A spectre is haunting the cosmos: Quantum stability of massive gravity with ghosts

Many theories of modified gravity with higher order derivatives are usually ignored because of serious problems that appear due to an additional ghost degree of freedom. Most dangerously, it causes an immediate decay of the vacuum. However, breaking Lorentz invariance can cure such abominable behavior. By analyzing a model that describes a massive graviton together with a remaining Boulware-Deser ghost mode we show that even ghostly theories of modified gravity can yield models that are viable at both classical and quantum levels and, therefore, they should not generally be ruled out. Furthermore, we identify the most dangerous quantum scattering process that has the main impact on the decay time and find differences to simple theories that only describe an ordinary scalar field and a ghost. Additionally, constraints on the parameters of the theory including some upper bounds on the Lorentz-breaking cutoff scale are presented. In particular, for a simple theory of massive gravity we find that a breaking of Lorentz invariance is allowed to happen even at scales above the Planck mass. Finally, we discuss the relevance to other theories of modified gravity.Comment: 18 pages, 3 figures, version published in JHE

Infrared Nonlocal Gravity Theories : Optimizing Science Return to Euclid Satellite Mission

Nichtlokale Gravitationstheorien sind Versuche Quantenkorrekturen in die Einstein-Hilbert-Wirkung miteinzubeziehen. Dies ist ein eleganter Weg, um offene Fragen der Allgemeinen Relativitätstheorie anzugehen. In dieser Dissertation haben wir hauptsächlich infrarot-relevante, nichtlokale Modifikationen von Gravitation als mögliche Quelle für die beschleunigte Expansion des Universums zu späten Zeiten untersucht. Wir zeigen, dass, wenn diese Korrekturen in der Effektiven Wirkung mit einer infrarot-relevanten Größenordnung auftreten, sie zu einer validen Kosmologie zu späten Zeiten führen können, die sowohl auf dem Hintergrund- als auch den Störungsniveaus mit allen beobachteten Daten übereinstimmt. Überdies können manche dieser Modelle besser mit den beobachteten Daten übereinstimmen als das LambdaCDM Standardmodell. Wir haben auch Probleme untersucht, die mit der theoretischen Formulierung nichtlokaler Gravitationsmodelle assoziiert werden, wie beispielsweise die Rolle der Anfangsbedingungen für die Lösungsräume. Wir haben herausgefunden, dass eine unvorsichtige Behandlung der Anfangsbedingungen zu einem Übersehen mancher physikalisch sinnvoller Lösungen führen kann. Desweiteren haben wir die Frage nach den klassischen Instabilitäten in tensoriellen nichtlokalen Gravitationsmodelle untersucht, woraus wir schließen, dass neue Mechanismen oder Symmetrien eingeführt werden müssen, um die Gültigkeit dieser Modelle zu etablieren

Instabilities in tensorial nonlocal gravity

We discuss the cosmological implications of nonlocal modifications of general relativity containing tensorial structures. Assuming the presence of standard radiation- and matter-dominated eras, we show that, except in very particular cases, the nonlocal terms contribute a rapidly growing energy density. These models therefore generically do not have a stable cosmological evolution.Comment: 10 pages, 2 figures. v2: version published in PR

Observational Constraints in Nonlocal Gravity: the Deser-Woodard Case

We study the cosmology of a specific class of nonlocal model of modified gravity, the so-called Deser-Woodard (DW) model, modifying the Einstein-Hilbert action by a term $\sim R f(\Box^{-1}R)$, where $f$ is a free function. Choosing $f$ so as to reproduce the $\Lambda{\rm CDM}$ cosmological background expansion history within the nonlocal model, we implement the model in a cosmological linear Einstein--Boltzmann solver and study the deviations to GR the model induces in the scalar and tensor perturbations. We observe that the DW nonlocal model describes a modified propagation for the gravitational waves, as well as a lower linear growth rate and a stronger lensing power as compared to $\Lambda{\rm CDM}$, up to several percents. Such prominent growth and lensing features lead to the inference of a significantly smaller value of $\sigma_8$ with respect to the one in $\Lambda{\rm CDM}$, given \textit{Planck} CMB+lensing data. The prediction for the linear growth rate $f \sigma_8$ within the DW model is therefore significantly smaller than the one in $\Lambda{\rm CDM}$ and the addition of growth rate data $f \sigma_8$ from Redshift-space distortion measurements to \textit{Planck} CMB+lensing, opens a (dominant) tension between Redshift-space distortion data and the reconstructed \textit{Planck} CMB lensing potential. However, model selection issues only result in "weak" evidences for $\Lambda{\rm CDM}$ against the DW model given the data. Such a fact shows that the datasets we consider are not constraining enough for distinguishing between the models. As we discuss, the addition of galaxy WL data or cosmological constraints from future galaxy clustering, weak lensing surveys, but also third generation gravitational wave interferometers, prove to be useful for discriminating modified gravity models such as the DW one from $\Lambda{\rm CDM}$, within the close future.Comment: 28 pages, 13 figures, v2: references added, typographical errors correcte