It is proposed that if quantum states of space-time are coherent on null surfaces, holographic Planck-scale fluctuations of inflationary horizons dominate the formation of primordial scalar curvature perturbations. It is shown that the reduction of quantum states on nearly-spherical emergent horizon surfaces around each observer creates a distinctive pattern whose correlations in the angular domain differ from the standard quantum theory of inflation. Causal constraints are used in a semiclassical model to formulate candidate directional symmetries. It is suggested that this hypothesis could provide a physical explanation for several well known anomalies measured in CMB anisotropy. New exact symmetries are predicted, such as a vanishing temperature correlation function at 90 degrees angular separation, that can be tested with current data.
There is a widespread belief among inflationary cosmologists that a local observer cannot sense super-horizon gravitons. The argument goes that a local observer would subsume super-horizon gravitons into a redefinition of his coordinate system. We show that adopting this view for pure gravity on de Sitter background leads to time variation in the Hubble parameter measured by a local observer. It also leads to a violation of the gravitational field equation $R = 4 Λ$ because that equation is obeyed by the full metric, rather than the one which has been cleansed of super-horizon modes.
Models are developed to estimate properties of relic cosmic perturbations with "spooky" nonlocal correlations on the inflationary horizon, analogous to those previously posited for information on black hole event horizons. Scalar curvature perturbations are estimated to emerge with a dimensionless power spectral density $Δ_S^2\approx H t_P$, the product of inflationary expansion rate $H$ with Planck time $t_P$, larger than standard inflaton fluctuations. Current measurements of the spectrum are used to derive constraints on parameters of the effective potential in a slow-roll background. It is…
In this paper we use conformal field theory techniques to constrain the form of the correlations functions of an inflationary scalar-vector model described by the interaction term $f_1(ϕ)F_{μν}F^{μν} + f_2(ϕ)\tilde{F}_{μν}F^{μν}$. We use the fact that the conformal group is the relevant symmetry group acting on super horizon scales in an inflationary de Sitter background. As a result, we find that super horizon conformal symmetry, constraints the form of the coupling functions $f_1, f_2$ to be homogeneous functions of the same degree. We derive the general form of the correlators involving sca…
We show that in single field inflationary models the super-horizon evolution of curvature perturbations on comoving slices $\mathcal{R}$, which can cause the production of primordial black holes (PBH), is not due to entropy perturbations, but to the background evolution effect on the conversion between entropy and curvature perturbations. We derive a general relation between the time derivative of comoving curvature perturbations and entropy perturbations, in terms of a conversion factor depending on the background evolution. Contrary to previous results derived in the uniform density gauge as…
We investigate inflationary correlation functions in single field inflation models. We adopt a BRST formalism where locality and covariance at the sub-horizon scale are manifest. The scalar and tensor perturbations are identified with those in the comoving gauge which become constant outside the cosmological horizon. Our construction reproduces the identical non-Gaussianity with the standard comoving gauge. The accumulation of almost scale invariant fluctuations could give rise to IR logarithmic corrections at the loop level. We investigate the influence of this effect on the sub-horizon dynam…
We address the problem of determining inflationary characteristics in a model independent way. We start from a recently proposed equation which allows to accurately calculate the value of the inflaton at horizon crossing $ϕ_k$. We then use an equivalent form of this equation to write a formula that relates the number of e-folds from horizon crossing to the pivot scale $N_{ke}+N_{ep}$ with the tensor-to-scalar index $r$, hence a general bound for $N_{ke}+N_{ep}$ follows. $N_{ke}$ is the number of e-folds from the scale factor $a_k$ during inflation to the end of inflation at $a_e$ and $N_{ep}$ …
Inflation can be parameterized by means of truncated flow equations. In this "horizon-flow" setup, generic results have been obtained, such as typical values for $r/(1-n_\mathrm{S})$. 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 de…
The evolution of inflationary fluctuations can be recast as an inverse scattering problem. In this context, we employ the Gel'fand-Levitan method from inverse-scattering theory to reconstruct the evolution of both the inflaton field freeze-out horizon and the Hubble parameter during inflation. We demonstrate this reconstruction procedure numerically for a scenario of slow-roll inflation, as well as for a scenario which temporarily departs from slow-roll. The field freeze-out horizon is reconstructed from the accessible primordial scalar power spectrum alone, while the reconstruction of the Hub…
The measurement of the inflationary stochastic gravitational-wave background (SGWB) is one of the main goals of future GW experiments. In direct GW experiments, an obstacle to achieving it is the isolation of the inflationary SGWB from the other types of SGWB. In this paper, as a distinguishable signature of the inflationary SGWB, we argue the detectability of its universal property: antipodal correlations, i.e., correlations of GWs from the opposite directions, as a consequence of the horizon re-entry. A phase-coherent method has been known to be of no use for detecting the angular correlatio…
The quantum mechanical generation of hypermagnetic and hyperlectric fields in four-dimensional conformally flat background geometries rests on the simultaneous continuity of the effective horizon and of the extrinsic curvature across the inflationary boundary. The junction conditions for the gauge fields are derived in general terms and corroborated by explicit examples with particular attention to the limit of a sudden (but nonetheless continuous) transition of the effective horizon. After reducing the dynamics to a pair of integral equations related by duality transformations, we compute the…
We study the quantum mechanical evolution of the tensor perturbations during inflation with non-linear tensor interactions. We first obtain the Lindblad terms generated by non-linear interactions by tracing out unobservable sub-horizon modes. Then we calculate explicitly the reduced density matrix for the super-horizon modes, and show that the probability of maintaining the unitarity of the squeezed state decreases in time. The decreased probability is transferred to other elements of the reduced density matrix including off-diagonal ones, so the evolution of the reduced density matrix describ…
In this work we study the imprints of bubble nucleation on primordial inflationary perturbations. We assume that the bubble is formed via the tunneling of a spectator field from the false vacuum of its potential to its true vacuum. We consider the configuration in which the observable CMB sphere is initially outside of the bubble. As the bubble expands, more and more regions of the exterior false vacuum, including our CMB sphere, fall into the interior of the bubble. The modes which leave the horizon during inflation at the time when the bubble wall collides with the observable CMB sphere are …
Slow-roll inflation may simultaneously solve the horizon problem and generate a near scale-free fluctuation spectrum P(k). These two processes are intimately connected via the initiation and duration of the inflationary phase. But a recent study based on the latest Planck release suggests that P(k) has a hard cutoff, k_min > 0, inconsistent with this conventional picture. Here we demonstrate quantitatively that most---perhaps all---slow-roll inflationary models fail to accommodate this minimum cutoff. We show that the small parameter `epsilon' must be > 0.9 throughout the inflationary period t…
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 argue that the preferred classical variables that emerge from a pure quantum state are determined by its entanglement structure in the form of redundant records: information shared between many subsystems. Focusing on the early universe, we ask how classical metric perturbations emerge from vacuum fluctuations in an inflationary background. We show that the squeezing of the quantum state for super-horizon modes, along with minimal gravitational interactions, leads to decoherence and to an exponential number of records of metric fluctuations on very large scales, $λ/λ_{\rm Hubble}>Δ_ζ^{-2/3}…
We study the Wigner function for the inflationary tensor perturbation defined in the real phase space. We compute explicitly the Wigner function including the contributions from the cubic self-interaction Hamiltonian of tensor perturbations. Then we argue that it is no longer an appropriate description for the probability distribution in the sense that quantum nature allows negativity around vanishing phase variables. This comes from the non-Gaussian wavefunction in the mixed state as a result of the non-linear interaction between super- and sub-horizon modes. We also show that this is related…
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 consider cosmological scenarios in which density perturbations are generated by the quantum fluctuations of the inflaton field at early times; the late time dynamics involves a modulus which first dominates the energy density of the universe and then decays to reheat the visible sector. By examining the evolution of energy density of the universe from the time of horizon exit of a pivot mode to the present day, and the fact that a modulus field decays via Planck suppressed interactions, we arrive at a relation which relates the mass of the modulus, inflationary observables/parameters and br…
PyTransport constitutes a straightforward code written in C++ together with Python scripts which automatically edit, compile and run the C++ code as a Python module. It has been written for Unix-like systems (OS X and Linux). Primarily the module employs the transport approach to inflationary cosmology to calculate the tree-level power-spectrum and bispectrum of user specified models of multi-field inflation, accounting for all sub and super-horizon effects. The transport method we utilise means only coupled differential equations need to be solved, and the implementation presented here combin…
Various inflationary scenarios can often be distinguished from one another by looking at the squeezed limit behavior of correlation functions. Therefore, it is useful to have a framework designed to study this limit in a more systematic and efficient way. We propose using an expansion in terms of weakly coupled super-horizon degrees of freedom, which is argued to generically exist in a near de Sitter space-time. The modes have a simple factorized form which leads to factorization of the squeezed-limit correlation functions with power-law behavior in $k_{\rm long}/k_{\rm short}$. This approach …
