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Register a new userConformal invariant cosmological perturbations via the covariant approach: multicomponent universe
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In recent years there has been a lot of interest in discussing frame dependences/independences of the cosmological perturbations under the conformal transformations. This problem has previously been investigated in terms of the covariant approach for a single component universe, and it was found that the covariant approach is very powerful to pick out the perturbative variables which are both gauge and conformal invariant. In this work, we extend the covariant approach to a universe with multicomponent fluids. We find that similar results can be derived, as expected. In addition, some other interesting perturbations are also identified to be conformal invariant, such as entropy perturbation between two different components.
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It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it is possible to do equivalent analysis in a certain frame in which the perturbation equations are simpler. In this paper we revisit the problem of conformal invariances of cosmological perturbations in terms of the covariant approach in which the perturbation variables have clear geometric and physical meanings. We show that with this approach the conformal invariant perturbations are easily identified.
In this paper we continue a study of cosmological perturbations in the conformal gravity theory. In previous work we had obtained a restricted set of solutions to the cosmological fluctuation equations, solutions that were required to be both transverse and synchronous. Here we present the general solution. We show that in a conformal invariant gravitational theory fluctuations around any background that is conformal to flat (backgrounds that include the cosmologically interesting Robertson-Walker and de Sitter geometries) can be constructed from the (known) solutions to fluctuations around a flat background. For this construction to hold it is not necessary that the perturbative geometry associated with the fluctuations itself be conformal to flat. Using this construction we show that in a conformal Robertson-Walker cosmology early universe fluctuations grow as $t^4$. We present the scalar, vector, tensor decomposition of the fluctuations in the conformal theory, and compare and contrast our work with the analogous treatment of fluctuations in the standard Einstein gravity theory.
Using our recent proposal for defining gauge invariant averages we give a general-covariant formulation of the so-called cosmological backreaction. Our effective covariant equations allow us to describe in explicitly gauge invariant form the way classical or quantum inhomogeneities affect the average evolution of our Universe.
In second order perturbation theory different definitions are known of gauge invariant perturbations in single field inflationary models. Consequently the corresponding gauge invariant cubic actions do not have the same form. Here we show that the cubic action for one choice of gauge invariant variables is unique in the following sense: the action for any other, non-linearly related variable can be brought to the same bulk action, plus additional boundary terms. These boundary terms correspond to the choice of hypersurface and generate extra, disconnected contributions to the bispectrum. We also discuss uniqueness of the action with respect to conformal frames. When expressed in terms of the gauge invariant curvature perturbation on uniform field hypersurfaces the action for cosmological perturbations has a unique form, independent of the original Einstein or Jordan frame. Crucial is that the gauge invariant comoving curvature perturbation is frame independent, which makes it extremely helpful in showing the quantum equivalence of the two frames, and therefore in calculating quantum effects in nonminimally coupled theories such as Higss inflation.
We discuss scalar-tensor realizations of the Anamorphic cosmological scenario recently proposed by Ijjas and Steinhardt. Through an analysis of the dynamics of cosmological perturbations we obtain constraints on the parameters of the model. We also study gravitational Parker particle production in the contracting Anamorphic phase and we compute the fraction between the energy density of created particles at the end of the phase and the background energy density. We find that, as in the case of inflation, a new mechanism is required to reheat the universe.
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