### On the Initial State and Consistency Relations

"... We study the effect of the initial state on the consistency conditions for adiabatic pertur-bations. In order to be consistent with the constraints of General Relativity, the initial state must be diffeomorphism invariant. As a result, we show that initial wavefunctional/density matrix has to satisf ..."

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We study the effect of the initial state on the consistency conditions for adiabatic pertur-bations. In order to be consistent with the constraints of General Relativity, the initial state must be diffeomorphism invariant. As a result, we show that initial wavefunctional/density matrix has to satisfy a Slavnov-Taylor identity similar to that of the action. We then investi-gate the precise ways in which modified initial states can lead to violations of the consistency relations. We find two independent sources of violations: i) the state can include initial non-Gaussianities; ii) even if the initial state is Gaussian, such as a Bogoliubov state, the modified 2-point function can modify the ~q → 0 analyticity properties of the vertex functional and result in violations of the consistency relations. ar X iv

### The Physical Squeezed Limit: Consistency Relations at Order q2

"... In single-field models of inflation the effect of a long mode with momentum q reduces to a dif-feomorphism at zeroth and first order in q. This gives the well-known consistency relations for the n-point functions. At order q2 the long mode has a physical effect on the short ones, since it induces cu ..."

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In single-field models of inflation the effect of a long mode with momentum q reduces to a dif-feomorphism at zeroth and first order in q. This gives the well-known consistency relations for the n-point functions. At order q2 the long mode has a physical effect on the short ones, since it induces curvature, and we expect that this effect is the same as being in a curved FRW uni-verse. In this paper we verify this intuition in various examples of the three-point function, whose behaviour at order q2 can be written in terms of the power spectrum in a curved universe. This gives a simple alternative understanding of the level of non-Gaussianity in single-field models. Non-Gaussianity is always parametrically enhanced when modes freeze at a physical scale kph, f shorter than H: fNL ∼ (kph, f/H)2. 1 Introduction and main results In single-field inflation, correlation functions of the curvature perturbation ζ and of tensor modes satisfy general, model-independent relations in the limit in which one of the momenta (or the sum of some of the momenta) becomes very small compared to the others: the so-called consistency relations [1–9]. Physically, they are based on the observation that the effect of a long mode on the

### What is the shape of the initial state?1

"... Abstract: We argue that a plausible operational definition for an initial state of the Uni-verse is the initial quantum state of the curvature perturbations generated during inflation. We provide a parameterization of this state and generalize the standard in-in formalism to incorporate the structur ..."

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Abstract: We argue that a plausible operational definition for an initial state of the Uni-verse is the initial quantum state of the curvature perturbations generated during inflation. We provide a parameterization of this state and generalize the standard in-in formalism to incorporate the structures in this state into the computation of correlators of the perturba-tions. Measurements of these correlators using both the CMB as well as large scale structure probe different structures in the initial state, as they give rise to bi- and tri-spectra peaked on different shapes of triangles and quadrilaterals in momentum space. In essence, the shapes implied by the correlators feed directly into information about the shape of the initial state and what physics could have preceded inflation to set this state up.

### Single-Field Consistency Relations of Large Scale Structure Part III: Test of the Equivalence Principle

"... The recently derived consistency relations for Large Scale Structure do not hold if the Equivalence Principle (EP) is violated. We show it explicitly in a toy model with two fluids, one of which is coupled to a fifth force. We explore the constraints that galaxy surveys can set on EP violation looki ..."

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The recently derived consistency relations for Large Scale Structure do not hold if the Equivalence Principle (EP) is violated. We show it explicitly in a toy model with two fluids, one of which is coupled to a fifth force. We explore the constraints that galaxy surveys can set on EP violation looking at the squeezed limit of the 3-point function involving two populations of objects. We find that one can explore EP violations of order 10−3 ÷ 10−4 on cosmological scales. Chameleon models are already very constrained by the requirement of screening within the Solar System and only a very tiny region of the parameter space can be explored with this method. We show that no violation of the consistency relations is expected in Galileon models. 1 ar X iv