Filippo Vernizzi

French National Centre for Scientific Research, Lutetia Parisorum, Île-de-France, France

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Publications (54)255.34 Total impact

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    ABSTRACT: Canonical models of single-field, slow-roll inflation do not lead to appreciable non-Gaussianity, unless derivative interactions of the inflaton become uncontrollably large. We propose a novel slow-roll scenario where scalar perturbations propagate at a subluminal speed, leading to sizeable equilateral non-Gaussianity, $f^{\rm equil}_{\rm NL}\propto 1/c_s^4$, largely insensitive to the ultraviolet physics. The model is based on a low-energy effective theory characterized by weakly broken invariance under internal galileon transformations, $\phi\to\phi+b_\mu x^\mu$, which protects the properties of perturbations from large quantum corrections. This provides the unique alternative to models such as DBI inflation in generating strongly subluminal/non-Gaussian scalar perturbations.
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    ABSTRACT: We introduce a new class of scalar-tensor theories of gravity that extend Horndeski, or "generalized Galileon," models. Despite possessing equations of motion of higher order in derivatives, we show that the true propagating degrees of freedom obey well-behaved second-order equations and are thus free from Ostrogradski instabilities, in contrast to standard lore. Remarkably, the covariant versions of the original Galileon Lagrangians-obtained by direct replacement of derivatives with covariant derivatives-belong to this class of theories. These extensions of Horndeski theories exhibit an uncommon, interesting phenomenology: The scalar degree of freedom affects the speed of sound of matter, even when the latter is minimally coupled to gravity.
    Physical Review Letters 05/2015; 114(21):211101. · 7.73 Impact Factor
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    ABSTRACT: Effective theories of a scalar $\phi$ invariant under the internal \textit{galileon symmetry} $\phi\to\phi+b_\mu x^\mu$ have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of \textit{weakly broken galileon invariance}, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon's quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.
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    ABSTRACT: We present a unifying treatment of dark energy and modified gravity that allows distinct conformal-disformal couplings of matter species to the gravitational sector. In this very general approach, we derive the conditions to avoid ghost and gradient instabilities. We compute the equations of motion for background quantities and linear perturbations. We illustrate our formalism with two simple scenarios, where either cold dark matter or a relativistic fluid is nonminimally coupled. This extends previous studies of coupled dark energy to a much broader spectrum of gravitational theories.
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    Jérôme Gleyzes, David Langlois, Filippo Vernizzi
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    ABSTRACT: We review and extend a novel approach that we introduced recently, to describe general dark energy or scalar-tensor models. Our approach relies on an ADM formulation based on the hypersurfaces where the underlying scalar field is uniform. The advantage of this approach is that it can describe in the same language and in a minimal way a vast number of existing models, such as quintessence models, $F(R)$ theories, scalar tensor theories, their Horndeski extensions and beyond. It also naturally includes Horava-Lifshitz theories. As summarized in this review, our approach provides a unified treatment of the linear cosmological perturbations about a FLRW universe, obtained by a systematic expansion of our general action up to quadratic order. This shows that the behaviour of these linear perturbations is generically characterized by five time-dependent functions. We derive the full equations of motion in the Newtonian gauge, and obtain in particular the equation of state for dark energy perturbations, in the Horndeski case, in terms of these functions. Our unifying description thus provides the simplest and most systematic way to confront theoretical models with current and future cosmological observations.
    International Journal of Modern Physics D 11/2014; 23(13). DOI:10.1142/S021827181443010X · 1.42 Impact Factor
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    ABSTRACT: We have recently proposed a new class of gravitational scalar-tensor theories free from ghost instabilities. As they generalize Horndeski theories, or "generalized" galileons, we call them G$^3$. These theories possess a simple formulation when the time hypersurfaces are chosen to coincide with the uniform scalar field hypersurfaces. We confirm that they do not suffer from Ostrogradski instabilities by presenting the details of the Hamiltonian formulation. We examine the coupling between these theories and matter. Moreover, we investigate how they transform under a disformal redefinition of the metric. Remarkably, these theories are preserved by disformal transformations, which also allow subfamilies of G$^3$ to be mapped into Horndeski theories.
    Journal of Cosmology and Astroparticle Physics 08/2014; 2015(02). DOI:10.1088/1475-7516/2015/02/018 · 5.88 Impact Factor
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    ABSTRACT: We show that the prediction for the primordial tensor power spectrum cannot be modified at leading order in derivatives. Indeed, one can always set to unity the speed of propagation of gravitational waves during inflation by a suitable disformal transformation of the metric, while a conformal one can make the Planck mass time-independent. Therefore, the tensor-to-scalar ratio unambiguously fixes the energy scale of inflation. Using the Effective Field Theory of Inflation, we check that predictions are independent of the choice of frame, as expected. The first corrections to the standard prediction come from two parity violating operators with three derivatives. Also the correlator $\langle\gamma\gamma\gamma\rangle$ is standard and only receives higher derivative corrections. These results hold also in multifield models of inflation and in alternatives to inflation and make the connection between a (quasi) scale-invariant tensor spectrum and inflation completely robust.
    Physical Review Letters 07/2014; 113(23). DOI:10.1103/PhysRevLett.113.231301 · 7.73 Impact Factor
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    ABSTRACT: We introduce a new class of scalar-tensor theories that extend Horndeski, or "generalized galileon", models. Despite possessing equations of motion of higher order in derivatives, we show that the true propagating degrees of freedom obey well-behaved second-order equations and are thus free from Ostrogradski instabilities, in contrast to the standard lore. Remarkably, the covariant versions of the original galileon Lagrangians-obtained by direct replacement of derivatives with covariant derivatives-belong to this class of theories. These extensions of Horndeski theories exhibit an uncommon, interesting phenomenology: the scalar degree of freedom affects the speed of sound of matter, even when the latter is minimally coupled to gravity.
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    Zhiqi Huang, Filippo Vernizzi
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    ABSTRACT: We compute the full cosmic microwave background temperature bispectrum generated by nonlinearities after single-field inflation. By integrating the photon temperature at second order along a perturbed geodesic in Newtonian gauge, we derive an expression for the observed temperature fluctuations that, for the first time, clarifies the separation of the gravitational lensing and time-delay effects from the purely second-order contributions. We then use the second-order Boltzmann code CosmoLib2nd to calculate these contributions and their bispectrum. Including the perturbations in the photon path, the numerically computed bispectrum exactly matches the expected squeezed limit. Moreover, the analytic squeezed-limit formula reproduces well the signal-to-noise ratio and shape of the full bispectrum, potentially facilitating the subtraction of the bias induced by second-order effects. For a cosmic-variance limited experiment with lmax=2000, the bias on a local signal is fNLloc=0.73 negligible for equilateral and orthogonal signals. The signal-to-noise ratio is unity at lmax̃3000, suggesting that second-order effects may hopefully be measured in the future.
    Physical Review D 12/2013; 89(2). DOI:10.1103/PhysRevD.89.021302 · 4.86 Impact Factor
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    ABSTRACT: The recently derived consistency relations for Large Scale Structure do not hold if the Equivalence Principle (EP) is violated. We show it explicitly in a toy model with two fluids, one of which is coupled to a fifth force. We explore the limits that galaxy surveys can set on EP violation looking at the squeezed limit of the 3-point function involving two populations of objects. We find that one can explore EP violations of order 10^{-3} - 10^{-4} on cosmological scales. Chameleon models are already very constrained by the requirement of screening within the Solar System and only a very tiny region of the parameter space can be explored with this method. We show that no violation of the consistency relations is expected in Galileon models.
    Journal of Cosmology and Astroparticle Physics 12/2013; 2014(06). DOI:10.1088/1475-7516/2014/06/009 · 5.88 Impact Factor
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    ABSTRACT: We generalize the recently derived single-field consistency relations of Large Scale Structure in two directions. First, we treat the effect of the long modes (with momentum q) on the short ones (with momentum k) non-perturbatively, by writing resummed consistency relations which do not require k/q \delta_q << 1. These relations do not make any assumptions on the short-scales physics and are extended to include (an arbitrary number of) multiple long modes, internal lines with soft momenta and soft loops. We do several checks of these relations in perturbation theory and we verify that the effect of soft modes always cancels out in equal-time correlators. Second, we write the relations directly in redshift space, without assuming the single-stream approximation: not only the long mode affects the short scales as a homogeneous gravitational field, but it also displaces them by its velocity along the line-of-sight. Redshift space consistency relations still vanish when short modes are taken at equal time: an observation of a signal in the squeezed limit would point towards multifield inflation or a violation of the equivalence principle.
    Journal of Cosmology and Astroparticle Physics 11/2013; 2014(02). DOI:10.1088/1475-7516/2014/02/051 · 5.88 Impact Factor
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    ABSTRACT: We derive consistency relations for the late universe (CDM and \Lambda CDM): relations between an n-point function of the density contrast \delta and an (n+1)-point function in the limit in which one of the (n+1) momenta becomes much smaller than the others. These are based on the observation that a long mode, in single-field models of inflation, reduces to a diffeomorphism since its freezing during inflation all the way until the late universe, even when the long mode is inside the horizon (but out of the sound horizon). These results are derived in Newtonian gauge, at first and second order in the small momentum q of the long mode and they are valid non-perturbatively in the short-scale \delta. In the non-relativistic limit our results match with (Kehagias and Riotto '12) and (Peloso and Pietroni '12). These relations are a consequence of diffeomorphism invariance; they are not satisfied in the presence of extra degrees of freedom during inflation or violation of the Equivalence Principle (extra forces) in the late universe.
    Journal of Cosmology and Astroparticle Physics 09/2013; DOI:10.1088/1475-7516/2013/12/025 · 5.88 Impact Factor
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    Federico Piazza, Filippo Vernizzi
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    ABSTRACT: The effective field theory of cosmological perturbations stems from considering a cosmological background solution as a state displaying spontaneous breaking of time translations and (adiabatic) perturbations as the related Nambu-Goldstone modes. With this insight, one can systematically develop a theory for the cosmological perturbations during inflation and, with minor modifications, also describe in full generality the gravitational interactions of dark energy, which are relevant for late-time cosmology. The formalism displays a unique set of Lagrangian operators containing an increasing number of cosmological perturbations and derivatives. We give an introductory description of the unitary gauge formalism for theories with broken gauge symmetry---that allows to write down the most general Lagrangian---and of the Stueckelberg "trick"---that allows to recover gauge invariance and to make the scalar field explicit. We show how to apply this formalism to gravity and cosmology and we reproduce the detailed analysis of the action in the ADM variables. We also review some basic applications to inflation and dark energy.
    Classical and Quantum Gravity 07/2013; 30(21). DOI:10.1088/0264-9381/30/21/214007 · 3.10 Impact Factor
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    ABSTRACT: We propose a minimal description of single field dark energy/modified gravity within the effective field theory formalism for cosmological perturbations, which encompasses most existing models. We start from a generic Lagrangian given as an arbitrary function of the lapse and of the extrinsic and intrinsic curvature tensors of the time hypersurfaces in unitary gauge, i.e. choosing as time slicing the uniform scalar field hypersurfaces. Focusing on linear perturbations, we identify seven Lagrangian operators that lead to equations of motion containing at most two (space or time) derivatives, the background evolution being determined by the time dependent coefficients of only three of these operators. We then establish a dictionary that translates any existing or future model whose Lagrangian can be written in the above form into our parametrized framework. As an illustration, we study Horndeski's-or generalized Galileon-theories and show that they can be described, up to linear order, by only six of the seven operators mentioned above. This implies, remarkably, that the dynamics of linear perturbations can be more general than that of Horndeski while remaining second order. Finally, in order to make the link with observations, we provide the entire set of linear perturbation equations in Newtonian gauge, the effective Newton constant in the quasi-static approximation and the ratio of the two gravitational potentials, in terms of the time-dependent coefficients of our Lagrangian.
    Journal of Cosmology and Astroparticle Physics 04/2013; 2013(08). DOI:10.1088/1475-7516/2013/08/025 · 5.88 Impact Factor
  • Zhiqi Huang, Filippo Vernizzi
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    ABSTRACT: We compute the cosmic microwave background temperature bispectrum generated by nonlinearities at recombination on all scales. We use CosmoLib2nd, a numerical Boltzmann code at second order to compute cosmic microwave background bispectra on the full sky. We consistently include all effects except gravitational lensing, which can be added to our result using standard methods. The bispectrum is peaked on squeezed triangles and agrees with the analytic approximation in the squeezed limit at the few percent level for all the scales where this is applicable. On smaller scales, we recover previous results on perturbed recombination. For cosmic-variance limited data to l_{max⁡}=2000, its signal-to-noise ratio is S/N=0.47, corresponding to f_{NL}^{eff}=-2.79, and will bias a local signal by f_{NL}^{loc}≃0.82.
    Physical Review Letters 03/2013; 110(10):101303. DOI:10.1103/PhysRevLett.110.101303 · 7.73 Impact Factor
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    ABSTRACT: We use the so-called eikonal approximation, recently introduced in the context of cosmological perturbation theory, to compute power spectra for multicomponent fluids. We demonstrate that, at any given order in standard perturbation theory, multipoint power spectra do not depend on the large-scale adiabatic modes. Moreover, we employ perturbation theories to decipher how nonadiabatic modes, such as a relative velocity between two different components, damp the small-scale matter power spectrum, a mechanism recently described in the literature. In particular, we do an explicit calculation at one-loop order of this effect. While the one-loop result eventually breaks down, we show how the damping effect can be fully captured by the help of the eikonal approximation. A relative velocity not only induces mode damping but also creates large-scale anisotropic modulations of the matter power spectrum amplitude. We illustrate this for the Local Group environment.
    Physical review D: Particles and fields 02/2013; 87(4). DOI:10.1103/PhysRevD.87.043530 · 4.86 Impact Factor
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    Zhiqi Huang, Filippo Vernizzi
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    ABSTRACT: We compute the cosmic microwave background temperature bispectrum generated by nonlinearities at recombination on all scales. We use CosmoLib$2^{\rm nd}$, a numerical Boltzmann code at second-order to compute CMB bispectra on the full sky. We consistently include all effects except gravitational lensing, which can be added to our result using standard methods. The bispectrum is peaked on squeezed triangles and agrees with the analytic approximation in the squeezed limit at the few per cent level for all the scales where this is applicable. On smaller scales, we recover previous results on perturbed recombination. For cosmic-variance limited data to $l_{\rm max} =2000$, its signal-to-noise is $S/N=0.47$ and will bias a local signal by $f_{\rm NL}^{\rm loc}\simeq 0.82$.
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    Giulia Gubitosi, Federico Piazza, Filippo Vernizzi
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    ABSTRACT: We propose a universal description of dark energy and modified gravity that includes all single-field models. By extending a formalism previously applied to inflation, we consider the metric universally coupled to matter fields and we write in terms of it the most general unitary gauge action consistent with the residual unbroken symmetries of spatial diffeomorphisms. Our action is particularly suited for cosmological perturbation theory: the background evolution depends on only three operators. All other operators start at least at quadratic order in the perturbations and their effects can be studied independently and systematically. In particular, we focus on the properties of a few operators which appear in non-minimally coupled scalar-tensor gravity and galileon theories. In this context, we study the mixing between gravity and the scalar degree of freedom. We assess the quantum and classical stability, derive the speed of sound of fluctuations and the renormalization of the Newton constant. The scalar can always be de-mixed from gravity at quadratic order in the perturbations, but not necessarily through a conformal rescaling of the metric. We show how to express covariant field-operators in our formalism and give several explicit examples of dark energy and modified gravity models in our language. Finally, we discuss the relation with the covariant EFT methods recently appeared in the literature.
    Journal of Cosmology and Astroparticle Physics 09/2012; 1302(2013):032. DOI:10.1088/1475-7516/2013/02/032 · 6.04 Impact Factor
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    ABSTRACT: Euclid is a European Space Agency medium class mission selected for launch in 2019 within the Cosmic Vision 2015-2025 programme. The main goal of Euclid is to understand the origin of the accelerated expansion of the Universe. Euclid will explore the expansion history of the Universe and the evolution of cosmic structures by measuring shapes and redshifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid's Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.
    Living Reviews in Relativity 06/2012; 16. DOI:10.12942/lrr-2013-6 · 16.53 Impact Factor
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    ABSTRACT: We compute the matter bispectrum in the presence of primordial local non-Gaussianity over a wide range of scales, including the very small nonlinear ones. We use the Halo Model approach, considering non-Gaussian corrections to the halo profiles, the halo mass function and the bias functions. We compare our results in the linear and mildly nonlinear scales to a large ensemble of Gaussian and non-Gaussian numerical simulations. We consider both squeezed and equilateral configurations, at redshift z = 0 and z = 1. For z = 0, the deviations between the Halo Model and the simulations are smaller than 10% in the squeezed limit, both in the Gaussian and non-Gaussian cases. The Halo Model allows to make predictions on scales much smaller than those reached by numerical simulations. For local non-Gaussian initial conditions with a parameter fNL = 100, we find an enhancement of the bispectrum in the squeezed configuration k = k3 = k2 >> k1 \sim 0.01 h^{-1} Mpc, of \sim 15% and \sim 25% on scales k \sim 1 h^{-1} Mpc, at z = 0 and z = 1 respectively. This is mainly due to the non-Gaussian corrections in the linear bias. Finally we provide a very simple expression valid for any scenario, i.e. for any choice of the halo profile, mass and bias functions, which allow for a fast evaluation of the bispectrum on squeezed configurations.
    Journal of Cosmology and Astroparticle Physics 05/2012; 2012(08). DOI:10.1088/1475-7516/2012/08/036 · 5.88 Impact Factor

Publication Stats

2k Citations
255.34 Total Impact Points

Institutions

  • 2003–2015
    • French National Centre for Scientific Research
      Lutetia Parisorum, Île-de-France, France
  • 2014
    • Institute of Geophysics, China Earthquake Administration
      Peping, Beijing, China
  • 2013
    • Columbia University
      • Institute for Strings, Cosmology, and Astroparticle Physics
      New York, New York, United States
    • Université Paris-Sud 11
      Orsay, Île-de-France, France
  • 2008–2013
    • Cea Leti
      Grenoble, Rhône-Alpes, France
    • Abdus Salam International Centre for Theoretical Physics
      Trst, Friuli Venezia Giulia, Italy
  • 2001–2012
    • University of Geneva
      • Department of Theoretical Physics
      Genève, Geneva, Switzerland
    • University of Oxford
      • Department of Physics
      Oxford, England, United Kingdom
  • 2004–2007
    • University of Helsinki
      • Department of Physical Sciences
      Helsinki, Southern Finland Province, Finland