Sergio Gonzalez-Martin

Quantum corrections to unimodular gravity

A bstractThe problem of the comological constant appears in a new light in Unimodular Gravity. In particular, the zero momentum piece of the potential (that is, the constant piece independent of the matter fields) does not automatically produce a cosmological constant proportional to it. The aim of this paper is to give some details on a calculation showing that quantum corrections do not renormalize the classical value of this observable.

Unimodular Gravity Redux

It is well known that the problem of the cosmological constant appears in a new light in unimodular gravity. In particular, the zero-momentum piece of the potential does not automatically produce a corresponding cosmological constant. Here we show that quantum corrections do not renormalize the classical value of this observable.

Asymptotic solutions in asymptotic safety

As already hinted at in Sect. 1.4.3, in order to understand fixed point solutions of the RG equation both physically and mathematically it is necessary to study their asymptotic behaviour. In this chapter we explain how to find the asymptotic form of fixed-point solutions in functional truncations, in particular the f(R) approximation.

Note on the gauge symmetries of unimodular gravity

It has been partially supported by the European Union FP7 ITN INVISIBLES (Marie Curie Actions, PITNGA-2011- 289442) and (HPRN-CT-200-00148); COST action MP1405 (Quantum Structure of Spacetime), COST action MP1210. 123018-3 FPA2012-31880 (MICINN, Spain), FPA2014-54154-P (MICINN, Spain), and S2009ESP-1473 (CA Madrid). This project has received funding from the European Union’ s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 690575. This project has also received funding from the European Union’ s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 674896. The authors acknowledge the support of the Spanish MINECO Centro de Excelencia Severo Ochoa program under Grant No. SEV-2012-0249

Unimodular trees versus Einstein trees

The maximally helicity violating tree-level scattering amplitudes involving three, four or five gravitons are worked out in Unimodular Gravity. They are found to coincide with the corresponding amplitudes in General Relativity. This a remarkable result, insofar as both the propagators and the vertices are quite different in the two theories.

Unimodular Gravity and General Relativity UV divergent contributions to the scattering of massive scalar particles

We work out the one-loop and order κ 2m2 φ UV divergent contributions, coming from Unimodular Gravity and General Relativity, to the S matrix element of the scattering process φ+φ → φ+φ in a λφ4 theory with mass mφ . We show that both Unimodular Gravity and General Relativity give rise to the same UV divergent contributions in Dimension Regularization. This seems to be at odds with the known result that in a multiplicative MS dimensional regularization scheme the General Relativity corrections, in the de Donder gauge, to the beta function βλ of the λ coupling do not vanish, whereas the Unimodular Gravity corrections, in a certain gauge, do vanish. Actually, we show that the UV divergent contributions to the 1PI Feynman diagrams which give rise to those non-vanishing corrections to βλ do not contribute to the UV divergent behaviour of the S matrix element of φ + φ → φ + φ and this shows that any physical consequence –such existence of asymptotic freedom due to gravitational interactions– drawn from the value of βλ is not physically meaningful.

Scattering of fermions in the Yukawa theory coupled to unimodular gravity

We compute the lowest order gravitational UV divergent radiative corrections to the S matrix element of the

Weyl gravity revisited

fermion + fermion\rightarrow fermion + fermion