to properly incorporate the effect of curvature in the density and velocity fluctuations on short scales, and discuss the reasons behind this discrepancy. We conclude with a few comments on practical implementations and future directions.
We forecast combined future constraints from the cosmic microwave background and large-scale structure on the models of primordial non-Gaussianity. We study the generalized local model of non-Gaussianity, where the parameter f_NL is promoted to a function of scale, and present the principal component analysis applicable to an arbitrary form of f_NL(k). We emphasize the complementarity between the CMB and LSS by using Planck, DES and BigBOSS surveys as examples, forecast constraints on the power-law f_NL(k) model, and introduce the figure of merit for measurements of scale-dependent non-Gaussianity.
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