Non-Gaussianity in the distribution of inflationary perturbations, measurable in statistics of the cosmic microwave background (CMB) and large scale structure fluctuations, can be used to probe non-trivial initial quantum states for these perturbatio
ns. The bispectrum shapes predicted for generic non-Bunch-Davies initial states are non-factorizable (non-separable) and are highly oscillatory functions of the three constituent wavenumbers. This can make the computation of CMB bispectra, in particular, computationally intractable. To efficiently compare with CMB data one needs to construct a separable template that has a significant similarity with the actual shape in momentum space. In this paper we consider a variety of inflationary scenarios, with different non-standard initial conditions, and how best to construct viable template matches. In addition to implementing commonly used separable polynomial and Fourier bases, we introduce a basis of localized piecewise spline functions. The spline basis is naturally nearly orthogonal, making it easy to implement and to extend to many modes. We show that, in comparison to existing techniques, the spline basis can provide better fits to the true bispectrum, as measured by the cosine between shapes, for sectors of the theory space of general initial states. As such, it offers a useful approach to investigate non-trivial features generated by fundamental properties of the inflationary Universe.
[Abridged] We consider how galaxy clustering data, from Mpc to Gpc scales, from upcoming large scale structure surveys, such as Euclid and DESI, can provide discriminating information about the bispectrum shape arising from a variety of inflationary
scenarios. Through exploring in detail the weighting of shape properties in the calculation of the halo bias and halo mass function we show how they probe a broad range of configurations, beyond those in the squeezed limit, that can help distinguish between shapes with similar large scale bias behaviors. We assess the impact, on constraints for a diverse set of non-Gaussian shapes, of galaxy clustering information in the mildly non-linear regime, and surveys that span multiple redshifts and employ different galactic tracers of the dark matter distribution. Fisher forecasts are presented for a Euclid-like spectroscopic survey of H$alpha$-selected emission line galaxies (ELGs) using recent revisions of the expected H$alpha$ luminosity function, and a DESI-like survey, of luminous red galaxies (LRGs) and [O-II] doublet-selected ELGs, in combination with Planck-like CMB temperature and polarization data. While ELG samples provide better probes of shapes that are divergent in the squeezed limit, LRG constraints, centered below $z<1$, yield stronger constraints on shapes with scale-independent large-scale halo biases, such as the equilateral template. The ELG and LRG samples provide complementary degeneracy directions for distinguishing between different shapes. If the Gaussian galaxy bias is constrained to better than a percent level, such as can be determined from the galaxy bispectrum or weak lensing, then the LSS and CMB data could provide complementary constraints that will enable differentiation of bispectra with distinct theoretical origins but with similar large scale, squeezed-limit properties.
A detection of primordial non-Gaussianity could transform our understanding of the fundamental theory of inflation. The precision promised by upcoming CMB and large-scale structure surveys raises a natural question: if a detection given a particular
template is made, what does this truly tell us about the underlying theory? In this paper we present a systematic way to constrain a wide range of non-Gaussian shapes, including general single and multi-field models and models with excited initial states. We present a separable, divergent basis able to recreate many shapes in the literature to high accuracy with between three and seven basis functions. The basis allows shapes to be grouped into broad template classes, satisfying theoretically-relevant priors on their divergence properties in the squeezed limit. We forecast how well a Planck-like CMB survey could not only detect a general non-Gaussian signal but discern more about its shape, using existing templates and new ones we propose. This approach offers an opportunity to tie together minimal theoretical priors with observational constraints on the shape in general, and in the squeezed limit, to gain a deeper insight into what drove inflation.
We show that brane inflation is very sensitive to tiny sharp features in extra dimensions, including those in the potential and in the warp factor. This can show up as observational signatures in the power spectrum and/or non-Gaussianities of the cos
mic microwave background radiation (CMBR). One general example of such sharp features is a succession of small steps in a warped throat, caused by Seiberg duality cascade using gauge/gravity duality. We study the cosmological observational consequences of these steps in brane inflation. Since the steps come in a series, the prediction of other steps and their properties can be tested by future data and analysis. It is also possible that the steps are too close to be resolved in the power spectrum, in which case they may show up only in the non-Gaussianity of the CMB temperature fluctuations and/or EE polarization. We study two cases. In the slow-roll scenario where steps appear in the inflaton potential, the sensitivity of brane inflation to the height and width of the steps is increased by several orders of magnitude comparing to that in previously studied large field models. In the IR DBI scenario where steps appear in the warp factor, we find that the glitches in the power spectrum caused by these sharp features are generally small or even unobservable, but associated distinctive non-Gaussianity can be large. Together with its large negative running of the power spectrum index, this scenario clearly illustrates how rich and different a brane inflationary scenario can be when compared to generic slow-roll inflation. Such distinctive stringy features may provide a powerful probe of superstring theory.
We consider theories in which there exists a nontrivial coupling between the dark matter sector and the sector responsible for the acceleration of the universe. Such theories can possess an adiabatic regime in which the quintessence field always sits
at the minimum of its effective potential, which is set by the local dark matter density. We show that if the coupling strength is much larger than gravitational, then the adiabatic regime is always subject to an instability. The instability, which can also be thought of as a type of Jeans instability, is characterized by a negative sound speed squared of an effective coupled dark matter/dark energy fluid, and results in the exponential growth of small scale modes. We discuss the role of the instability in specific coupled CDM and Mass Varying Neutrino (MaVaN) models of dark energy, and clarify for these theories the regimes in which the instability can be evaded due to non-adiabaticity or weak coupling.
We consider the cosmological constraints on theories in which there exists a nontrivial coupling between the dark matter sector and the sector responsible for the acceleration of the universe, in light of the most recent supernovae, large scale struc
ture and cosmic microwave background data. For a variety of models, we show that the strength of the coupling of dark matter to a quintessence field is constrained to be less than 7% of the coupling to gravity. We also show that long range interactions between fermionic dark matter particles mediated by a light scalar with a Yukawa coupling are constrained to be less than 5% of the strength of gravity at a distance scale of 10 Mpc. We show that all of the models we consider are quantum mechanically weakly coupled, and argue that some other models in the literature are ruled out by quantum mechanical strong coupling.
If inflation is to be considered in an unbiased way, as possibly originating from one of a wide range of underlying theories, then observations need not be simply applied to reconstructing the inflaton potential, V(phi), or a specific kinetic term, a
s in DBI inflation, but rather to reconstruct the inflationary action in its entirety. We discuss the constraints that can be placed on a general single field action from measurements of the primordial scalar and tensor fluctuation power spectra and non-Gaussianities. We also present the flow equation formalism for reconstructing a general inflationary Lagrangian, L(X,phi), with X={1/2}partial_muphipartial^muphi, in a general gauge, that reduces to canonical and DBI inflation in the specific gauge partial L/partial X = c_s^{-1}.
We compare the Infrared Dirac-Born-Infeld (IR DBI) brane inflation model to observations using a Bayesian analysis. The current data cannot distinguish it from the LambdaCDM model, but is able to give interesting constraints on various microscopic pa
rameters including the mass of the brane moduli potential, the fundamental string scale, the charge or warp factor of throats, and the number of the mobile branes. We quantify some distinctive testable predictions with stringy signatures, such as the large non-Gaussianity, and the large, but regional, running of the spectral index. These results illustrate how we may be able to probe aspects of string theory using cosmological observations.
We consider theories with a nontrivial coupling between the matter and dark energy sectors. We describe a small scale instability that can occur in such models when the coupling is strong compared to gravity, generalizing and correcting earlier treat
ments. The instability is characterized by a negative sound speed squared of an effective coupled dark matter/dark energy fluid. Our results are general, and applicable to a wide class of coupled models and provide a powerful, redshift-dependent tool, complementary to other constraints, with which to rule many of them out. A detailed analysis and applications to a range of models are presented in a longer companion paper.
