Abstract
We explore the possible cosmological consequences of a running Newton’s constant, G(⎕), as suggested by the non-trivial ultraviolet fixed point scenario for Einstein gravity with a cosmological constant term. Here, we examine what possible effects a scale-dependent coupling might have on large-scale cosmological density perturbations. Starting from a set of manifestly covariant effective field equations, we develop the linear theory of density perturbations for a non-relativistic perfect fluid. The result is a modified equation for the matter density contrast, which can be solved and thus provides an estimate for the corrections to the growth index parameter, ɤ.
Highlights
Recent years have seen the development of a bewildering variety of alternative theories of gravity, in addition to the more traditional ones, such as scalar-tensor, higher derivative and dilaton gravities, just to mention a few examples
It is well known that for theories with a non-trivial ultraviolet fixed point [26,27,28,29,30,31], the long distance universal scaling properties are uniquely determined, up to subleading correction to exponents and scaling amplitudes, by the scaling dimensions obtained by renormalization group methods in the vicinity of the Ultra Violet (UV) fixed point [32,33,34,35,36]
These sets of results form the basis for universal predictions in the non-linear sigma model [37,38,39], which provides today the second most accurate test of quantum field theory [40], after the g − 2 prediction for QED (Quantum Electro-Dynamics)
Summary
Recent years have seen the development of a bewildering variety of alternative theories of gravity, in addition to the more traditional ones, such as scalar-tensor, higher derivative and dilaton gravities, just to mention a few examples. It is well known that for theories with a non-trivial ultraviolet fixed point [26,27,28,29,30,31], the long distance (and infrared) universal scaling properties are uniquely determined, up to subleading correction to exponents and scaling amplitudes, by the (generally nontrivial) scaling dimensions obtained by renormalization group methods in the vicinity of the UV fixed point [32,33,34,35,36] These sets of results form the basis for universal predictions in the non-linear sigma model [37,38,39], which provides today the second most accurate test of quantum field theory [40], after the g − 2 prediction for QED (Quantum Electro-Dynamics) (for a comprehensive set of references, see [8,34], and the references therein).
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