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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.

Inflation can be parametrized by means of truncated flow equations. In this "horizon-flow" setup, generic results have been obtained, such as typical values for r/( 1 - ns). They are sometimes referred to as intrinsic features of inflation itself. In this paper we first show that the phenomenological class of inflationary potentials sampled by horizon flow is directly responsible for such predictions. They are therefore anything but generic. Furthermore, the horizon-flow setup is shown to rely on trajectories in phase space that differ from the slow roll. For a given potential, we demonstrate that this renders horizon flow blind to entire relevant inflationary regimes, for which the horizon-flow trajectory is shown to be unstable. This makes horizon flow a biased parametrization of inflation. [ABSTRACT FROM AUTHOR]

Hybrid inflation is a two-field model where inflation ends because of a tachyonic instability, the duration of which is determined by stochastic effects and has important observational implications. Making use of the recursive approach to the stochastic formalism presented in [L. P. Levasseur, preceding article, Phys. Rev. D 88. 083537 (2013)], these effects are consistently computed. Through an analysis of backreaction, this method is shown to converge in the valley but points toward an (expected) instability in the waterfall. It is further shown that the quasistationarity of the auxiliary field distribution breaks down in the case of a short-lived waterfall. We find that the typical dispersion of the waterfall field at the critical point is then diminished, thus increasing the duration of the waterfall phase and jeopardizing the possibility of a short transition. Finally, we find that stochastic effects worsen the blue tilt of the curvature perturbations by an O(1) factor when compared with the usual slow-roll contribution. [ABSTRACT FROM AUTHOR]

Hybrid inflation is a two-field model where inflation ends due to an instability. In the neighborhood of the instability point, the potential is very flat and the quantum fluctuations dominate over the classical motion of the inflaton and waterfall fields. In this article, we study this regime in the framework of stochastic inflation. We numerically solve the two coupled Langevin equations controlling the evolution of the fields and compute the probability distributions of the total number of e-folds and of the inflation exit point. Then, we discuss the physical consequences of our results, in particular, the question of how the quantum diffusion can affect the observable predictions of hybrid inflation. [ABSTRACT FROM AUTHOR]

We introduce a new method permitting the analytical determination of entanglement entropy (and related quantities) between configurations of a quantum field, which is either free or in interaction with a classical source, at two distinct spatial locations. We show how such a setup can be described by a bipartite, continuous Gaussian system. This allows us to derive explicit and exact formulas for the entanglement entropy, the mutual information and the quantum discord, solely in terms of the Fourier-space power spectra of the field. This contrasts with previous studies, which mostly rely on numerical considerations. As an illustration, we apply our formalism to massless fields in flat space, where exact expressions are derived that only involve the ratio between the size of the regions over which the field is coarse-grained, and the distance between these regions. In particular, we recover the well-known fact that mutual information decays as the fourth power of this ratio at large distances, as previously observed in numerical works. Our method leads to the first analytical derivation of this result, and to an exact formula that also applies to arbitrary distances. Finally, we determine the quantum discord and find that it identically vanishes (unless coarse-graining is performed over smeared spheres, in which case it obeys the same suppression at large distance as mutual information). [ABSTRACT FROM AUTHOR]

We present a general and systematic study of how a Bell experiment on the cosmic microwave background could be carried out. We introduce different classes of pseudo-spin operators and show that, if the system is placed in a two-mode squeezed state as inflation predicts, they all lead to a violation of the Bell inequality. However, we also discuss the obstacles that one faces in order to realize this program in practice and show that they are probably insurmountable. We suggest alternative methods that could reveal the quantum origin of cosmological structures without relying on Bell experiments. [ABSTRACT FROM AUTHOR]

Temporal Bell inequalities, or Leggett-Garg inequalities (LGIs), are studied for continuous-variable systems placed in a squeezed state. The importance of those systems lies in their broad applicability, which allows the description of many different physical settings in various branches of physics, ranging from cosmology to condensed matter physics and from optics to quantum information theory. Leggett-Garg inequality violations are explored and systematically mapped in squeezing parameter space. Configurations for which LGI violation occurs are found, but it is shown that no violation can be obtained if all squeezing angles vanish, contrary to what happens for the spatial Bell inequalities. We also assess the effect of decoherence on the detectability of such violations. Our study opens up the possibility of new experimental designs for the observation of LGI violation. [ABSTRACT FROM AUTHOR]

Bell inequalities for continuous-variable bipartite systems are studied. The inequalities are expressed in terms of pseudo-spin operators, and quantum expectation values are calculated for generic two-mode squeezed states characterized by a squeezing parameter r and a squeezing angle φ. Allowing for generic values of the squeezing angle is especially relevant when φ is not under experimental control, such as in cosmic inflation, where small quantum fluctuations in the early universe are responsible for structures formation. Compared to previous studies restricted to φ = 0 and to a fixed orientation of the pseudo-spin operators, allowing for φ ≠ 0 and optimizing the angular configuration leads to a completely new and rich phenomenology. Two dual schemes of approximation are designed that allow for comprehensive exploration of the squeezing parameter space. In particular, it is found that Bell inequalities can be violated when the squeezing parameter r is large enough, r ≳ 1.12, and the squeezing angle φ is small enough, φ ≲ 0.34e-r. [ABSTRACT FROM AUTHOR]

In the hope of avoiding model dependence of the cosmological observables, phenomenological parametrizations of cosmic inflation have recently been proposed. Typically, they are expressed in terms of two parameters associated with an expansion of the inflationary quantities matching the belief that inflation is characterized by two numbers only, the tensor-to-scalar ratio and the scalar spectral index. We give different arguments and examples showing that these new approaches are either not generic or insufficient to make predictions at the accuracy level needed by the cosmological data. We conclude that disconnecting inflation from high energy physics and gravity might not be the most promising way to learn about the physics of the early Universe. [ABSTRACT FROM AUTHOR]

We investigate the implications for inflation of the detection of 5-modes polarization in the cosmic microwave background by BICEP2. We show that the hypothesis of the primordial origin of the measurement is favored only by the first four band powers, while the others would prefer unreasonably large values of the tensor-to-scalar ratio. Using only those four band powers, we carry out a complete analysis in the cosmological and inflationary slow-roll parameter space using the BICEP2 polarization measurements alone and extract the Bayesian evidences and complexities for all the Encyclopcedia Inflationaris models. This allows us to determine the most probable and simplest BICEP2 inflationary scenarios. Although this list contains the simplest monomial potentials, it also includes many other scenarios, suggesting that focusing model building efforts on large field models only is unjustified at this stage. We demonstrate that the sets of inflationary models preferred by Planck alone and BICEP2 alone are almost disjoint, indicating a clear tension between the two data sets. We address this tension with a Bayesian measure of compatibility between BICEP2 and Planck. We find that for models favored by Planck the two data sets tend to be incompatible, whereas there is moderate evidence of compatibility for the BICEP2 preferred models. As a result, it would be premature to draw any conclusion on the best Planck models, such as Starobinsky and/or Kahler moduli inflation. For the subset of scenarios not exhibiting data sets incompatibility, we update the evidences and complexities using both data sets together. [ABSTRACT FROM AUTHOR]

Simple models of single-field inflation in the very early universe can generate the observed amplitude and scale dependence of the primordial density perturbation, but models with multiple fields can provide an equally good fit to current data. We show how future observations will be able to distinguish between currently favored models. If a curvaton field generates the primordial perturbations after inflation, we show how the total duration of inflation can be measured. [ABSTRACT FROM AUTHOR]