Chirality of the gravitational-wave background and pulsar-timing arrays

We describe the signatures of a circularly polarized gravitational-wave background on the timing residuals obtained with pulsar-timing arrays. Most generally, the circular polarization will depend on the gravitational-wave direction, and we describe this angular dependence in terms of spherical harmonics. While the amplitude of the monopole (the overall chirality of the gravitational-wave background) cannot be detected, measures of the anisotropy are theoretically conceivable. We provide expressions for the minimum-variance estimators for the circular-polarization anisotropy. We evaluate the smallest detectable signal as a function of the signal-to-noise ratio with which the isotropic GW signal is detected and the number of pulsars (assumed to be roughly uniformly spread throughout the sky) in the survey. We find that the overall dipole of the circular polarization and a few higher overall multipoles, are detectable in a survey with $\gtrsim100$ pulsars if their amplitude is close to maximal and once the isotropic signal is established with a signal-to-noise ratio $\gtrsim400$. Even if the anisotropy can be established, though, there will be limited information on its direction. Similar arguments apply to astrometric searches for gravitational waves.Comment: 7 pages, 2 figure

Modified gravitational-wave propagation and standard sirens

Studies of dark energy at advanced gravitational-wave (GW) interferometers normally focus on the dark energy equation of state $w_{\rm DE}(z)$. However, modified gravity theories that predict a non-trivial dark energy equation of state generically also predict deviations from general relativity in the propagation of GWs across cosmological distances, even in theories where the speed of gravity is equal to $c$. We find that, in generic modified gravity models, the effect of modified GW propagation dominates over that of $w_{\rm DE}(z)$, making modified GW propagation a crucial observable for dark energy studies with standard sirens. We present a convenient parametrization of the effect in terms of two parameters $(\Xi_0,n)$, analogue to the $(w_0,w_a)$ parametrization of the dark energy equation of state, and we give a limit from the LIGO/Virgo measurement of $H_0$ with the neutron star binary GW170817. We then perform a Markov Chain Monte Carlo analysis to estimate the sensitivity of the Einstein Telescope (ET) to the cosmological parameters, including $(\Xi_0,n)$, both using only standard sirens, and combining them with other cosmological datasets. In particular, the Hubble parameter can be measured with an accuracy better than $1\%$ already using only standard sirens while, when combining ET with current CMB+BAO+SNe data, $\Xi_0$ can be measured to $0.8\%$ . We discuss the predictions for modified GW propagation of a specific nonlocal modification of gravity, recently developed by our group, and we show that they are within the reach of ET. Modified GW propagation also affects the GW transfer function, and therefore the tensor contribution to the ISW effect.Comment: 25 pages, 23 figures: v3: several significant improvement

Testing nonlocal gravity with Lunar Laser Ranging

We study the impact of the limit on $|\dot{G}|/G$ from Lunar Laser Ranging on "nonlocal gravity", i.e. on models of the quantum effective action of gravity that include nonlocal terms relevant in the infrared, such as the "RR" and "RT" models proposed by our group, and the Deser-Woodard (DW) model. We elaborate on the analysis of Barreira et al. [1] and we confirm their findings that (under plausible assumptions such as the absence of strong backreaction from non-linear structures), the RR model is ruled out. We also show that the mechanism of "perfect screening for free" suggested for the DW model actually does not work and the DW model is also ruled out. In contrast, the RT model passes all phenomenological consistency tests and is still a viable candidate.Comment: 46 pages, 4 figure

The gravitational-wave luminosity distance in modified gravity theories

In modified gravity the propagation of gravitational waves (GWs) is in general different from that in general relativity. As a result, the luminosity distance for GWs can differ from that for electromagnetic signals, and is affected both by the dark energy equation of state $w_{\rm DE}(z)$ and by a function $\delta(z)$ describing modified propagation. We show that the effect of modified propagation in general dominates over the effect of the dark energy equation of state, making it easier to distinguish a modified gravity model from $\Lambda$CDM. We illustrate this using a nonlocal modification of gravity, that has been shown to fit remarkably well CMB, SNe, BAO and structure formation data, and we discuss the prospects for distinguishing nonlocal gravity from $\Lambda$CDM with the Einstein Telescope. We find that, depending on the exact sensitivity, a few tens of standard sirens with measured redshift at $z\sim 0.4$, or a few hundreds at $1 < z < 2$, could suffice.Comment: 6 pages, 3 figures; v4: minor modifications; the version to appear in PR

Nonlocal gravity. Conceptual aspects and cosmological predictions

Even if the fundamental action of gravity is local, the corresponding quantum effective action, that includes the effect of quantum fluctuations, is a nonlocal object. These nonlocalities are well understood in the ultraviolet regime but much less in the infrared, where they could in principle give rise to important cosmological effects. Here we systematize and extend previous work of our group, in which it is assumed that a mass scale $\Lambda$ is dynamically generated in the infrared, giving rise to nonlocal terms in the quantum effective action of gravity. We give a detailed discussion of conceptual aspects related to nonlocal gravity and of the cosmological consequences of these models. The requirement of providing a viable cosmological evolution severely restricts the form of the nonlocal terms, and selects a model (the so-called RR model) that corresponds to a dynamical mass generation for the conformal mode. For such a model: (1) there is a FRW background evolution, where the nonlocal term acts as an effective dark energy with a phantom equation of state, providing accelerated expansion without a cosmological constant. (2) Cosmological perturbations are well behaved. (3) Implementing the model in a Boltzmann code and comparing with observations we find that the RR model fits the CMB, BAO, SNe, structure formation data and local $H_0$ measurements at a level statistically equivalent to $\Lambda$CDM. (4) Bayesian parameter estimation shows that the value of $H_0$ obtained in the RR model is higher than in $\Lambda$CDM, reducing to $2.0\sigma$ the tension with the value from local measurements. (5) The RR model provides a prediction for the sum of neutrino masses that falls within the limits set by oscillation and terrestrial experiments. (6) Gravitational waves propagate at the speed of light, complying with the limit from GW170817/GRB 170817A.Comment: 60 pages, 12 figures; v2: references adde

Teoria efficace dell'inflazione con simmetria galileiana

La teoria dell'inflazione cosmologica nasce per fornire una spiegazione dell'estrema uniformità della temperatura della CMB e della geometria sostanzialmente piatta dell'Universo attuale che, all'interno della cosmologia relativistica standard, richiederebbero un “fine tuning” delle condizioni iniziali dell'Universo. Tali problemi vengono risolti in modo naturale se si ammette l'esistenza di un rapido ma intenso periodo di espansione accelerata nelle primissime fasi di vita dell'Universo, alla fine del quale l'evoluzione sarebbe proseguita come descritto dalla cosmologia standard. Un ottimo candidato a guidare l'inflazione è un campo scalare che in opportune condizioni simula gli effetti di una costante cosmologica e produce dunque un'espansione accelerata. Il più grande successo dell'inflazione sta comunque nella sua capacità di fornire una spiegazione della formazione delle perturbazioni di densità primordiali, i germi delle grandi strutture formate in seguito dal collasso gravitazionale. Le informazioni su tali perturbazioni primordiali provengono dallo studio delle piccole anisotropie nella radiazione di fondo, che rivela una loro distribuzione approssimativamente gaussiana con piccole deviazioni. Lo studio di queste ultime non-gaussianità ci permette di discriminare tra vari modelli di inflazione. Il modello più semplice di inflazione è quello di slow-roll, dove la dinamica di un campo scalare è guidata da un potenziale molto piatto che domina sul termine cinetico; tuttavia un modello di questo tipo predice non-gaussianità troppo piccole per essere osservabili nel prossimo futuro, giustificando così l'introduzione di modelli più complessi. In questo lavoro di tesi si prende in considerazione un modello di inflazione descritto da una teoria efficace con interazioni “higher derivative”, quindi con più di una derivata per campo, che restituisca però equazioni del moto del secondo ordine in modo da non contenere gradi di libertà ulteriori e instabili. Tale condizione è raggiungibile considerando una teoria per un campo scalare invariante sotto la simmetria interna detta galileiana. Si considera dapprima la situazione in assenza di gravità, dove la simmetria vincola molto la struttura della teoria, tanto che sono possibili solo un numero finito di termini lagrangiani. Le correzioni radiative sono in grado di generare solo operatori con almeno due derivate per campo (che rispettano quindi la simmetria) soppressi ad energie minori del cutoff della teoria, mentre i potenziali operatori dello stesso ordine di quelli originari, ma che non rispettano la simmetria galileiana, non vengono generati. Quando si estende la teoria al caso di spazio curvo attraverso il metodo di accoppiamento minimale, la simmetria ne risulta rotta, ma tale rottura è caratterizzata da una scala di energia molto maggiore del cutoff ultravioletto della teoria stessa. In questo senso si dirà che la simmetria galileiana è rotta solo debolmente e si parlerà di “weakly broken galileon (WBG) invariance”. Considereremo una classe di teorie WBG accoppiate alla gravità e studieremo le equazioni di Friedmann corrispondenti che governano la dinamica del background, mostrando l'esistenza di soluzioni cosmologiche inflazionarie. Per affrontare lo studio delle fluttuazioni attorno alla soluzione uniforme per il campo scalare galileonico (e di tipo FRW per la metrica), è conveniente utilizzare la gauge unitaria in cui il grado di libertà scalare proveniente dalla fluttuazione del campo è inglobato dalle fluttuazioni della metrica. Questa gauge rompe l'invarianza della teoria sotto diffeomorfismi richiesta dalla relatività generale, in quanto implica la scelta di una coordinata temporale ben precisa. Tuttavia l'invarianza può essere ripristinata mediante la reintroduzione di un grado di libertà scalare corrispondente al bosone di Goldstone che realizza i diffeomorfismi temporali. Con tale procedura lo studio delle conseguenze cosmologiche della teoria risulta semplificato grazie al disaccoppiamento della dinamica del Goldstone da quella della metrica al di sopra di una certa energia minore della scala H data dal parametro di Hubble durante l'inflazione. Possiamo dunque calcolare le non-gaussianità previste dal modello, le più rilevanti delle quali sono fornite dalla funzione di correlazione a tre punti. Le non-gaussianità sono calcolate in termini dei parametri della teoria e, sotto ipotesi naturali che vengono discusse, è possibile ottenere valori compatibili con i limiti attuali, dati dal satellite Planck, e abbastanza grandi da essere esplorati nel prossimo futuro

Quantum origin of dark energy and the Hubble tension

Local measurements of the Hubble parameter obtained from the distance ladder at low redshift are in tension with global values inferred from cosmological standard rulers. A key role in the tension is played by the assumptions on the cosmological history, in particular on the origin of dark energy. Here we consider a scenario where dark energy originates from the amplification of quantum fluctuations of a light field in inflation. We show that spatial correlations inherited from inflationary quantum fluctuations can reduce the Hubble tension down to one standard deviation, thus relieving the problem with respect to the standard cosmological model. Upcoming missions, like Euclid, will be able to test the predictions of models in this class

Spatial correlations of dark energy from quantum fluctuations during inflation

This paper contains a detailed study of the properties of a simple model attempting to explain dark energy as originated from quantum fluctuations of a light spectator scalar field in inflation. In Belgacem and Prokopec [Phys. Lett. B 831, 137174 (2022)] we recently outlined how Starobinsky's stochastic formalism can be used to study the spatial correlations imprinted on dark energy by its quantum origin in this model and we studied their possible role in relieving the Hubble tension. Here we provide a more comprehensive derivation of the results in Belgacem and Prokopec and we refine some of our estimates, comparing to the approximate results obtained previously. Among the main results, we analyze the noncoincident correlators predicted by a full field theoretical treatment and their relation with those computed within the stochastic formalism. We find that in the region where stochastic theory predicts significant sub-Hubble correlators it is in disagreement with field theoretical predictions. However, agreement can be restored by introducing a reduced speed of sound for the scalar field. We also discuss an alternative approach to the problem of studying correlators within the stochastic formalism based directly on the evolution of probability distributions. We find that the two approaches give the same answer for 2-point functions of the field, but not for 4-point functions relevant to density correlators and we discuss the behavior of the two methods with respect to Wick's theorem

New horizons for fundamental physics with LISA

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of gravitational waves can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas

Gravity in the infrared and effective nonlocal models

We provide a systematic and updated discussion of a research line carried out by our group over the last few years, in which gravity is modified at cosmological distances by the introduction of nonlocal terms, assumed to emerge at an effective level from the infrared behavior of the quantum theory. The requirement of producing a viable cosmology turns out to be very stringent and basically selects a unique model, in which the nonlocal term describes an effective mass for the conformal mode. We discuss how such a specific structure could emerge from a fundamental local theory of gravity, and we perform a detailed comparison of this model with the most recent cosmological datasets, confirming that it fits current data at the same level as $\Lambda$CDM. Most notably, the model has striking predictions in the sector of tensor perturbations, leading to a very large effect in the propagation of gravitational wave (GWs) over cosmological distances. At the redshifts relevant for the next generation of GW detectors such as Einstein Telescope, Cosmic Explorer and LISA, this leads to deviations from GR that could be as large as $80\%$, and could be verified with the detection of just a single coalescing binary with electromagnetic counterpart. This would also have potentially important consequences for the search of the counterpart since, for a given luminosity distance to the source, as inferred through the GW signal, the actual source redshift could be significantly different from that predicted by $\Lambda$CDM. At the redshifts relevant for advanced LIGO/Virgo/Kagra the effect is smaller, but still potentially observable over a few years of runs at target sensitivity.Comment: 84 pages, 22 figure