We present the first attempt to use a combination of CMB, LIGO, and PPTA data to constrain both the tilt and the running of primordial tensor power spectrum through constraints on the gravitational wave energy density generated in the early universe. Combining measurements at different cosmological scales highlights how complementary data can be used to test the predictions of early universe models including the inflationary consistency relation. Current data prefers a slightly positive tilt ($n_t = 0.06^{+0.63}_{-0.89}$) and a negative running ($n_{t, {\rm run}} < -0.22$) for the tensor power spectrum spectrum. Interestingly, the addition of direct gravitational wave detector data alone puts strong bounds on the tensor-to-scalar ratio $r < 0.2$ since the large positive tensor tilt preferred by the \textit{Planck} temperature power spectrum is no longer allowed. Adding the recently released BICEP2/KECK and Planck 353 GHz Polarization cross correlation data puts an even stronger bound $r<0.1$ . We comment on possible effects of a large positive tilt on the background expansion and show that depending on the assumptions regarding the UV cutoff ($k_{\rm UV}/k_* = 10^{24}$) of the primordial spectrum of gravitational waves, the strongest bounds on $n_t = 0.07^{+0.52}_{-0.80}$ are derived from this effect.
In this work we explore the possibility of variations in the primordial scalar power spectrum around the power-law shape, as predicted by single-field slow-roll inflationary scenarios. We search for the trace of these fluctuations in a semi-blind, model-independent way on the observations of the Cosmic Microwave Background (CMB) sky. In particular we use two sets of perturbation patterns, specific patterns with typical features such as oscillations, bumps and transitions, as well as perturbation modes, constructed from the eigenanalysis of the forecasted or measured covariance of perturbation …
We reconsider the derivation of soft theorems associated with nonlinearly-realized symmetries in cosmology. Utilizing the path integral, we derive a generalized consistency relation that relates a squeezed $(N+1)$-point correlation function to an $N$-point function, where the relevant soft mode is at early rather than late time. This generalized (early-late-time) version has wider applicability than the standard consistency relation where all modes are evaluated at late times. We elucidate the conditions under which the latter follows from the former. A key ingredient is the physical mode cond…
We show how the inclusion of non-perturbative, {\em dynamical} quantum effects on the evolution of the inflaton can allow for an inflationary phase that is both consistent with cosmological constraints {\em and} avoids the problems associated with the so-called swampland conditions. In particular, for concave potentials such as those preferred by the Planck data, spinodal instabilities associated with tachyonic masses for long wavelength modes induce a second round of inflation, which in essence decouples the tree-level potential from the inflationary phase. We illustrate these points using na…
In single-field inflationary models the bispectra are usually given in the $ζ$-gauge, because its temporal part leads to the super-horizon conservation of fluctuations. However, this property is independent of the choice of {\it spatial} gauge, so in this letter we explore this freedom. We compute the variation of the bispectra under the most general spatial gauge transformation that is globally defined and privileges no point, direction or scale. In the squeezed configuration we then obtain a generalization of the classic $ζ$-gauge consistency relations, which we also derive through the `larg…
We discuss new consistency relations for single field models of inflation capable of generating primordial black holes (PBH), and their observational implications for CMB $μ$-space distortions. These inflationary models include a short period of non-attractor evolution: the scale-dependent profile of curvature perturbation is characterized by a pronounced dip, followed by a rapid growth leading to a peak responsible for PBH formation. We investigate the squeezed and the collapsed limits of three and four point functions of curvature perturbation around the dip, showing that they satisfy consis…
We investigate the effect of damped oscillations on a nearly flat inflationary potential and the features they produce in the power-spectrum and bi-spectrum. We compare the model with the Planck data using Plik unbinned and CamSpec clean likelihood and we are able to obtain noticeable improvement in fit compared to the power-law $Λ$CDM model. We are able to identify three plausible candidates each for the two likelihoods used. We find that the best-fit to Plik and CamSpec likelihoods match closely to each other. The improvement comes from various possible outliers at the intermediate to small …
We use conformal symmetry to constrain the shape of inflationary correlators in the presence of long-lived vector field perturbations. Applying conformal Ward identities, we derive general expressions, up to amplitudes and normalization factors, for the two and three point correlators in the presence of vector fields mediated by the interaction $f(ϕ)\left(F_{μν}F^{μν}+α\tilde{F}_{μν}F^{μν}\right)$, where $f(ϕ)$ is a suitable coupling function between the scalar and the vector field. The previous interaction allows for isotropy and parity symmetry breaking and is consistent with super horizon c…
We derive the predictions of quantum gravity with fakeons on the amplitudes and spectral indices of the scalar and tensor fluctuations in inflationary cosmology. The action is $R+R^{2}$ plus the Weyl-squared term. The ghost is eliminated by turning it into a fakeon, that is to say a purely virtual particle. We work to the next-to-leading order of the expansion around the de Sitter background. The consistency of the approach puts a lower bound ($ m_{χ}>m_{ϕ}/4$) on the mass $m_{χ}$ of the fakeon with respect to the mass $m_{ϕ}$ of the inflaton. The tensor-to-scalar ratio $r$ is predicted within…
While during inflation a phase of increasing gauge coupling allows for a scale-invariant hyperelectric spectrum, when the coupling decreases a flat hypermagnetic spectrum can be generated for typical wavelengths larger than the effective horizon. After the gauge coupling flattens out the late-time hypermagnetic power spectra outside the horizon in the radiation epoch are determined by the hyperelectric fields at the end of inflation whereas the opposite is true in the case of decreasing coupling. Instead of imposing an abrupt freeze after inflation, we consider a smooth evolution of the mode f…
We analyze the physical content of squeezed bispectra involving long-wavelength tensor perturbations, showing that these modes cannot be gauged away, except for the exact (unphysical) limit of infinite wavelength, $k = 0$. This result has a direct implication on the validity of the Maldacena consistency relation, respected by a subclass of inflationary models. Consequently, in the squeezed limit, as in the case of the scalar-scalar-scalar bispectrum, squeezed mixed correlators could be observed by future experiments, remaining a key channel to study Early Universe physics and discriminate amon…
Provided the consistency relations are not violated, the recent Bicep2 observations pin down the absolute normalization, the spectral slope and the maximal frequency of the cosmic graviton background produced during inflation. The properly normalized spectra are hereby computed from the lowest frequencies (of the order of the present Hubble rate) up to the highest frequency range in the GHz region. Deviations from the conventional paradigm cannot be excluded and are examined by allowing for different physical possibilities including, in particular, a running of the tensor spectral index, an ex…
When the different wavelengths of the scalar and tensor modes of the geometry are all assigned on the same space-like hypersurface the maximally amplified frequencies of the spectrum remain smaller than the Planck mass only if the duration of a stage of accelerated expansion and the corresponding tensor to scalar ratio are severely constrained. All the different wavelengths can be initialized on the same space-like hypersurface at the onset of inflation but this strategy and the related conclusions are plausible only for classical inhomogeneities. We argue that a whole class of potential const…
