DE&MG Publications – Page 2

Cosmological evolution in DHOST theories

Posted on October 29, 2018November 6, 2018 by Valeria Pettorino

Abstract

In the context of Degenerate Higher-Order Scalar-Tensor (DHOST) theories, we study cosmological solutions and their stability properties. In particular, we explicitly illustrate the crucial role of degeneracy by showing how the higher order homogeneous equations in the physical frame (where matter is minimally coupled) can be recast in a system of equations that do not involve higher order derivatives. We study the fixed points of the dynamics, finding the conditions for having a de Sitter attractor at late times. Then we consider the coupling to matter field (described for convenience by a k-essence Lagrangian) and find the conditions to avoid gradient and ghost instabilities at linear order in cosmological perturbations, extending previous work. Finally, we apply these results to a simple subclass of DHOST theories, showing that de Sitter attractor conditions, no ghost and no gradient instabilities conditions (both in the self-accelerating era and in the matter dominated era) can be compatible.

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

Posted on October 24, 2018November 6, 2018 by Valeria Pettorino

Abstract

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 $3 σ$ , provided the present best-fit values remain.

Breaking degeneracies in modified gravity with higher (than 2nd) order weak-lensing statistics

Posted on May 16, 2018September 19, 2019 by Samuel Farrens

Abstract

General relativity (GR) has been well tested up to solar system scales, but it is much less certain that standard gravity remains an accurate description on the largest, that is, cosmological, scales. Many extensions to GR have been studied that are not yet ruled out by the data, including by that of the recent direct gravitational wave detections. Degeneracies among the standard model (ΛCDM) and modified gravity (MG) models, as well as among different MG parameters, must be addressed in order to best exploit information from current and future surveys and to unveil the nature of dark energy. We propose various higher-order statistics in the weak-lensing signal as a new set of observables able to break degeneracies between massive neutrinos and MG parameters. We have tested our methodology on so-called f(R) models, which constitute a class of viable models that can explain the accelerated universal expansion by a modification of the fundamental gravitational interaction. We have explored a range of these models that still fit current observations at the background and linear level, and we show using numerical simulations that certain models which include massive neutrinos are able to mimic ΛCDM in terms of the 3D power spectrum of matter density fluctuations. We find that depending on the redshift and angular scale of observation, non-Gaussian information accessed by higher-order weak-lensing statistics can be used to break the degeneracy between f(R) models and ΛCDM. In particular, peak counts computed in aperture mass maps outperform third- and fourth-order moments.

Model-independent reconstruction of the linear anisotropic stress

Posted on May 1, 2018December 3, 2018 by Valeria Pettorino

Abstract

In this work, we use recent data on the Hubble expansion rate $H (z)$ , the quantity $f σ_{8} (z)$ from redshift space distortions and the statistic $E_{g}$ from clustering and lensing observables to constrain in a model-independent way the linear anisotropic stress parameter $η$ . This estimate is free of assumptions about initial conditions, bias, the abundance of dark matter and the background expansion. We denote this observable estimator as $η_{o b s}$ . If $η_{o b s}$ turns out to be different from unity, it would imply either a modification of gravity or a non-perfect fluid form of dark energy clustering at sub-horizon scales. Using three different methods to reconstruct the underlying model from data, we report the value of $η_{o b s}$ at three redshift values, $z = 0.29, 0.58, 0.86$ . Using the method of polynomial regression, we find $η_{o b s} = 0.57 \pm 1.05$ , $η_{o b s} = 0.48 \pm 0.96$ , and $η_{o b s} = - 0.11 \pm 3.21$ , respectively. Assuming a constant $η_{o b s}$ in this range, we find $η_{o b s} = 0.49 \pm 0.69$ . We consider this method as our fiducial result, for reasons clarified in the text. The other two methods give for a constant anisotropic stress $η_{o b s} = 0.15 \pm 0.27$ (binning) and $η_{o b s} = 0.53 \pm 0.19$ (Gaussian Process). We find that all three estimates are compatible with each other within their $1 σ$ error bars. While the polynomial regression method is compatible with standard gravity, the other two methods are in tension with it.

Testing (modified) gravity with 3D and tomographic cosmic shear

Posted on February 16, 2018February 16, 2018 by Valeria Pettorino

Abstract

Cosmic shear, the weak gravitational lensing caused by the large-scale structure, is one of the primary probes to test gravity with current and future surveys. There are two main techniques to analyse a cosmic shear survey; a tomographic method, where correlations between the lensing signal in different redshift bins are used to recover redshift information, and a 3D approach, where the full redshift information is carried through the entire analysis. Here we compare the two methods, by forecasting cosmological constraints for future surveys like Euclid. We extend the 3D formalism for the first time to theories beyond the standard model, belonging to the Horndeski class. This includes the majority of universally coupled extensions to LCDM with one scalar degree of freedom in addition to the metric, which are still in agreement with current observations. Given a fixed background, the evolution of linear perturbations in Horndeski gravity is described by a set of four functions of time only. We model their time evolution assuming proportionality to the dark energy density fraction and place Fisher matrix constraints on the proportionality coefficients. We find that a 3D analysis can constrain Horndeski theories better than a tomographic one, in particular with a decrease in the errors on the Horndeski parameters of the order of 20 - 30%. This paper shows for the first time a quantitative comparison on an equal footing between Fisher matrix forecasts for both a fully 3D and a tomographic analysis of cosmic shear surveys. The increased sensitivity of the 3D formalism comes from its ability to retain information on the source redshifts along the entire analysis.

Summary

A new paper has been put on the arXiv, led by Alessio Spurio Mancini, PhD student of CosmoStat member Valeria Pettorino in collaboration with R. Reischke, B.M. Scháefer (Heidelberg) and M. Zumalacárregui (Berkeley LBNL and Paris Saclay IPhT).
The authors investigate the performance of a 3D analysis of cosmic shear measurements vs a tomographic analysis as a probe of Horndeski theories of modified gravity, setting constraints by means of a Fisher matrix analysis on the parameters that describe the evolution of linear perturbations, using the specifications of a future Euclid-like experiment. Constraints are shown on both the modified gravity parameters and on a set of standard cosmological parameters, including the sum of neutrino masses. The analysis is restricted to angular modes ell < 1000 and k < 1 h/Mpc to avoid the deeply non-linear regime of structure growth. Below the main results of the paper.

The signal-to-noise ratio of both a 3D analysis as well as a tomographic one is very similar.
3D cosmic shear provides tighter constraints than tomography for most cosmological parameters, with both methods showing very similar degeneracies.
The gain of 3D vs tomography is particularly significant for the sum of the neutrino masses (factor 3). For the Horndeski parameters the
gain is of the order of 20 - 30 % in the errors.
In Horndeski theories, braiding and the effective Newton coupling parameters (\alpha_B and \alpha_M) are constrained better if the kineticity is higher.
We investigated the impact on non-linear scales, and introduced an artificial screening scale, which pushes the deviations from General Relativity to zero below its value. The gain when including the non-linear signal calls for the development of analytic or semi-analytic prescriptions for the treatment of non-linear scales in ΛCDM and modified gravity.

Self-accelerating universe in scalar-tensor theories after GW170817

Posted on December 18, 2017November 6, 2018 by Valeria Pettorino

Abstract

The recent simultaneous detection of gravitational waves and a gamma ray burst from a neutron star merger significantly shrank the space of viable scalar-tensor theories by demanding that the speed of gravity is equal to that of light. The survived theories belong to the class of degenerate higher order scalar-tensor theories. We study whether these theories are suitable as dark energy candidates. We find scaling solutions in the matter dominated universe that lead to de Sitter solutions at late times without the cosmological constant, realising self-acceleration. We evaluate quasi-static perturbations around self-accelerating solutions and show that the stringent constraints coming from astrophysical objects and gravitational waves can be satisfied, leaving interesting possibilities to test these theories by cosmological observations.

Vainshtein mechanism after GW170817

Posted on November 17, 2017November 6, 2018 by Valeria Pettorino

Abstract

The almost simultaneous detection of gravitational waves and a short gamma-ray burst from a neutron star merger has put a tight constraint on the difference between the speed of gravity and light. In the four-dimensional scalar-tensor theory with second order equations of motion, the Horndeski theory, this translates into a significant reduction of the viable parameter space of the theory. Recently, extensions of Horndeski theory, which are free from Ostrogradsky ghosts despite the presence of higher order derivatives in the equations of motion, have been identified and classified exploiting the degeneracy criterium. In these new theories, the fifth force mediated by the scalar field must be suppressed in order to evade the stringent Solar System constraints. We study the Vainshtein mechanism in the most general degenerate higher order scalar-tensor theory in which light and gravity propagate at the same speed. We find that the Vainshtein mechanism generally works outside a matter source but it is broken inside matter, similarly to beyond Horndeski theories. This leaves interesting possibilities to test these theories that are compatible with gravitational wave observations using astrophysical objects.

Linear and non-linear Modified Gravity forecasts with future surveys

Posted on March 3, 2017June 27, 2017 by Valeria Pettorino

Abstract

Modified Gravity theories generally affect the Poisson equation and the gravitational slip (effective anisotropic stress) in an observable way, that can be parameterized by two generic functions (η and μ) of time and space. We bin the time dependence of these functions in redshift and present forecasts on each bin for future surveys like Euclid. We consider both Galaxy Clustering and Weak Lensing surveys, showing the impact of the non-linear regime, treated with two different semi-analytical approximations. In addition to these future observables, we use a prior covariance matrix derived from the Planck observations of the Cosmic Microwave Background. Our results show that η and μ in different redshift bins are significantly correlated, but including non-linear scales reduces or even eliminates the correlation, breaking the degeneracy between Modified Gravity parameters and the overall amplitude of the matter power spectrum. We further decorrelate parameters with a Zero-phase Component Analysis and identify which combinations of the Modified Gravity parameter amplitudes, in different redshift bins, are best constrained by future surveys. We also extend the analysis to two particular parameterizations of the time evolution of μ and η and consider, in addition to Euclid, also SKA1, SKA2, DESI: we find in this case that future surveys will be able to constrain the current values of η and μ at the 2−5% level when using only linear scales (wavevector k < 0.15 h/Mpc), depending on the specific time parameterization; sensitivity improves to about 1% when non-linearities are included.

Summary

A new paper has been put on the arXiv by new CosmoStat member Valeria Pettorino, her PhD student Santiago Casas, in collaboration with Martin Kunz (Geneva) and Matteo Martinelli (Leiden).
The authors discuss forecasts in Modified Gravity cosmologies, described by two generic functions of time and space [Planck Dark Energy and Modified Gravity 2015, Asaba et al 2013,Bull 2015, Alonso et al 2016]. Their amplitude is constrained in different redshift bins. The authors elaborate on the impact of non-linear scales, showing that their inclusion (via a non-linear semi-analytical prescription applied to Modified Gravity) enables to highly reduce correlation among different redshift bins, even before any decorrelation procedure is applied. This is visually seen in the figure below (Fig.4 of arXiv), for the case of Galaxy Clustering: the correlation Matrix of the cosmological parameters (including the amplitudes of the Modified Gravity functions, binned in redshift) is much more diagonal in the non-linear case (right panel) than in the linear one (left panel).

A decorrelation procedure (Zero-phase Component Analysis, ZCA) is anyway used to extract those combinations which are best constrained by future surveys such as Euclid. With respect to Principal Component Analysis, ZCA allows to find a new vector of uncorrelated variables that is as similar as possible to the original vector of variables.

The authors further consider two smooth time functions whose main allowed to depart from General Relativity only at late times (late-time parameterization) or able to detach also at early times (early-time parameterization). The Fisher Matrix forecasts for standard and Modified gravity parameters, for different surveys (Euclid, SKA1, SKA2) is shown in the plot below (extracted from Fig.15 of arXiv), in which Galaxy Clustering and Weak Lensing probes are combined. Left panel refers to linear analysis, right panel includes a non-linear treatment.

Authors:	M. Crisostomi , K. Koyama, D. Langlois, K. Noui and D. A. Steer
Journal:
Year:	2018
Download:	arXiv

Authors:	Noemi Frusciante (U. Lisbon (main)), Simone Peirone (Leiden U.), Santiago Casas (CEA Paris-Saclay), Nelson A. Lima (U. Heidelberg, ITP)
Journal:	Submitted to PRD
Year:	10/2018
Download:	Inspire\| Arxiv

Authors:	A. Peel, V. Pettorino, C. Giocoli, J.-L. Starck, M. Baldi
Journal:	A&A
Year:	2018
Download:	ADS \| arXiv

Authors:	Ana Marta Pinho, Santiago Casas, Luca Amendola
Journal:	Accepted for JCAP
Year:	05/2018
Download:	Inspire\| Arxiv

Authors:	A. Spurio Mancini, R. Reischke, V. Pettorino, B.M. Scháefer, M. Zumalacárregui
Journal:	Submitted to MNRAS
Year:	2018
Download:	ADS \| arXiv

Authors:	Marco Crisostomi and Kazuya Koyama
Journal:	PRD
Year:	2018
Download:	arXiv

Authors:	S. Casas, M. Kunz, M. Martinelli, V. Pettorino
Journal:	Physics Letters B
Year:	2017
Download:	ADS \| arXiv

Abstract

Noemi Frusciante (U. Lisbon (main)), Simone Peirone (Leiden U.), Santiago Casas (CEA Paris-Saclay), Nelson A. Lima (U. Heidelberg, ITP)

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Breaking degeneracies in modified gravity with higher (than 2nd) order weak-lensing statistics

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