15,522 research outputs found
Do the gravitational corrections to the beta functions of the quartic and Yukawa couplings have an intrinsic physical meaning?
We study the beta functions of the quartic and Yukawa couplings of General
Relativity and Unimodular Gravity coupled to the and Yukawa
theories with masses. We show that the General Relativity corrections to those
beta functions as obtained from the 1PI functional by using the standard MS
multiplicative renormalization scheme of Dimensional Regularization are gauge
dependent and, further, that they can be removed by a non-multiplicative,
though local, field redefinition. An analogous analysis is carried out when
General Relativity is replaced with Unimodular Gravity. Thus we show that any
claim made about the change in the asymptotic behaviour of the quartic and
Yukawa couplings made by General Relativity and Unimodular Gravity lack
intrinsic physical meaning.Comment: 6 pages, 7 figure
The Renormalization Group flow of unimodular f(R) gravity
Unimodular gravity is classically equivalent to General Relativity. This
equivalence extends to actions which are functions of the curvature scalar. At
the quantum level, the dynamics could differ. Most importantly, the
cosmological constant is not a coupling in the unimodular action, providing a
new vantage point from which to address the cosmological constant fine-tuning
problem. Here, a quantum theory based on the asymptotic safety scenario is
studied, and evidence for an interacting fixed point in unimodular f(R) gravity
is found. We study the fixed point and its properties, and also discuss the
compatibility of unimodular asymptotic safety with dynamical matter, finding
evidence for its compatibility with the matter degrees of freedom of the
Standard Model.Comment: 17 pages, 2 figures; new version with some clarifications, identical
to version to appear in JHE
The cosmological constant as a boundary term
We compare the path integral for transition functions in unimodular gravity
and in general relativity. In unimodular gravity the cosmological constant is a
property of states that are specified at the boundaries whereas in general
relativity the cosmological constant is a parameter of the action. Unimodular
gravity with a nondynamical background spacetime volume element has a time
variable that is canonically conjugate to the cosmological constant. Wave
functions depend on time and satisfy a Schr\"odinger equation. On the contrary,
in the covariant version of unimodular gravity with a 3-form gauge field,
proposed by Henneaux and Teitelboim, wave functions are time independent and
satisfy a Wheeler-DeWitt equation, as in general relativity. The 3-form gauge
field integrated over spacelike hypersurfaces becomes a "cosmic time" only in
the semiclassical approximation. In unimodular gravity the smallness of the
observed cosmological constant has to be explained as a property of the initial
state.Comment: 22 pages, minor corrections, agrees with published versio
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