Primordial black holes in non-Gaussian regimes

Primordial black holes (PBHs) can form in the early Universe from the collapse of rare, large density fluctuations. They have never been observed, but this fact is enough to constrain the amplitude of fluctuations on very small scales which cannot be otherwise probed. Because PBHs form only in very rare large fluctuations, the number of PBHs formed is extremely sensitive to changes in the shape of the tail of the fluctuation distribution - which depends on the amount of non-Gaussianity present. We first study how local non-Gaussianity of arbitrary size up to fifth order affects the abundance and constraints from PBHs, finding that they depend strongly on even small amounts of non-Gaussianity and the upper bound on the allowed amplitude of the power spectrum can vary by several orders of magnitude. The sign of the non-linearity parameters (f_{NL}, g_{NL}, etc) are particularly important. We also study the abundance and constraints from PBHs in the curvaton scenario, in which case the complete non-linear probability distribution is known, and find that truncating to any given order (i.e. to order f_{NL} or g_{NL}, etc) does not give accurate results

Long-short wavelength mode coupling tightens primordial black hole constraints

The effects of non-Gaussianity on the constraints on the primordial curvature perturbation power spectrum from primordial black holes (PBHs) are considered. We extend previous analyses to include the effects of coupling between the modes of the horizon scale at the time the PBH forms and superhorizon modes. We consider terms of up to third order in the Gaussian perturbation. For the weakest constraints on the abundance of PBHs in the early universe (corresponding to a fractional energy density of PBHs of 10−5 at the time of formation), in the case of Gaussian perturbations, constraints on the power spectrum are Pζ<0.05 but can be significantly tighter when even a small amount of non-Gaussianity is considered, to Pζ<0.01, and become approximately Pζ<0.003 in more special cases. Surprisingly, even when there is negative skew (which naively would suggest fewer areas of high density, leading to weaker constraints), we find that the constraints on the power spectrum become tighter than the purely Gaussian case—in strong contrast with previous results. We find that the constraints are highly sensitive to both the non-Gaussianity parameters as well as the amplitude of superhorizon perturbations

Scale-invariant Perturbations from Chaotic Inflation

Vacuum fluctuations in the inflaton field driving chaotic inflation with a quadratic potential give a red spectrum of primordial density perturbations, n=0.97. However angular fluctuations in an O(N)-symmetric quadratic potential have a very nearly scale-invariant spectrum, n=0.9998. We investigate the possibility that these isocurvature field perturbations could give the dominant contribution to the primordial density perturbation after inflation.Comment: 10 pages, LaTeX with RevTex, no figure

General formula for the running of local fNL

We compute the scale dependence of fNL for models of multi-field inflation, allowing for an arbitrary field space metric. We show that, in addition to multi-field effects and self interactions, the curved field space metric provides another source of scale dependence, which arises from the field-space Riemann curvature tensor and its derivatives. The scale dependence may be detectable within the near future if the amplitude of fNL is not too far from the current observational bounds

The Standard Model Higgs as the origin of the hot Big Bang

If the Standard Model (SM) Higgs is weakly coupled to the inflationary sector, the Higgs is expected to be universally in the form of a condensate towards the end of inflation. The Higgs decays rapidly after inflation - via non-perturbative effects - into an out-of-equilibrium distribution of SM species, which thermalize soon afterwards. If the post-inflationary equation of state of the universe is stiff, $w \simeq +1$, the SM species eventually dominate the total energy budget. This provides a natural origin for the relativistic thermal plasma of SM species, required for the onset of the `hot Big Bang' era. The viability of this scenario requires the inflationary Hubble scale $H_*$ to be lower than the instability scale for Higgs vacuum decay, the Higgs not to generate too large curvature perturbations at cosmological scales, and the SM dominance to occur before Big Bang Nucleosynthesis. We show that successful reheating into the SM can only be obtained in the presence of a non-minimal coupling to gravity $\xi \gtrsim 1$, with a reheating temperature of $T_{\rm RH} \gtrsim \mathcal{O}(10^{10})\xi^{3/2}(H_*/10^{14}{\rm GeV})^2~{\rm GeV}$.Comment: 6 pages, 2 figures, minor changes with new figures to match published version in PL

Review of local non-Gaussianity from multi-field inflation

We review models which generate a large non-Gaussianity of the local form. We first briefly consider three models which generate the non-Gaussianity either at or after the end of inflation; the curvaton scenario, modulated (p)reheating and an inhomogeneous end of inflation. We then focus on ways of generating the non-Gaussianity during inflation. We derive general conditions which a product or sum separable potential must satisfy in order to generate a large local bispectrum during slow-roll inflation. As an application we consider two-field hybrid inflation. We then derive a formalism not based on slow roll which can be applied to models in which the slow-roll parameters become large before inflation ends. An exactly soluble two-field model is given in which this happens. Finally we also consider further non-Gaussian observables; a scale dependence of f_NL and the trispectrum.Comment: 22 pages, 2 figures. Invited review for the special issue "Testing the Gaussianity and Statistical Isotropy of the Universe" for Advances in Astronomy. v2: Numerous references and comments adde

Scale dependence of fNLf_{NL} in N-flation

Adopting the horizon-crossing approximation, we derive the spectral index of $f_{NL}$ in general N-flation model. Axion N-flation model is taken as a typical model for generating a large $f_{NL}$ which characterizes the size of local form bispectrum. We find that its tilt $n_{f_{NL}}$ is negligibly small when all inflatons have the same potential, but a negative detectable $n_{f_{NL}}$ can be achieved in the axion N-flation with different decay constants for different inflatons. The measurement of $n_{f_{NL}}$ can be used to support or falsify the axion N-flation in the near future.Comment: 15 pages, 2 figures; a subsection with detectable scale dependence of f_NL added; more discussions added and version accepted for publication in JCA

Comprehensive analysis of the simplest curvaton model

We carry out a comprehensive analysis of the simplest curvaton model, which is based on two non-interacting massive fields. Our analysis encompasses cases where the inflaton and curvaton both contribute to observable perturbations, and where the curvaton itself drives a second period of in inflation. We consider both power spectrum and non-Gaussianity observables, and focus on presenting constraints in model parameter space. The fully curvaton-dominated regime is in some tension with observational data, while an admixture of inflaton-generated perturbations improves the fit. The inflating curvaton regime mimics the predictions of Nflation. Some parts of parameter space permitted by power spectrum data are excluded by non-Gaussianity constraints. The recent BICEP2 results [1] require that the in inflaton perturbations provide a significant fraction of the total perturbation, ruling out the usual curvaton scenario in which the inflaton perturbations are negligible, though not the admixture regime where both inflaton and curvaton contribute to the spectrum

A non-Gaussian landscape

Primordial perturbations with wavelengths greater than the observable universe shift the effective background fields in our observable patch from their global averages over the inflating space. This leads to a landscape picture where the properties of our observable patch depend on its location and may significantly differ from the expectation values predicted by the underlying fundamental inflationary model. We show that if multiple fields are present during inflation, this may happen even if our horizon exit would be preceded by only a few e-foldings of inflation. Non-Gaussian statistics are especially affected: for example models of local non-Gaussianity predicting |f_NL|>> 10 over the entire inflating volume can have a probability up to a few tens of percent to generate a non-detectable bispectrum in our observable patch |fNL^{obs.}|<10. In this work we establish systematic connections between the observable local properties of primordial perturbations and the global properties of the inflating space which reflect the underlying high energy physics. We study in detail the implications of both a detection and non-detection of primordial non-Gaussianity by Planck, and discover novel ways of characterising the naturalness of different observational configurations