Abstract
We show that in the single component situation all perturbationvariables in the comoving gauge are conformally invariant to allperturbation orders. Generally we identify a special time slicing, theuniform-conformal transformation slicing, where all perturbations areagain conformally invariant to all perturbation orders. We applythis result to the δN formalism, and show its conformalinvariance.
Highlights
A large class of extensions of general relativity is described in the context of scalar-tensor theories of gravity [1], where a space-time metric gμν is coupled to a scalar field φ, with the other matter contents such as fermion fields being minimally coupled to gravity
In (2.2), we have explicitly shown the invariance to all perturbation orders, and have shown that why the invariance is natural in the uniform Ω slicing (UΩS) which is the same as the uniform field gauge, or equivalently comoving gauge, in the single component case
When the universe is dominated by a single component φ, the comoving slice is the same as the UΩS, Rc = Rc
Summary
A large class of extensions of general relativity is described in the context of scalar-tensor theories of gravity [1], where a space-time metric gμν is coupled to a scalar field φ, with the other matter contents such as fermion fields being minimally coupled to gravity. We will show that in the single component case all perturbations in the comoving slicing are conformally invariant to fully non-linear order. Once this is given, we can see that in the context of the δN formalism it is a matter of gauge transformation between different coordinate systems which impose different slicing conditions. Under this slicing condition it is obvious, almost a tautology, that all perturbed quantities are naturally invariant under the conformation transformation This result applies even in multiple component situation: see (3.8) and (3.9) for relations implied by this slicing condition to non-linear orders of perturbation. The UΩS corresponds to the uniform-field slicing or the uniform-F slicing, respectively, and we may call it as the UFS
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