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<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e2396" altimg="si412.svg"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> gravity with broken Weyl gauge symmetry, cosmological backreaction, and its effects on CMB anisotropy

We propose a new class of f(R) theory where its Weyl gauge symmetry is broken in the primordial era of the universe. This symmetry forces one to adopt a new scalar field, namely a Weyl field and a gauge vector boson. Furthermore, an equivalent form of the Einstein–Hilbert Lagrangian with a non-minimally coupled scalar field corresponding to the function f(R) is found. Due to the geometrical feature of the Weyl field, it turns out that the symmetry breaking induces a non-minimal coupling, which cannot be expected in the standard f(R) theories. We explain how this affects the evolution of the universe at cosmological scales. It is shown that there may be a value shift in the Planck constant and the cosmological constant. This can be regarded as a genuine exemplification of the cosmological backreaction. Furthermore, one also finds new features in the evolution of perturbational variables and cosmic microwave background anisotropy. Moreover, we prove that when a specific f(R) model invokes inflation, the amplitude of the primordial gravitational waves affects the evolution of scalar perturbation due to the new non-minimal coupling. As a case study, we explain how this can be embodied in the Starobinsky inflation. Finally, we discuss some impacts that this physics can bear and the possibility of giving a new restriction of the estimation of cosmological variables such as the gravitational wave amplitude with experiments.

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