arXiv subjects

Noemi Frusciante

Publications and source records attributed to Noemi Frusciante.

At least 55 records · Page 3Linked to original sources

arXiv2019

The role of the tachyonic instability in Horndeski gravity

The tachyonic instability is associated with the unboundedness of the Hamiltonian from below and results in an unstable low-$k$ regime. In the cosmological exploration of modified gravity, it is seldom taken into account, with more focus given to the popular no-ghost and no-gradient conditions. The latter though are intrinsically high-$k$ statements. Here we combine all three conditions into a full set of requirements that we show to guarantee stability on the whole range of cosmological scales. We then explore the impact of the different conditions on the parameter space of scalar-tensor gravity, with particular emphasis on the no-tachyon one. We focus on Horndeski gravity and also consider separately the two subclasses of $f(R)$ and Generalized Brans Dicke theories. We identify several interesting features, for instance in the parameter space of designer $f(R)$ on a $w$CDM background, shedding light on previous findings. When looking at the phenomenological functions $Σ$ and $μ$, associated to the weak lensing and clustering potential respectively, we find that in the case of Generalized Brans Dicke the no-tachyon condition clearly cuts models with $μ\,,\,Σ>1$. This effect is less prevalent in the Horndeski case due to the larger amount of free functions in the theory.

gr-qc↗

arXiv2019

Tracker and scaling solutions in DHOST theories

In quadratic-order degenerate higher-order scalar-tensor (DHOST) theories compatible with gravitational-wave constraints, we derive the most general Lagrangian allowing for tracker solutions characterized by $\dotϕ/H^p={\rm constant}$, where $\dotϕ$ is the time derivative of a scalar field $ϕ$, $H$ is the Hubble expansion rate, and $p$ is a constant. While the tracker is present up to the cubic-order Horndeski Lagrangian $L=c_2X-c_3X^{(p-1)/(2p)} \square ϕ$, where $c_2, c_3$ are constants and $X$ is the kinetic energy of $ϕ$, the DHOST interaction breaks this structure for $p \neq 1$. Even in the latter case, however, there exists an approximate tracker solution in the early cosmological epoch with the nearly constant field equation of state $w_ϕ=-1-2p\dot{H}/(3H^2)$. The scaling solution, which corresponds to $p=1$, is the unique case in which all the terms in the field density $ρ_ϕ$ and the pressure $P_ϕ$ obey the scaling relation $ρ_ϕ \propto P_ϕ \propto H^2$. Extending the analysis to the coupled DHOST theories with the field-dependent coupling $Q(ϕ)$ between the scalar field and matter, we show that the scaling solution exists for $Q(ϕ)=1/(μ_1 ϕ+μ_2)$, where $μ_1$ and $μ_2$ are constants. For the constant $Q$, i.e., $μ_1=0$, we derive fixed points of the dynamical system by using the general Lagrangian with scaling solutions. This result can be applied to the model construction of late-time cosmic acceleration preceded by the scaling $ϕ$-matter-dominated epoch.

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arXiv2018

Most general cubic-order Horndeski Lagrangian allowing for scaling solutions and the application to dark energy

In cubic-order Horndeski theories where a scalar field $ϕ$ is coupled to nonrelativistic matter with a field-dependent coupling $Q(ϕ)$, we derive the most general Lagrangian having scaling solutions on the isotropic and homogenous cosmological background. For constant $Q$ including the case of vanishing coupling, the corresponding Lagrangian reduces to the form $L=Xg_2(Y)-g_3(Y)\square ϕ$, where $X=-\partial_μϕ\partial^μϕ/2$ and $g_2, g_3$ are arbitrary functions of $Y=Xe^{λϕ}$ with constant $λ$. We obtain the fixed points of the scaling Lagrangian for constant $Q$ and show that the $ϕ$-matter-dominated-epoch ($ϕ$MDE) is present for the cubic coupling $g_3(Y)$ containing inverse power-law functions of $Y$. The stability analysis around the fixed points indicates that the $ϕ$MDE can be followed by a stable critical point responsible for the cosmic acceleration. We propose a concrete dark energy model allowing for such a cosmological sequence and show that the ghost and Laplacian instabilities can be avoided even in the presence of the cubic coupling.

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arXiv2018

The road ahead of Horndeski: cosmology of surviving scalar-tensor theories

In the context of the effective field theory of dark energy (EFT) we perform agnostic explorations of Horndeski gravity. We choose two parametrizations for the free EFT functions, namely a power law and a dark energy density-like behaviour on a non trivial Chevallier-Polarski-Linder background. We restrict our analysis to those EFT functions which do not modify the speed of propagation of gravitational waves. Among those, we prove that one specific function cannot be constrained by data, since its contribution to the observables is below the cosmic variance, although we show it has a relevant role in defining the viable parameter space. We place constraints on the parameters of these models combining measurements from present day cosmological datasets and we prove that the next generation galaxy surveys can improve such constraints by one order of magnitude. We then verify the validity of the quasi-static limit within the sound horizon of the dark field, by looking at the phenomenological functions $μ$ and $Σ$, associated respectively to clustering and lensing potentials. Furthermore, we notice up to $5\%$ deviations in $μ, Σ$ with respect to General Relativity at scales smaller than the Compton one. For the chosen parametrizations and in the quasi-static limit, future constraints on $μ$ and $Σ$ can reach the $1\%$ level and will allow us to discriminate between certain models at more than $3σ$, provided the present best-fit values remain.

astro-ph.CO↗

arXiv2018

New scaling solutions in cubic Horndeski theories

We propose a viable dark energy scenario in the presence of cubic Horndeski interactions and a standard scalar-field kinetic term with two exponential potentials. We show the existence of new scaling solutions along which the cubic coupling $G_3$ provides an important contribution to the field density that scales in the same way as the background fluid density. The solutions finally exit to the epoch of cosmic acceleration driven by a scalar-field dominated fixed point arising from the second exponential potential. We clarify the viable parameter space in which all the theoretically consistent conditions including those for the absence of ghost and Laplacian instabilities are satisfied on scaling and scalar-field dominated critical points. In comparison to Quintessence with the same scalar potential, we find that the cubic coupling gives rise to some novel features: (i) the allowed model parameter space is wider in that a steeper potential can drive the cosmic acceleration; (ii) the dark energy equation of state $w_ϕ$ today can be closer to $-1$ relative to Quintessence; (iii) even if the density associated with the cubic coupling dominates over the standard field density in the scaling era, the former contribution tends to be suppressed at low redshifts. We also compute quantities associated with the growth of matter perturbations and weak lensing potentials under the quasi-static approximation in the sub-horizon limit and show that the cubic coupling leads to the modified evolution of perturbations which can be distinguished from Quintessence.

gr-qc↗

arXiv2018

Do current cosmological observations rule out all Covariant Galileons?

We revisit the cosmology of Covariant Galileon gravity in view of the most recent cosmological data sets, including weak lensing. As a higher derivative theory, Covariant Galileon models do not have a $Λ$CDM limit and predict a very different structure formation pattern compared with the standard $Λ$CDM scenario. Previous cosmological analyses suggest that this model is marginally disfavoured, yet can not be completely ruled out. In this work we use a more recent and extended combination of data, and we allow for more freedom in the cosmology, by including a massive neutrino sector with three different mass hierarchies. We use the Planck measurements of Cosmic Microwave Background temperature and polarization; Baryonic Acoustic Oscillations measurements by BOSS DR12; local measurements of $H_0$; the joint light-curve analysis supernovae sample; and, for the first time, weak gravitational lensing from the KiDS collaboration. We find, that in order to provide a reasonable fit, a non-zero neutrino mass is indeed necessary, but we do not report any sizable difference among the three neutrino hierarchies. Finally, the comparison of the Bayesian Evidence to the $Λ$CDM one shows that in all the cases considered, Covariant Galileon models are statistically ruled out by cosmological data.

astro-ph.CO↗

arXiv2017

Tackling non-linearities with the effective field theory of dark energy and modified gravity

We present the extension of the effective field theory framework to the mildly non-linear scales. The effective field theory approach has been successfully applied to the late time cosmic acceleration phenomenon and it has been shown to be a powerful method to obtain predictions about cosmological observables on linear scales. However, mildly non-linear scales need to be consistently considered when testing gravity theories because a large part of the data comes from those scales. Thus, non-linear corrections to predictions on observables coming from the linear analysis can help in discriminating among different gravity theories. We proceed firstly by identifying the necessary operators which need to be included in the effective field theory Lagrangian in order to go beyond the linear order in perturbations and then we construct the corresponding non-linear action. Moreover, we present the complete recipe to map any single field dark energy and modified gravity models into the non-linear effective field theory framework by considering a general action in the Arnowitt-Deser-Misner formalism. In order to illustrate this recipe we proceed to map the beyond-Horndeski theory and low-energy Horava gravity into the effective field theory formalism. As a final step we derived the 4th order action in term of the curvature perturbation. This allowed us to identify the non-linear contributions coming from the linear order perturbations which at the next order act like source terms. Moreover, we confirm that the stability requirements, ensuring the positivity of the kinetic term and the speed of propagation for scalar mode, are automatically satisfied once the viability of the theory is demanded at linear level. The approach we present here will allow to construct, in a model independent way, all the relevant predictions on observables at mildly non-linear scales.

gr-qc↗

arXiv2017

EFTCAMB/EFTCosmoMC: Numerical Notes v3.0

EFTCAMB/EFTCosmoMC are publicly available patches to the CAMB/CosmoMC codes implementing the effective field theory approach to single scalar field dark energy and modified gravity models. With the present numerical notes we provide a guide to the technical details of the code. Moreover we reproduce, as they appear in the code, the complete set of the modified equations and the expressions for all the other relevant quantities used to construct these patches. We submit these notes to the arXiv to grant full and permanent access to this material which provides very useful guidance to the numerical implementation of the EFT framework. We will update this set of notes when relevant modifications to the EFTCAMB/EFTCosmoMC codes will be released. The present version is based on the version of EFTCAMB/EFTCosmoMC Sep17.

astro-ph.IM↗

arXiv2017

A de Sitter limit analysis for dark energy and modified gravity models

The effective field theory of dark energy and modified gravity is supposed to well describe, at low energies, the behaviour of the gravity modifications due to one extra scalar degree of freedom. The usual curvature perturbation is very useful when studying the conditions for the avoidance of ghost instabilities as well as the positivity of the squared speeds of propagation for both the scalar and tensor modes, or the Stückelberg field performs perfectly when investigating the evolution of linear perturbations. We show that the viable parameters space identified by requiring no-ghost instabilities and positive squared speeds of propagation does not change by performing a field redefinition, while the requirement of the avoidance of tachyonic instability might instead be different. Therefore, we find interesting to associate to the general modified gravity theory described in the effective field theory framework, a perturbation field which will inherit the whole properties of the theory. In the present paper we address the following questions: 1) how can we define such a field? and 2) what is the mass of such a field as the background approaches a final de Sitter state? We define a gauge invariant quantity which identifies the density of the dark energy perturbation field valid for any background. We derive the mass associated to the gauge invariant dark energy field on a de Sitter background, which we retain to be still a good approximation also at very low redshift ($z\simeq 0$). On this background we also investigate the value of the speed of propagation and we find that there exist classes of theories which admit a non-vanishing speed of propagation, even among the Horndeski model, for which in literature it has previously been found a zero speed. We finally apply our results to specific well known models.

gr-qc↗

arXiv2017

On the stability conditions for theories of modified gravity in presence of matter fields

We present a thorough stability analysis of modified gravity theories in the presence of matter fields. We use the Effective Field Theory framework for Dark Energy and Modified Gravity to retain a general approach for the gravity sector and a Sorkin-Schutz action for the matter one. Then, we work out the proper viability conditions to guarantee in the scalar sector the absence of ghosts, gradient and tachyonic instabilities. The absence of ghosts can be achieved by demanding a positive kinetic matrix, while the lack of a gradient instability is ensured by imposing a positive speed of propagation for all the scalar modes. In case of tachyonic instability, the mass eigenvalues have been studied and we work out the appropriate expressions. For the latter, an instability occurs only when the negative mass eigenvalue is much larger, in absolute value, than the Hubble parameter. We discuss the results for the minimally coupled quintessence model showing for a particular set of parameters two typical behaviours which in turn lead to a stable and an unstable configuration. Moreover, we find that the speeds of propagation of the scalar modes strongly depend on matter densities, for the beyond Horndeski theories. Our findings can be directly employed when testing modified gravity theories as they allow to identify the correct viability space.

gr-qc↗

arXiv2016

An Extended action for the effective field theory of dark energy: a stability analysis and a complete guide to the mapping at the basis of EFTCAMB

We present a generalization of the effective field theory (EFT) formalism for dark energy and modified gravity models to include operators with higher order spatial derivatives. This allows the extension of the EFT framework to a wider class of gravity theories such as Horava gravity. We present the corresponding extended action, both in the EFT and the Arnowitt-Deser-Misner (ADM) formalism, and proceed to work out a convenient mapping between the two, providing a self contained and general procedure to translate a given model of gravity into the EFT language at the basis of the Einstein-Boltzmann solver EFTCAMB. Putting this mapping at work, we illustrate, for several interesting models of dark energy and modified gravity, how to express them in the ADM notation and then map them into the EFT formalism. We also provide for the first time, the full mapping of GLPV models into the EFT framework. We next perform a thorough analysis of the physical stability of the generalized EFT action, in absence of matter components. We work out viability conditions that correspond to the absence of ghosts and modes that propagate with a negative speed of sound in the scalar and tensor sector, as well as the absence of tachyonic modes in the scalar sector. Finally, we extend and generalize the phenomenological basis in terms of $α$-functions introduced to parametrize Horndeski models, to cover all theories with higher order spatial derivatives included in our extended action. We elaborate on the impact of the additional functions on physical quantities, such as the kinetic term and the speeds of propagation for scalar and tensor modes.

gr-qc↗

arXiv2016

Horava Gravity in the Effective Field Theory formalism: from cosmology to observational constraints

We consider Horava gravity within the framework of the effective field theory (EFT) of dark energy and modified gravity. We work out a complete mapping of the theory into the EFT language for an action including all the operators which are relevant for linear perturbations with up to sixth order spatial derivatives. We then employ an updated version of the EFTCAMB/EFTCosmoMC package to study the cosmology of the low-energy limit of Horava gravity and place constraints on its parameters using several cosmological data sets. In particular we use cosmic microwave background (CMB) temperature-temperature and lensing power spectra by Planck 2013, WMAP low-l polarization spectra, WiggleZ galaxy power spectrum, local Hubble measurements, Supernovae data from SNLS, SDSS and HST and the baryon acoustic oscillations measurements from BOSS, SDSS and 6dFGS. We get improved upper bounds, with respect to those from Big Bang Nucleosynthesis, on the deviation of the cosmological gravitational constant from the local Newtonian one. At the level of the background phenomenology, we find a relevant rescaling of the Hubble rate at all epoch, which has a strong impact on the cosmological observables; at the level of perturbations, we discuss in details all the relevant effects on the observables and find that in general the quasi-static approximation is not safe to describe the evolution of perturbations. Overall we find that the effects of the modifications induced by the low-energy Horava gravity action are quite dramatic and current data place tight bounds on the theory parameters.

astro-ph.CO↗

arXiv2014

Effective Field Theory of Cosmic Acceleration: constraining dark energy with CMB data

We introduce EFTCAMB/EFTCosmoMC as publicly available patches to the commonly used CAMB/CosmoMC codes. We briefly describe the structure of the codes, their applicability and main features. To illustrate the use of these patches, we obtain constraints on parametrized pure EFT and designer $f(R)$ models, both on $Λ$CDM and $w$CDM background expansion histories, using data from Planck temperature and lensing potential spectra, WMAP low-$\ell$ polarization spectra (WP), and baryon acoustic oscillation (BAO). Upon inspecting theoretical stability of the models on the given background, we find non-trivial parameter spaces that we translate into viability priors. We use different combinations of data sets to show their individual effects on cosmological and model parameters. Our data analysis results show that, depending on the adopted data sets, in the $w$CDM background case this viability priors could dominate the marginalized posterior distributions. Interestingly, with Planck+WP+BAO+lensing data, in $f(R)$ gravity models, we get very strong constraints on the constant dark energy equation of state, $w_0\in(-1,-0.9997)\,\,(95% {\rm C.L.})$.

astro-ph.CO↗

arXiv2014

EFTCAMB/EFTCosmoMC: massive neutrinos in dark cosmologies

We revisit the degeneracy between massive neutrinos and generalized theories of gravity in the framework of effective field theory of cosmic acceleration. In particular we consider f(R) theories and a class of non-minimally coupled models parametrized via a coupling to gravity which is linear in the scale factor. In the former case, we find a slightly lower degeneracy with respect to what found so far in the literature, due to the fact that we implement exact designer f(R) models and evolve the full linear dynamics of perturbations. As a consequence, our bounds are slightly tighter on the f(R) parameter but looser on the summed neutrino mass. We also set a new upper bound on the Compton wavelength parameter ${\rm Log}_{10}B_0<-4.1$ at 95% C.L. with fixed summed neutrino mass ($\sum m_ν=0.06$ eV) in f(R) gravity with the combined data sets from cosmic microwave background temperature and lensing power spectra of Planck collaboration as well as galaxy power spectrum from WiggleZ dark energy survey. We do not observe a sizable degeneracy between massive neutrinos and modified gravity in the linear parametrization of non-minimally gravitational coupling model. The analysis is performed with an updated version of the EFTCAMB/EFTCosmoMC package, which is now publicly available and extends the first version of the code with the consistent inclusion of massive neutrinos, tensor modes, several alternative background histories and designer quintessence models.

astro-ph.CO↗

arXiv2014

Effective Field Theory of Cosmic Acceleration: an implementation in CAMB

We implement the effective field theory (EFT) approach to dark energy and modified gravity in the public Einstein-Boltzmann solver CAMB. The resulting code, which we dub EFTCAMB, is a powerful and versatile tool that can be used for several objectives. It can be employed to evolve the full dynamics of linear scalar perturbations in any given single field dark energy or modified gravity model, once the latter is mapped into the EFT formalism. It offers a numerical implementation of EFT as a model-independent framework to test gravity on cosmological scales. EFTCAMB has a built-in check for the fulfillment of general stability conditions such as the absence of ghost and superluminal propagation of perturbations. It handles phantom-divide crossing models and does not contain any quasi-static approximation, but rather evolves the full dynamics of perturbations on linear scales. As we will show, the latter is an important feature in view of the accuracy and scale range of upcoming surveys. We show the reliability and applicability of our code by evolving the dynamics of linear perturbations and extracting predictions for power spectra in several models. In particular we perform a thorough analysis of f(R) theories, comparing our outputs with those of an existing code for LCDM backgrounds, and finding an agreement that can reach 0.1% for models with a Compton wavelength consistent with current cosmological data. We then showcase the flexibility of our code studying two different scenarios. First we produce new results for designer f(R) models with a time-varying dark energy equation of state. Second, we extract predictions for linear observables in some parametrized EFT models with a phantom-divide crossing equation of state for dark energy.

astro-ph.CO↗

arXiv2014

Effective Field Theory of Dark Energy: a Dynamical Analysis

The effective field theory (EFT) of dark energy relies on three functions of time to describe the background dynamics. The viability of these functions is investigated here by means of a thorough dynamical analysis. While the system is underdetermined, and one can always find a set of functions reproducing any expansion history, we are able to determine general compatibility conditions for these functions by requiring a viable background cosmology. In particular, we identify a set of variables that allows us to transform the non-autonomous system of equations into an infinite-dimensional one characterized by a significant recursive structure. We then analyze several autonomous sub-systems, obtained truncating the original one at increasingly higher dimension, that correspond to increasingly general models of dark energy and modified gravity. Furthermore, we exploit the recursive nature of the system to draw some general conclusions on the different cosmologies that can be recovered within the EFT formalism and the corresponding compatibility requirements for the EFT functions. The machinery that we set up serves different purposes. It offers a general scheme for performing dynamical analysis of dark energy and modified gravity models within the model independent framework of EFT; the general results, obtained with this technique, can be projected into specific models, as we show in one example. It also can be used to determine appropriate ansatze for the three EFT background functions when studying the dynamics of cosmological perturbations in the context of large scale structure tests of gravity.

astro-ph.CO↗

arXiv2013

Gradient expansion of superhorizon perturbations in G-inflation

We develop the gradient expansion formalism for shift-symmetric Galileon-type actions. We focus on backgrounds that undergo inflation, work in the synchronous gauge, and obtain a general solution up to second order without imposing extra conditions at first order. The solution simplifies during the late stages of inflation. We also define a curvature perturbation conserved up to first order.

astro-ph.CO↗

arXiv2013

Lagrangian bias in the local bias model

It is often assumed that the halo-patch fluctuation field can be written as a Taylor series in the initial Lagrangian dark matter density fluctuation field. We show that if this Lagrangian bias is local, and the initial conditions are Gaussian, then the two-point cross-correlation between halos and mass should be linearly proportional to the mass-mass auto-correlation function. This statement is exact and valid on all scales; there are no higher order contributions, e.g., from terms proportional to products or convolutions of two-point functions, which one might have thought would appear upon truncating the Taylor series of the halo bias function. In addition, the auto-correlation function of locally biased tracers can be written as a Taylor series in the auto-correlation function of the mass; there are no terms involving, e.g., derivatives or convolutions. Moreover, although the leading order coefficient, the linear bias factor of the auto-correlation function is just the square of that for the cross-correlation, it is the same as that obtained from expanding the mean number of halos as a function of the local density only in the large-scale limit. In principle, these relations allow simple tests of whether or not halo bias is indeed local in Lagrangian space. We discuss why things are more complicated in practice. We also discuss our results in light of recent work on the renormalizability of halo bias, demonstrating that it is better to renormalize than not. We use the Lognormal model to illustrate many of our findings.

astro-ph.CO↗