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Authors
Edmund J. Copeland
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We investigate the evolution of scalar metric perturbations across a sudden cosmological transition, allowing for an inhomogeneous surface stress at the transition leading to a discontinuity in the local expansion rate, such as might be expected in a big crunch/big bang event. We assume that the transition occurs when some function of local matter variables reaches a critical value, and that the surface stress is also a function of local matter variables. In particular we consider the case of a single scalar field and show that a necessary condition for the surface stress tensor to be perturbed at the transition is the presence of a non-zero intrinsic entropy perturbation of the scalar field. We present the matching conditions in terms of gauge-invariant variables assuming a sudden transition to a fluid-dominated universe with barotropic equation of state. For adiabatic perturbations the comoving curvature perturbation is continuous at the transition, while the Newtonian potential may be discontinuous if there is a discontinuity in the background Hubble expansion.
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Primordial perturbations in our universe are believed to have a quantum origin, and can be described by the wavefunction of the universe (or equivalently, cosmological correlators). It follows that these observables must carry the imprint of the founding principle of quantum mechanics: unitary time evolution. Indeed, it was recently discovered that unitarity implies an infinite set of relations among tree-level wavefunction coefficients, dubbed the Cosmological Optical Theorem. Here, we show that unitarity leads to a systematic set of Cosmological Cutting Rules which constrain wavefunction coefficients for any number of fields and to any loop order. These rules fix the discontinuity of an n-loop diagram in terms of lower-loop diagrams and the discontinuity of tree-level diagrams in terms of tree-level diagrams with fewer external fields. Our results apply with remarkable generality, namely for arbitrary interactions of fields of any mass and any spin with a Bunch-Davies vacuum around a very general class of FLRW spacetimes. As an application, we show how one-loop corrections in the Effective Field Theory of inflation are fixed by tree-level calculations and discuss related perturbative unitarity bounds. These findings greatly extend the potential of using unitarity to bootstrap cosmological observables and to restrict the space of consistent effective field theories on curved spacetimes.
I show that the problem of realizing inflation in theories with random potentials of a limited number of fields can be solved, and agreement with the observational data can be naturally achieved if at least one of these fields has a non-minimal kinetic term of the type used in the theory of cosmological $alpha$-attractors.
Recently in various theoretical works, path-breaking progress has been made in recovering the well-known Page Curve of an evaporating black hole with Quantum Extremal Islands, proposed to solve the long-standing black hole information loss problem related to the unitarity issue. Motivated by this concept, in this paper, we study cosmological circuit complexity in the presence (or absence) of Quantum Extremal Islands in the negative (or positive) Cosmological Constant with radiation in the background of Friedmann-Lema$hat{i}$tre-Robertson-Walker (FLRW) space-time i.e the presence and absence of islands in anti-de Sitter and the de Sitter spacetime having SO(2, 3) and SO(1, 4) isometries respectively. Without using any explicit details of any gravity model, we study the behaviour of the circuit complexity function with respect to the dynamical cosmological solution for the scale factors for the above-mentioned two situations in FLRW space-time using squeezed state formalism. By studying the cosmological circuit complexity, Out-of-Time Ordered Correlators, and entanglement entropy of the modes of the squeezed state, in different parameter spaces, we conclude the non-universality of these measures. Their remarkably different features in the different parameter spaces suggest their dependence on the parameters of the model under consideration.
We investigate cosmological perturbations of scalar-tensor theories in Palatini formalism. First we introduce an action where the Ricci scalar is conformally coupled to a function of a scalar field and its kinetic term and there is also a k-essence term consisting of the scalar and its kinetic term. This action has three frames that are equivalent to one another: the original Jordan frame, the Einstein frame where the metric is redefined, and the Riemann frame where the connection is redefined. For the first time in the literature, we calculate the quadratic action and the sound speed of scalar and tensor perturbations in three different frames and show explicitly that they coincide. Furthermore, we show that for such action the sound speed of gravitational waves is unity. Thus, this model serves as dark energy as well as an inflaton even though the presence of the dependence of the kinetic term of a scalar field in the non-minimal coupling, different from the case in metric formalism. We then proceed to construct the L3 action called Galileon terms in Palatini formalism and compute its perturbations. We found that there are essentially 10 different(inequivalent) definitions in Palatini formalism for a given Galileon term in metric formalism. We also see that,in general, the L3 terms have a ghost due to Ostrogradsky instability and the sound speed of gravitational waves could potentially deviate from unity, in sharp contrast with the case of metric formalism. Interestingly, once we eliminate such a ghost, the sound speed of gravitational waves also becomes unity. Thus, the ghost-free L3 terms in Palatini formalism can still serve as dark energy as well as an inflaton, like the case in metric formalism.
We find new, simple cosmological solutions with flat, open, and closed spatial geometries, contrary to the previous wisdom that only the open model is allowed. The metric and the St{u}ckelberg fields are given explicitly, showing nontrivial configurations of the St{u}ckelberg in the usual Friedmann-Lema^{i}tre-Robertson-Walker coordinates. The solutions exhibit self-acceleration, while being free from ghost instabilities. Our solutions can accommodate inhomogeneous dust collapse represented by the Lema^{i}tre-Tolman-Bondi metric as well. Thus, our results can be used not only to describe homogeneous and isotropic cosmology but also to study gravitational collapse in massive gravity.
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