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Register a new userPath integral for multi-field inflation
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We develop the path integral formalism for studying cosmological perturbations in multi-field inflation, which is particularly well suited to study quantum theories with gauge symmetries such as diffeomorphism invariance. We formulate the gauge fixing conditions based on the Poisson brackets of the constraints, from which we derive two convenient gauges that are appropriate for multi-field inflation. We then adopt the in-in formalism to derive the most general expression for the power spectrum of the curvature perturbation including the corrections from the interactions of the curvature mode with other light degrees of freedom. We also discuss the contributions of the interactions to the bispectrum.
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We study the consequences of spatial coordinate transformation in multi-field inflation. Among the spontaneously broken de Sitter isometries, only dilatation in the comoving gauge preserves the form of the metric and thus results in quantum-protected Slavnov-Taylor identities. We derive the corresponding consistency relations between correlation functions of cosmological perturbations in two different ways, by the connected and one-particle-irreducible Greens functions. The lowest-order consistency relations are explicitly given, and we find that even in multi-field inflation the consistency relations in the soft limit are independent of the detail of the matter sector.
We have investigated if the vector field can give rise to an accelerating phase in the early universe. We consider a timelike vector field with a general quadratic kinetic term in order to preserve an isotropic background spacetime. The vector field potential is required to satisfy the three minimal conditions for successful inflation: i) $rho>0$, ii) $rho+3P < 0$ and iii) the slow-roll conditions. As an example, we consider the massive vector potential and small field type potential as like in scalar driven inflation.
In holographic inflation, the $4D$ cosmological dynamics is postulated to be dual to the renormalization group flow of a $3D$ Euclidean conformal field theory with marginally relevant operators. The scalar potential of the $4D$ theory ---in which inflation is realized--- is highly constrained, with use of the Hamilton--Jacobi equations. In multi-field holographic realizations of inflation, fields additional to the inflaton cannot display underdamped oscillations (that is, their wavefunctions contain no oscillatory phases independent of the momenta). We show that this result is exact, independent of the number of fields, the field space geometry and the shape of the inflationary trajectory followed in multi-field space. In the specific case where the multi-field trajectory is a straight line or confined to a plane, it can be understood as the existence of an upper bound on the dynamical masses $m$ of extra fields of the form $m leq 3 H / 2$ up to slow roll corrections. This bound corresponds to the analytic continuation of the well known Breitenlohner--Freedman bound found in AdS spacetimes in the case when the masses are approximately constant. The absence of underdamped oscillations implies that a detection of cosmological collider oscillatory patterns in the non-Gaussian bispectrum would not only rule out single field inflation, but also holographic inflation or any inflationary model based on the Hamilton--Jacobi equations. Hence, future observations have the potential to exclude, at once, an entire class of inflationary theories, regardless of the details involved in their model building.
The difficulty of building metastable vacua in string theory has led some to conjecture that, in the string theory landscape, potentials satisfy $left| abla V/Vright|geq csim mathcal{O}(1)$. This condition, which is supported by different explicit constructions, suggests that the EFTs which lead to metastable de-Sitter vacua belong to what is dubbed as swampland. This condition endangers the paradigm of single field inflation. In this paper, we show how scalar excited initial states cannot rescue single field inflation from the swampland, as they produce large local scalar non-gaussianity, which is in conflict with the Planck upper bound. Instead, we demonstrate that one can salvage single field inflation using excited initial states for tensor perturbations, which in this case produce only large flattened non-gaussianity in the tensor bispectrum. We comment on the possible methods one can prepare such excited initial conditions for the tensor perturbations.
We develop an effective-field-theory (EFT) framework for inflation with various symmetry breaking pattern. As a prototype, we formulate anisotropic inflation from the perspective of EFT and construct an effective action of the Nambu-Goldstone bosons for the broken time translation and rotation symmetries. We also calculate the statistical anisotropy in the scalar two-point correlation function for concise examples of the effective action.
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