arXiv subjects

Paolo Creminelli

Publications and source records attributed to Paolo Creminelli.

At least 55 records · Page 3Linked to original sources

arXiv2013

Consistency Relations for the Conformal Mechanism

We systematically derive the consistency relations associated to the non-linearly realized symmetries of theories with spontaneously broken conformal symmetry but with a linearly-realized de Sitter subalgebra. These identities relate (N+1)-point correlation functions with a soft external Goldstone to N-point functions. These relations have direct implications for the recently proposed conformal mechanism for generating density perturbations in the early universe. We study the observational consequences, in particular a novel one-loop contribution to the four-point function, relevant for the stochastic scale-dependent bias and CMB mu-distortion.

hep-th↗

arXiv2012

Khronon inflation

We study the possibility that the approximate time shift symmetry during inflation is promoted to the full invariance under time reparametrization t \to \tilde t(t), or equivalently under field redefinition of the inflaton ϕ\to \tildeϕ(ϕ). The symmetry allows only two operators at leading order in derivatives, so that all n-point functions of scalar perturbations are fixed in terms of the power spectrum normalization and the speed of sound. During inflation the decaying mode only decays as 1/a and this opens up the possibility to violate some of the consistency relations in the squeezed limit, although this violation is suppressed by the (small) breaking of the field reparametrization symmetry. In particular one can get terms in the 3-point function that are only suppressed by 1/k_L in the squeezed limit k_L \to 0 compared to the local shape.

hep-th↗

arXiv2012

Subluminal Galilean Genesis

We put forward an improved version of the Galilean Genesis model that addresses the problem of superluminality. We demote the full conformal group to Poincare symmetry plus dilations, supplemented with approximate galilean shift invariance in the UV and at small field values. In this way fluctuations around the NEC-violating cosmological background are made substantially subluminal, and superluminality cannot be reached by any small change of the solution, in contrast with the original model. Dilation invariance still protects the scale-invariance of correlation functions of a massless test scalar - which is the source of the observed cosmological fluctuations - but the explicit breaking of the conformal group can be potentially observed in higher-order correlators. We also highlight a subtlety in matching the NEC-violating phase with the standard cosmological evolution, and discuss the possible couplings of the Galileon to gravity.

hep-th↗

arXiv2012

Conformal consistency relations for single-field inflation

We generalize the single-field consistency relations to capture not only the leading term in the squeezed limit---going as 1/q^3, where q is the small wavevector---but also the subleading one, going as 1/q^2. This term, for an (n+1)-point function, is fixed in terms of the variation of the n-point function under a special conformal transformation; this parallels the fact that the 1/q^3 term is related with the scale dependence of the n-point function. For the squeezed limit of the 3-point function, this conformal consistency relation implies that there are no terms going as 1/q^2. We verify that the squeezed limit of the 4-point function is related to the conformal variation of the 3-point function both in the case of canonical slow-roll inflation and in models with reduced speed of sound. In the second case the conformal consistency conditions capture, at the level of observables, the relation among operators induced by the non-linear realization of Lorentz invariance in the Lagrangian. These results mean that, in any single-field model, primordial correlation functions of ζare endowed with an SO(4,1) symmetry, with dilations and special conformal transformations non-linearly realized by ζ. We also verify the conformal consistency relations for any n-point function in models with a modulation of the inflaton potential, where the scale dependence is not negligible. Finally, we generalize (some of) the consistency relations involving tensors and soft internal momenta.

hep-th↗

arXiv2012

Conformal invariance of scalar perturbations in inflation

In inflationary models where the source of scalar perturbations is not the inflaton, but one or more scalars with negligible coupling with the inflaton, the resulting perturbations are not only scale invariant, but fully conformally invariant with conformal dimension close to zero. This is closely related to the fact that correlation functions can only depend on the de Sitter invariant distances. These properties follow from the isometries of the inflationary de Sitter space and are thus completely independent of the dynamics. The 3-point function is fixed in terms of two constants, while the 4-point function is a function of two parameters (instead of five as in the absence of conformal invariance). The conformal invariance of correlators can be directly checked in Fourier space, as we show in an explicit example. A detection of a non-conformal correlation function, for example an equilateral 3-point function, would imply that the source of perturbations is not decoupled from the inflaton.

hep-th↗

arXiv2011

The (not so) squeezed limit of the primordial 3-point function

We prove that, in a generic single-field model, the consistency relation for the 3-point function in the squeezed limit receives corrections that vanish quadratically in the ratio of the momenta, i.e. as (k_L/k_S)^2. This implies that a detection of a bispectrum signal going as 1/k_L^2 in the squeezed limit, that is suppressed only by one power of k_L compared with the local shape, would rule out all single-field models. The absence of this kind of terms in the bispectrum holds also for multifield models, but only if all the fields have a mass much smaller than H. The detection of any scale dependence of the bias, for scales much larger than the size of the haloes, would disprove all single-field models. We comment on the regime of squeezing that can be probed by realistic surveys.

astro-ph.CO↗

arXiv2011

The CMB bispectrum in the squeezed limit

The CMB bispectrum generated by second-order effects at recombination can be calculated analytically when one of the three modes has a wavelength much longer than the other two and is outside the horizon at recombination. This was pointed out in \cite{Creminelli:2004pv} and here we correct their results. We derive a simple formula for the bispectrum, $f_{NL}^{loc} = - (1/6+ \cos 2 θ) \cdot (1- 1/2 \cdot d \ln (l_S^2 C_{S})/d \ln l_S)$, where $C_S$ is the short scale spectrum and $θ$ the relative orientation between the long and the short modes. This formula is exact and takes into account all effects at recombination, including recombination-lensing, but neglects all late-time effects such as ISW-lensing. The induced bispectrum in the squeezed limit is small and will negligibly contaminate the Planck search for a local primordial signal: this will be biased only by $f_{NL}^{loc}\approx-0.4$. The above analytic formula includes the primordial non-Gaussianity of any single-field model. It also represents a consistency check for second-order Boltzmann codes: we find substantial agreement with the CMBquick code.

astro-ph.CO↗

arXiv2011

Galilean symmetry in the effective theory of inflation: new shapes of non-Gaussianity

We study the consequences of imposing an approximate Galilean symmetry on the Effective Theory of Inflation, the theory of small perturbations around the inflationary background. This approach allows us to study the effect of operators with two derivatives on each field, which can be the leading interactions due to non-renormalization properties of the Galilean Lagrangian. In this case cubic non-Gaussianities are given by three independent operators, containing up to six derivatives, two with a shape close to equilateral and one peaking on flattened isosceles triangles. The four-point function is larger than in models with small speed of sound and potentially observable with the Planck satellite.

hep-th↗

arXiv2010

Galilean Genesis: an alternative to inflation

We propose a novel cosmological scenario, in which standard inflation is replaced by an expanding phase with a drastic violation of the Null Energy Condition (NEC): \dot H >> H^2. The model is based on the recently introduced Galileon theories, that allow NEC violating solutions without instabilities. The unperturbed solution describes a Universe that is asymptotically Minkowski in the past, expands with increasing energy density until it exits the regime of validity of the effective field theory and reheats. This solution is a dynamical attractor and the Universe is driven to it, even if it is initially contracting. The study of perturbations of the Galileon field reveals some subtleties, related to the gross violation of the NEC and it shows that adiabatic perturbations are cosmologically irrelevant. The model, however, suggests a new way to produce a scale invariant spectrum of isocurvature perturbations, which can later be converted to adiabatic: the Galileon is forced by symmetry to couple to the other fields as a dilaton; the effective metric it yields on the NEC violating solution is that of de Sitter space, so that all light scalars will automatically acquire a nearly scale-invariant spectrum of perturbations.

hep-th↗

arXiv2010

Spherical collapse in quintessence models with zero speed of sound

We study the spherical collapse model in the presence of quintessence with negligible speed of sound. This case is particularly motivated for w<-1 as it is required by stability. As pressure gradients are negligible, quintessence follows dark matter during the collapse. The spherical overdensity behaves as a separate closed FLRW universe, so that its evolution can be studied exactly. We derive the critical overdensity for collapse and we use the extended Press-Schechter theory to study how the clustering of quintessence affects the dark matter mass function. The effect is dominated by the modification of the linear dark matter growth function. A larger effect occurs on the total mass function, which includes the quintessence overdensities. Indeed, here quintessence constitutes a third component of virialized objects, together with baryons and dark matter, and contributes to the total halo mass by a fraction ~ (1+w) Omega_Q / Omega_m. This gives a distinctive modification of the total mass function at low redshift.

astro-ph.CO↗

arXiv2009

Sachs-Wolfe at second order: the CMB bispectrum on large angular scales

We calculate the Cosmic Microwave Background anisotropy bispectrum on large angular scales in the absence of primordial non-Gaussianities, assuming exact matter dominance and extending at second order the classic Sachs-Wolfe result δT/T=Φ/3. The calculation is done in Poisson gauge. Besides intrinsic contributions calculated at last scattering, one must consider integrated effects. These are associated to lensing, and to the time dependence of the potentials (Rees-Sciama) and of the vector and tensor components of the metric generated at second order. The bispectrum is explicitly computed in the flat-sky approximation. It scales as l^(-4) in the scale invariant limit and the shape dependence of its various contributions is represented in 3d plots. Although all the contributions to the bispectrum are parametrically of the same order, the full bispectrum is dominated by lensing. In the squeezed limit it corresponds to f_NL^local = -1/6 - cos(2 θ), where θis the angle between the short and the long modes; the angle dependent contribution comes from lensing. In the equilateral limit it corresponds to f_NL^equil ~ 3.13.

astro-ph.CO↗

arXiv2009

CMBPol Mission Concept Study: Probing Inflation with CMB Polarization

We summarize the utility of precise cosmic microwave background (CMB) polarization measurements as probes of the physics of inflation. We focus on the prospects for using CMB measurements to differentiate various inflationary mechanisms. In particular, a detection of primordial B-mode polarization would demonstrate that inflation occurred at a very high energy scale, and that the inflaton traversed a super-Planckian distance in field space. We explain how such a detection or constraint would illuminate aspects of physics at the Planck scale. Moreover, CMB measurements can constrain the scale-dependence and non-Gaussianity of the primordial fluctuations and limit the possibility of a significant isocurvature contribution. Each such limit provides crucial information on the underlying inflationary dynamics. Finally, we quantify these considerations by presenting forecasts for the sensitivities of a future satellite experiment to the inflationary parameters.

astro-ph↗

arXiv2009

The Effective Theory of Quintessence: the w<-1 Side Unveiled

We study generic single-field dark energy models, by a parametrization of the most general theory of their perturbations around a given background, including higher derivative terms. In appropriate limits this approach reproduces standard quintessence, k-essence and ghost condensation. We find no general pathology associated to an equation of state w_Q < -1 or in crossing the phantom divide w_Q = -1. Stability requires that the w_Q < -1 side of dark energy behaves, on cosmological scales, as a k-essence fluid with a virtually zero speed of sound. This implies that one should set the speed of sound to zero when comparing with data models with w_Q < -1 or crossing the phantom divide. We summarize the theoretical and stability constraints on the quintessential plane (1+w_Q) vs. speed of sound squared.

astro-ph↗

arXiv2008

The Phase Transition to Eternal Inflation

For slow-roll inflation we study the phase transition to the eternal regime. Starting from a finite inflationary volume, we consider the volume of the universe at reheating as order parameter. We show that there exists a critical value for the classical inflaton speed, \dotϕ^2/H^4 = 3/(2 π^2), where the probability distribution for the reheating volume undergoes a sharp transition. In particular, for sub-critical inflaton speeds all distribution moments become infinite. We show that at the same transition point the system develops a non-vanishing probability of having a strictly infinite reheating volume, while retaining a finite probability for finite values. Our analysis represents the exact quantum treatment of the system at lowest order in the slow-roll parameters and H^2/M_Pl^2.

hep-th↗

arXiv2008

Action approach to cosmological perturbations: the 2nd order metric in matter dominance

We study nonlinear cosmological perturbations during the post-inflationary evolution, using the equivalence between a perfect barotropic fluid and a derivatively coupled scalar field with Lagrangian [-(\partial ϕ)^2]^[(1+w)/2w]. Since this Lagrangian is just a special case of k-inflation, this approach is analogous to the one employed in the study of non-Gaussianities from inflation. We use this method to derive the second order metric during matter dominance in the comoving gauge directly as function of the primordial inflationary perturbation ζ. Going to Poisson gauge, we recover the metric previously derived in the literature.

astro-ph↗

arXiv2008

The Effective Field Theory of Inflation

We study the effective field theory of inflation, i.e. the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models. The scalar mode can be eaten by the metric by going to unitary gauge. In this gauge, the most general theory is built with the lowest dimension operators invariant under spatial diffeomorphisms, like g^{00} and K_{mu nu}, the extrinsic curvature of constant time surfaces. This approach allows us to characterize all the possible high energy corrections to simple slow-roll inflation, whose sizes are constrained by experiments. Also, it describes in a common language all single field models, including those with a small speed of sound and Ghost Inflation, and it makes explicit the implications of having a quasi de Sitter background. The non-linear realization of time diffeomorphisms forces correlation among different observables, like a reduced speed of sound and an enhanced level of non-Gaussianity.

hep-th↗

arXiv2007

A smooth bouncing cosmology with scale invariant spectrum

We present a bouncing cosmology which evolves from the contracting to the expanding phase in a smooth way, without developing instabilities or pathologies and remaining in the regime of validity of 4d effective field theory. A nearly scale invariant spectrum of perturbations is generated during the contracting phase by an isocurvature scalar with a negative exponential potential and then converted to adiabatic. The model predicts a slightly blue spectrum, n_S >~ 1, no observable gravitational waves and a high (but model dependent) level of non-Gaussianities with local shape. The model represents an explicit and predictive alternative to inflation, although, at present, it is clearly less compelling.

hep-th↗

arXiv2007

Estimators for local non-Gaussianities

We study the Likelihood function of data given f_NL for the so-called local type of non-Gaussianity. In this case the curvature perturbation is a non-linear function, local in real space, of a Gaussian random field. We compute the Cramer-Rao bound for f_NL and show that for small values of f_NL the 3-point function estimator saturates the bound and is equivalent to calculating the full Likelihood of the data. However, for sufficiently large f_NL, the naive 3-point function estimator has a much larger variance than previously thought. In the limit in which the departure from Gaussianity is detected with high confidence, error bars on f_NL only decrease as 1/ln Npix rather than Npix^-1/2 as the size of the data set increases. We identify the physical origin of this behavior and explain why it only affects the local type of non-Gaussianity, where the contribution of the first multipoles is always relevant. We find a simple improvement to the 3-point function estimator that makes the square root of its variance decrease as Npix^-1/2 even for large f_NL, asymptotically approaching the Cramer-Rao bound. We show that using the modified estimator is practically equivalent to computing the full Likelihood of f_NL given the data. Thus other statistics of the data, such as the 4-point function and Minkowski functionals, contain no additional information on f_NL. In particular, we explicitly show that the recent claims about the relevance of the 4-point function are not correct. By direct inspection of the Likelihood, we show that the data do not contain enough information for any statistic to be able to constrain higher order terms in the relation between the Gaussian field and the curvature perturbation, unless these are orders of magnitude larger than the size suggested by the current limits on f_NL.

astro-ph↗