Constraining Galileon inflation

In this short paper, we present constraints on the Galileon inflationary model from the CMB bispectrum. We employ a principal-component analysis of the independent degrees of freedom constrained by data and apply this to the WMAP 9-year data to constrain the free parameters of the model. A simple Bayesian comparison establishes that support for the Galileon model from bispectrum data is at best weak

On the redundancy of operators and the bispectrum in the most general second-order scalar-tensor theory

In this short note we explain how to use the linear equation of motions to simplify the third-order action for the cosmological fluctuations. No field redefinition is needed in this exact procedure which considerably limits the range of independent cubic operators, and hence of possible shapes of the primordial bispectrum. We demonstrate this in the context of the most general single-field scalar-tensor theory with second-order equations of motion, whose third-order action has been calculated recently in arXiv:1107.2642 and 1107.3917. In particular, we show that the three cubic operators initially pointed out in these works as new compared to k-inflation can actually be expressed in terms of standard k-inflationary operators.Comment: 9 pages. Wordings changed; matches version published in JCA

A Statistical Approach to Multifield Inflation: Many-field Perturbations Beyond Slow Roll

We study multifield contributions to the scalar power spectrum in an ensemble of six-field inflationary models obtained in string theory. We identify examples in which inflation occurs by chance, near an approximate inflection point, and we compute the primordial perturbations numerically, both exactly and using an array of truncated models. The scalar mass spectrum and the number of fluctuating fields are accurately described by a simple random matrix model. During the approach to the inflection point, bending trajectories and violations of slow roll are commonplace, and 'many-field' effects, in which three or more fields influence the perturbations, are often important. However, in a large fraction of models consistent with constraints on the tilt the signatures of multifield evolution occur on unobservably large scales. Our scenario is a concrete microphysical realization of quasi-single-field inflation, with scalar masses of order $H$, but the cubic and quartic couplings are typically too small to produce detectable non-Gaussianity. We argue that our results are characteristic of a broader class of models arising from multifield potentials that are natural in the Wilsonian sense.Comment: 39 pages, 17 figures. References added. Matches version published in JCA

Potential-driven Galileon inflation

For the models of inflation driven by the potential energy of an inflaton field $\phi$, the covariant Galileon Lagrangian $(\partial\phi)^2\Box \phi$ generally works to slow down the evolution of the field. On the other hand, if the Galileon self-interaction is dominant relative to the standard kinetic term, we show that there is no oscillatory regime of inflaton after the end of inflation. This is typically accompanied by the appearance of the negative propagation speed squared $c_s^2$ of a scalar mode, which leads to the instability of small-scale perturbations. For chaotic inflation and natural inflation we clarify the parameter space in which inflaton oscillates coherently during reheating. Using the WMAP constraints of the scalar spectral index and the tensor-to-scalar ratio as well, we find that the self coupling $\lambda$ of the potential $V(\phi)=\lambda \phi^4/4$ is constrained to be very much smaller than 1 and that the symmetry breaking scale $f$ of natural inflation cannot be less than the reduced Planck mass $M_{\rm pl}$. We also show that, in the presence of other covariant Galileon Lagrangians, there are some cases in which inflaton oscillates coherently even for the self coupling $\lambda$ of the order of 0.1, but still the instability associated with negative $c_s^2$ is generally present.Comment: 22 pages, 15 figure

A general proof of the equivalence between the \delta N and covariant formalisms

Recently, the equivalence between the \delta N and covariant formalisms has been shown (Suyama et al. 2012), but they essentially assumed Einstein gravity in their proof. They showed that the evolution equation of the curvature covector in the covariant formalism on uniform energy density slicings coincides with that of the curvature perturbation in the \delta N formalism assuming the coincidence of uniform energy and uniform expansion (Hubble) slicings, which is the case on superhorizon scales in Einstein gravity. In this short note, we explicitly show the equivalence between the \delta N and covariant formalisms without specifying the slicing condition and the associated slicing coincidence, in other words, regardless of the gravity theory.Comment: 7 pages,a reference added, to be published in EP

Primordial fluctuations and non-Gaussianities from multifield DBI Galileon inflation

We study a cosmological scenario in which the DBI action governing the motion of a D3-brane in a higher-dimensional spacetime is supplemented with an induced gravity term. The latter reduces to the quartic Galileon Lagrangian when the motion of the brane is non-relativistic and we show that it tends to violate the null energy condition and to render cosmological fluctuations ghosts. There nonetheless exists an interesting parameter space in which a stable phase of quasi-exponential expansion can be achieved while the induced gravity leaves non trivial imprints. We derive the exact second-order action governing the dynamics of linear perturbations and we show that it can be simply understood through a bimetric perspective. In the relativistic regime, we also calculate the dominant contribution to the primordial bispectrum and demonstrate that large non-Gaussianities of orthogonal shape can be generated, for the first time in a concrete model. More generally, we find that the sign and the shape of the bispectrum offer powerful diagnostics of the precise strength of the induced gravity.Comment: 34 pages including 9 figures, plus appendices and bibliography. Wordings changed and references added; matches version published in JCA

Inflationary signatures of single-field models beyond slow-roll

If the expansion of the early Universe was not close to de Sitter, the statistical imprints of the primordial density perturbation on the cosmic microwave background can be quite different from those derived in slow-roll inflation. In this paper we study the inflationary signatures of all single-field models which are free of ghost-like instabilities. We allow for a rapid change of the Hubble parameter and the speed of sound of scalar fluctuations, in a way that is compatible with a nearly scale-invariant spectrum of perturbations, as supported by current cosmological observations. Our results rely on the scale-invariant approximation, which is different from the standard slow-roll approximation. We obtain the propagator of scalar fluctuations and compute the bispectrum, keeping next-order corrections proportional to the deviation of the spectral index from unity. These theories offer an explicit example where the shape and scale-dependences of the bispectrum are highly non-trivial whenever slow-roll is not a good approximation.Comment: v1: 36 pages, including tables, appendices and references. v2: abstract improved, references added, minor clarifications throughout the text; matches version published in JCA

Decoding the bispectrum of single-field inflation

Galileon fields arise naturally from the decoupling limit of massive gravities, and possess special self-interactions which are protected by a spacetime generalization of Galilean symmetry. We briefly revisit the inflationary phenomenology of Galileon theories. Working from recent computations of the fluctuation Lagrangian to cubic order in the most general model with second-order equations of motion, we show that a distinct shape is present but with suppressed amplitude. A similar shape has been found in other higher-derivative models. It may be visible in a theory tuned to suppress the leading-order shapes, or if the overall bispectrum has large amplitude. Using a partial-wave expansion of the bispectrum, we suggest a possible origin for the frequent appearance of this shape. It follows that models with very disparate microphysics can produce very similar bispectra. We argue that it may be more profitable to distinguish these models by searching for relations between the amplitudes of these common shapes. We illustrate this method using the example of DBI and k-inflation.Comment: v1: 25 pages, including tables, an appendix and references. v2: minor clarifications about the lowest-order consistency relations; matches version published in JCA

Massive Gravity on de Sitter and Unique Candidate for Partially Massless Gravity

We derive the decoupling limit of Massive Gravity on de Sitter in an arbitrary number of space-time dimensions d. By embedding d-dimensional de Sitter into d+1-dimensional Minkowski, we extract the physical helicity-1 and helicity-0 polarizations of the graviton. The resulting decoupling theory is similar to that obtained around Minkowski. We take great care at exploring the partially massless limit and define the unique fully non-linear candidate theory that is free of the helicity-0 mode in the decoupling limit, and which therefore propagates only four degrees of freedom in four dimensions. In the latter situation, we show that a new Vainshtein mechanism is at work in the limit m^2\to 2 H^2 which decouples the helicity-0 mode when the parameters are different from that of partially massless gravity. As a result, there is no discontinuity between massive gravity and its partially massless limit, just in the same way as there is no discontinuity in the massless limit of massive gravity. The usual bounds on the graviton mass could therefore equivalently well be interpreted as bounds on m^2-2H^2. When dealing with the exact partially massless parameters, on the other hand, the symmetry at m^2=2H^2 imposes a specific constraint on matter. As a result the helicity-0 mode decouples without even the need of any Vainshtein mechanism.Comment: 30 pages. Some clarifications and references added. New subsection 'Symmetry and Counting in the Full Theory' added. New appendix 'St\"uckelberg fields in the Na\"ive approach' added. Matches version published in JCA

Non-gaussianity from the bispectrum in general multiple field inflation

We study the non-gaussianity from the bispectrum in multi-field inflation models with a general kinetic term. The models include the multi-field K-inflation and the multi-field Dirac-Born-Infeld (DBI) inflation as special cases. We find that, in general, the sound speeds for the adiabatic and entropy perturbations are different and they can be smaller than 1. Then the non-gaussianity can be enhanced. The multi-field DBI-inflation is shown to be a special case where both sound speeds are the same due to a special form of the kinetic term. We derive the exact second and third order actions including metric perturbations. In the small sound speed limit and at leading order in the slow-roll expansion, we derive the three point function for the curvature perturbation which depends on both adiabatic and entropy perturbations. The contribution from the entropy perturbations has a different momentum dependence if the sound speed for the entropy perturbations is different from the adiabatic one, which provides a possibility to distinguish the multi-field models from single field models. On the other hand, in the multi-field DBI case, the contribution from the entropy perturbations has the same momentum dependence as the pure adiabatic contributions and it only changes the amplitude of the three point function. This could help to ease the constraints on the DBI-inflation models.Comment: 16 pages, no figur