Higher derivative theories with constraints : Exorcising Ostrogradski's Ghost

We prove that the linear instability in a non-degenerate higher derivative theory, the Ostrogradski instability, can only be removed by the addition of constraints if the original theory's phase space is reduced.Comment: 17 pages, no figures, version published in JCA

A Class of Effective Field Theory Models of Cosmic Acceleration

We explore a class of effective field theory models of cosmic acceleration involving a metric and a single scalar field. These models can be obtained by starting with a set of ultralight pseudo-Nambu-Goldstone bosons whose couplings to matter satisfy the weak equivalence principle, assuming that one boson is lighter than all the others, and integrating out the heavier fields. The result is a quintessence model with matter coupling, together with a series of correction terms in the action in a covariant derivative expansion, with specific scalings for the coefficients. After eliminating higher derivative terms and exploiting the field redefinition freedom, we show that the resulting theory contains nine independent free functions of the scalar field when truncated at four derivatives. This is in contrast to the four free functions found in similar theories of single-field inflation, where matter is not present. We discuss several different representations of the theory that can be obtained using the field redefinition freedom. For perturbations to the quintessence field today on subhorizon lengthscales larger than the Compton wavelength of the heavy fields, the theory is weakly coupled and natural in the sense of t'Hooft. The theory admits a regime where the perturbations become modestly nonlinear, but very strong nonlinearities lie outside its domain of validity.Comment: 43 pages, 2 figures; Version 3 publication versio

Large non-Gaussianities in the Effective Field Theory Approach to Single-Field Inflation: the Bispectrum

The methods of effective field theory are used to study generic theories of inflation with a single inflaton field and to perform a general analysis of the associated non-Gaussianities. We investigate the amplitudes and shapes of the various generic three-point correlators, the bispectra, which may be generated by different classes of single-field inflationary models. Besides the well-known results for the DBI-like models and the ghost inflationary theories, we point out that curvature-related interactions may give rise to large non-Gaussianities in the form of bispectra characterized by a flat shape which, quite interestingly, is independently produced by several interaction terms. In a subsequent work, we will perform a similar general analysis for the non-Gaussianities generated by the generic four-point correlator, the trispectrum.Comment: Version matching the one published in JCAP, 2 typos fixed, references added. 30 pages, 20 figure

Large non-Gaussianities in the Effective Field Theory Approach to Single-Field Inflation: the Trispectrum

We perform the analysis of the trispectrum of curvature perturbations generated by the interactions characterizing a general theory of single-field inflation obtained by effective field theory methods. We find that curvature-generated interaction terms, which can in general give an important contribution to the amplitude of the four-point function, show some new distinctive features in the form of their trispectrum shape-function. These interesting interactions are invariant under some recently proposed symmetries of the general theory and, as shown explicitly, do allow for a large value of the trispectrum.Comment: 29 pages, 13 figure

Spectral Distortions of the CMB as a Probe of Inflation, Recombination, Structure Formation and Particle Physics

Following the pioneering observations with COBE in the early 1990s, studies of the cosmic microwave background (CMB) have focused on temperature and polarization anisotropies. CMB spectral distortions - tiny departures of the CMB energy spectrum from that of a perfect blackbody - provide a second, independent probe of fundamental physics, with a reach deep into the primordial Universe. The theoretical foundation of spectral distortions has seen major advances in recent years, which highlight the immense potential of this emerging field. Spectral distortions probe a fundamental property of the Universe - its thermal history - thereby providing additional insight into processes within the cosmological standard model (CSM) as well as new physics beyond. Spectral distortions are an important tool for understanding inflation and the nature of dark matter. They shed new light on the physics of recombination and reionization, both prominent stages in the evolution of our Universe, and furnish critical information on baryonic feedback processes, in addition to probing primordial correlation functions at scales inaccessible to other tracers. In principle the range of signals is vast: many orders of magnitude of discovery space could be explored by detailed observations of the CMB energy spectrum. Several CSM signals are predicted and provide clear experimental targets, some of which are already observable with present-day technology. Confirmation of these signals would extend the reach of the CSM by orders of magnitude in physical scale as the Universe evolves from the initial stages to its present form. The absence of these signals would pose a huge theoretical challenge, immediately pointing to new physics.Comment: Astro2020 Science White Paper, 5 pages text, 13 pages in total, 3 Figures, minor update to reference

Probing anisotropies of the Stochastic Gravitational Wave Background with LISA

We investigate the sensitivity of the Laser Interferometer Space Antenna (LISA) to the anisotropies of the Stochastic Gravitational Wave Background (SGWB). We first discuss the main astrophysical and cosmological sources of SGWB which are characterized by anisotropies in the GW energy density, and we build a Signal-to-Noise estimator to quantify the sensitivity of LISA to different multipoles. We then perform a Fisher matrix analysis of the prospects of detectability of anisotropic features with LISA for individual multipoles, focusing on a SGWB with a power-law frequency profile. We compute the noise angular spectrum taking into account the specific scan strategy of the LISA detector. We analyze the case of the kinematic dipole and quadrupole generated by Doppler boosting an isotropic SGWB. We find that β ΩGW ∼ 2 × 10-11 is required to observe a dipolar signal with LISA. The detector response to the quadrupole has a factor ∼ 103 β relative to that of the dipole. The characterization of the anisotropies, both from a theoretical perspective and from a map-making point of view, allows us to extract information that can be used to understand the origin of the SGWB, and to discriminate among distinct superimposed SGWB sources

Accelerated expansion from ghost-free bigravity: a statistical analysis with improved generality

We study the background cosmology of the ghost-free, bimetric theory of gravity. We perform an extensive statistical analysis of the model using both frequentist and Bayesian frameworks and employ the constraints on the expansion history of the Universe from the observations of supernovae, the cosmic microwave background and the large scale structure to estimate the model's parameters and test the goodness of the fits. We explore the parameter space of the model with nested sampling to find the best-fit chi-square, obtain the Bayesian evidence, and compute the marginalized posteriors and mean likelihoods. We mainly focus on a class of sub-models with no explicit cosmological constant (or vacuum energy) term to assess the ability of the theory to dynamically cause a late-time accelerated expansion. The model behaves as standard gravity without a cosmological constant at early times, with an emergent extra contribution to the energy density that converges to a cosmological constant in the far future. The model can in most cases yield very good fits and is in perfect agreement with the data. This is because many points in the parameter space of the model exist that give rise to time-evolution equations that are effectively very similar to those of the $\Lambda$CDM. This similarity makes the model compatible with observations as in the $\Lambda$CDM case, at least at the background level. Even though our results indicate a slightly better fit for the $\Lambda$CDM concordance model in terms of the $p$-value and evidence, none of the models is statistically preferred to the other. However, the parameters of the bigravity model are in general degenerate. A similar but perturbative analysis of the model as well as more data will be required to break the degeneracies and constrain the parameters, in case the model will still be viable compared to the $\Lambda$CDM.Comment: 42 pages, 9 figures; typos corrected in equations (2.12), (2.13), (3.7), (3.8) and (3.9); more discussions added (footnotes 5, 8, 10 and 13) and abstract, sections 4.2, 4.3 and 5 (conclusions) modified in response to referee's comments; references added; acknowledgements modified; all results completely unchanged; matches version accepted for publication in JHE

Probing the inflationary particle content: extra spin-2 field

We study how inflationary observables associated with primordial tensor modes are affected by coupling the minimal field content with an extra spin-2 particle during inflation. We work with a model that is ghost-free at the fully non-linear level and show how the new degrees of freedom modify standard consistency relations for the tensor bispectrum. The extra interacting spin-2 field is necessarily massive and unitarity dictates its mass be in the $m \gtrsim H$ range. Despite the fact that this bound selects a decaying solution for the corresponding tensor mode, cosmological correlators still carry the imprints of such "fossil" fields. Remarkably, fossil(s) of spin $\geq 1$ generate distinctive anisotropies in observables such as the tensor power spectrum. We show how this plays out in our set-up.Comment: 25 pages, 3 figure

EuCAPT White Paper: Opportunities and Challenges for Theoretical Astroparticle Physics in the Next Decade

Astroparticle physics is undergoing a profound transformation, due to a series of extraordinary new results, such as the discovery of high-energy cosmic neutrinos with IceCube, the direct detection of gravitational waves with LIGO and Virgo, and many others. This white paper is the result of a collaborative effort that involved hundreds of theoretical astroparticle physicists and cosmologists, under the coordination of the European Consortium for Astroparticle Theory (EuCAPT). Addressed to the whole astroparticle physics community, it explores upcoming theoretical opportunities and challenges for our field of research, with particular emphasis on the possible synergies among different subfields, and the prospects for solving the most fundamental open questions with multi-messenger observations.Comment: White paper of the European Consortium for Astroparticle Theory (EuCAPT). 135 authors, 400 endorsers, 133 pages, 1382 reference

Cosmology with the Laser Interferometer Space Antenna

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational wave observations by LISA to probe the universe