Abstract
We study the inflationary perturbations in general (classically) scale-invariant theories. Such scenario is motivated by the hierarchy problem and provides natural inflationary potentials and dark matter candidates. We analyse in detail all sectors (the scalar, vector and tensor perturbations) giving general formulae for the potentially observable power spectra, as well as for the curvature spectral index n_mathrm{s} and the tensor-to-scalar ratio r. We show that the conserved Hamiltonian for all perturbations does not feature negative energies even in the presence of the Weyl-squared term if the appropriate quantisation is performed and argue that this term does not lead to phenomenological problems at least in some relevant setups. The general formulae are then applied to a concrete no-scale model, which includes the Higgs and a scalar, “the planckion”, whose vacuum expectation value generates the Planck mass. Inflation can be triggered by a combination of the planckion and the Starobinsky scalar and we show that no tension with observations is present even in the case of pure planckion inflation, if the coefficient of the Weyl-squared term is large enough. In general, even quadratic inflation is allowed in this case. Moreover, the Weyl-squared term leads to an isocurvature mode, which currently satisfies the observational bounds, but it may be detectable with future experiments.
Highlights
If one supposes that nature does not have fundamental scales and all observed masses are dynamically generated one is led to conjecture that the fundamental theory of gravity contains only terms quadratic in curvature in addition to all possible scale-invariant couplings to matter. The requirement that this four-derivative gravity theory cures the Higgs naturalness problem leads to the possibility of testing this hypothesis with observations of the early universe
The present work is intended to be a complete study of inflationary perturbations in general scale-invariant theories
Notice that H appearing in the second term of the left-hand-side of this equation can be replaced by the corresponding quantity in the pure de Sitter case: Eq (2.25) shows that the difference between the pure de Sitter H and the spacetime that takes into account the dynamics of the scalar fields is beyond the next-to-leading order slow-roll approximation that we are using here
Summary
In this work we consider general (classically) scale-invariant theories. The action is. In the second way one supposes that some strongly coupled sector (such as an SU(n) gauge theory) confines and generates the observed scales through its coupling to the other sectors (e.g. its gravitational couplings) [1]. After this has happened the Planck mass, the weak scale, the cosmological constant, etc appear in the Lagrangian as effective parameters. We will introduce these quantities directly in the action This will allow us to be more general and cover arbitrary renormalisable models
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