Scale-invariant alternatives to general relativity. The inflation–dark-energy connection


Abstract

We discuss the cosmological phenomenology of biscalar--tensor models
displaying a maximally symmetric Einstein--frame kinetic sector and
constructed on the basis of scale symmetry and volume--preserving
diffeomorphisms. These theories contain a single dimensionful
parameter $\Lambda_0$---associated with the invariance under the
aforementioned restricted coordinate transformations---and a massless
dilaton field. At large field values these scenarios lead to inflation
with no generation of isocurvature perturbations. The corresponding
predictions depend only on two dimensionless parameters, which
characterize the curvature of the field--manifold and the leading
order behavior of the inflationary potential. For $\Lambda_0=0$ the
scale symmetry is unbroken and the dilaton admits only derivative
couplings to matter, evading all fifth force constraints. For
$\Lambda_0\neq 0$ the field acquires a run-away potential that can
support a dark energy dominated era at late times. We confront a
minimalistic realization of this appealing framework with observations
using a Markov-Chain-Monte-Carlo approach, with likelihoods from
present BAO, SNIa and CMB data. A Bayesian model comparison indicates
a preference for the considered model over $\Lambda$CDM, under certain
assumptions for the priors. The impact of possible consistency
relations among the early and late Universe dynamics that can appear
within this setting is discussed with the use of correlation
matrices. The results indicate that a precise determination of the
inflationary observables and the dark energy equation--of--state could
significantly constraint the model parameters.

Distinguishing standard and modified gravity cosmologies with machine learning

 

Authors: A. Peel, F. Lalande, J.-L. Starck, V. Pettorino, J. Merten,  C. Giocoli, M. Meneghetti,  M. Baldi
Journal: Submitted to PRL
Year: 2018
Download: ADS | arXiv


Abstract

We present a convolutional neural network to identify distinct cosmological scenarios based on the weak-lensing maps they produce. Modified gravity models with massive neutrinos can mimic the standard concordance model in terms of Gaussian weak-lensing observables, limiting a deeper understanding of what causes cosmic acceleration. We demonstrate that a network trained on simulated clean convergence maps, condensed into a novel representation, can discriminate between such degenerate models with 83%-100% accuracy. Our method outperforms conventional statistics by up to 40% and is more robust to noise.

On the dissection of degenerate cosmologies with machine learning

 

Authors: J. Merten,  C. Giocoli, M. Baldi, M. Meneghetti, A. Peel, F. Lalande, J.-L. Starck, V. Pettorino
Journal: Submitted to MNRAS
Year: 2018
Download: ADS | arXiv


Abstract

Based on the DUSTGRAIN-pathfinder suite of simulations, we investigate observational degeneracies between nine models of modified gravity and massive neutrinos. Three types of machine learning techniques are tested for their ability to discriminate lensing convergence maps by extracting dimensional reduced representations of the data. Classical map descriptors such as the power spectrum, peak counts and Minkowski functionals are combined into a joint feature vector and compared to the descriptors and statistics that are common to the field of digital image processing. To learn new features directly from the data we use a Convolutional Neural Network (CNN). For the mapping between feature vectors and the predictions of their underlying model, we implement two different classifiers; one based on a nearest-neighbour search and one that is based on a fully connected neural network. We find that the neural network provides a much more robust classification than the nearest-neighbour approach and that the CNN provides the most discriminating representation of the data. It achieves the cleanest separation between the different models and the highest classification success rate of 59% for a single source redshift. Once we perform a tomographic CNN analysis, the total classification accuracy increases significantly to 76% with no observational degeneracies remaining. Visualising the filter responses of the CNN at different network depths provides us with the unique opportunity to learn from very complex models and to understand better why they perform so well.

Cosmological evolution in DHOST theories

 

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


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


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

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

 

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


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

 

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


Abstract

In this work, we use recent data on the Hubble expansion rate H(z), the quantity fσ8(z) from redshift space distortions and the statistic Eg 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 ηobs. If ηobs 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 ηobs at three redshift values, z=0.29,0.58,0.86. Using the method of polynomial regression, we find ηobs=0.57±1.05, ηobs=0.48±0.96, and ηobs=0.11±3.21, respectively. Assuming a constant ηobs in this range, we find ηobs=0.49±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 ηobs=0.15±0.27 (binning) and ηobs=0.53±0.19 (Gaussian Process). We find that all three estimates are compatible with each other within their 1σ 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

 

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


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

 

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


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

 

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


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.