Graham G. Ross’s research while affiliated with University of Oxford and other places

We analyse Starobinsky inflation in the presence of the Brout Englert Higgs (BEH) boson with a non-minimal coupling to the Ricci scalar, R. The latter induces a coupling of the massive scaleron associated with the $R^2$ term to the BEH boson and this leads to a radiative correction to the BEH mass that must be fine tuned to keep the scalar light. For the case of $R^2$ driven inflation this requires a high level of fine tuning of order 1 part in $10^{8}$; for the case of Higgs inflation it is very much greater. We consider a scale invariant extension of the $R^2$/Higgs model and find that for $R^2$ driven inflation but not for Higgs inflation the required fine tuning is significantly reduced to one part in $10^{3-4}$. We consider the vacuum stability of the fine tuned model and its reheating and dilaton abundance after inflation. We also discuss possible gravitational wave signals associated with the model and the constraint on the mass of scalar or fermion dark matter candidates if they are produced by the gravitational couplings of the scalaron.

The Starobinsky model of inflation remains consistent with observation, forty years after its introduction. It provides a well motivated origin for the scalar inflaton, the “scaleron” with a mass of O(1013) GeV, emerging as a graviton degree of freedom from R2 corrections to Einstein-Hilbert gravity. However the coupling of such a heavy state to the BEH (“Higgs”) scalar is problematic as its quantum loop corrections can induce an unacceptably large contribution to the radiatively induced BEH scalar mass. The calculation of these corrections is normally done by Weyl transforming to the Einstein frame, yet at the quantum level Weyl transformations are fraught with ambiguities. However the recent realization that there exist “gravitational contact interactions” largely sidesteps these ambiguities. Such contact terms are necessarily present, coming from t-channel graviton exchange interactions, and they show that the theory defined in the “Jordan frame” is identical to the theory in the Einstein frame, with additional Planck-scale suppressed interactions that take on the form of a Weyl transformation. This avoids ambiguous nonlinear field redefinitions, and reliable loop calculations are possible leading to a consistent low energy theory in an expansion in 1/M2. Taking account of the contact terms we study the radiative corrections to the BEH mass in the mixed Higgs/R2 model with explicit scale breaking, and in an extension of the model in which exact scale symmetry is spontaneously broken.

The Starobinsky model of inflation remains consistent with observation, forty years after its introduction. It provides a well motivated origin for the scalar inflaton, the "scaleron" with a mass of $O(10^{11})$ GeV, emerging as a graviton degree of freedom from $R^2$ corrections to Einstein-Hilbert gravity. However the coupling of such a heavy state to the BEH ("Higgs") scalar is problematic as its quantum loop corrections can induce an unacceptably large contribution to the radiatively induced BEH scalar mass. The calculation of these corrections is normally done by Weyl transforming to the Einstein frame, yet at the quantum level Weyl transformations are fraught with ambiguities. However the recent realization that there exist "gravitational contact interactions" largely sidesteps these ambiguities. Such contact terms are necessarily present, coming from t-channel graviton exchange interactions, and they dictate that the theory is always in an Einstein frame, with additional Planck-scale suppressed interactions that take on the form of a Weyl transformation. This avoids ambiguous nonlinear field redefinitions, and reliable loop calculations are possible leading to a consistent low energy theory in an expansion in $1/M^2$. Taking account of the contact terms we study the radiative corrections to the BEH mass in the original Starobinsky model with explicit scale breaking, and in an extension of the model in which exact scale symmetry is spontaneously broken.

Theories of scalars and gravity, with nonminimal interactions, ∼(MP2+F(ϕi))R+L(ϕi), have graviton exchange induced contact terms. These terms arise in single particle reducible diagrams with vertices, ∝q2, that cancel the Feynman propagator denominator, 1/q2, and are familiar in various other physical contexts. In gravity these lead to additional terms in the action such as ∼F(ϕi)Tμμ(ϕi)/MP2 and F(ϕi)∂2F(ϕi)/MP2. The contact terms are equivalent to induced operators obtained by a Weyl transformation that removes the nonminimal interactions, leaving a minimal Einstein-Hilbert gravitational action. This demonstrates explicitly the equivalence of different representations of the action under Weyl transformations, both classically and quantum mechanically. To avoid such “hidden contact terms” one is compelled to go to the minimal Einstein-Hilbert representation.

Theories of scalars and gravity, with non-minimal interactions, $\sim (M_P^2 +\alpha \phi^2 )R -V(\phi)+...$, have graviton exchange induced contact terms. These terms arise in single particle reducible diagrams with vertices $\propto q^2$ that cancel the Feynman propagator denominator $1/q^2$ and are familiar in various other physical contexts. In gravity these lead to additional terms in the action such as $\sim \alpha \phi^2 V(\phi)/M_P^2$. The contact terms are equivalent to induced operators obtained by a Weyl transformation that removes the non-minimal interactions, leaving a minimal Einstein-Hilbert gravitational action. This demonstrates explicitly the equivalence of different representations of the action under Weyl transformations, both classically and quantum mechanically. To avoid such "hidden contact terms" one is compelled to go to the minimal Einstein-Hilbert representation.

Weyl (scale)-invariant theories of scalars and gravity can generate all mass scales spontaneously. In this paper, we study a particularly simple version—scale-invariant R2 gravity—and show that, during an inflationary period, it leads to fluctuations which, for a particular parameter choice, are almost indistinguishable from normal R2 inflation. Current observations place tight constraints on the primary coupling constant of this theory and predict a tensor to scalar ratio, 0.0033>r>0.0026, which is testable with the next generation of cosmic microwave background experiments.

Weyl (scale) invariant theories of scalars and gravity can generate all mass scales spontaneously. In this paper we study a particularly simple version -- scale invariant $R^2$ gravity -- and show that, during an inflationary period, it leads to fluctuations which, for a particular parameter choice, are almost indistinguishable from normal $R^2$ inflation. Current observations place tight constraints on the primary coupling constant of this theory and predict a tensor to scalar ratio, $0.0033 > r > 0.0026$, which is testable with the next generation of cosmic microwave background experiments.

A bstract An analytical formalism, including RG running at two loop order, is used to link the supersymmetric and GUT spectra in any GUT model in which the three gauge couplings unify. In each specific GUT model, one can then fully explore the interplay between the pattern of supersymmetry breaking and the prediction for the proton lifetime. With this formalism at hand, we study three concrete GUT models: (i) Minimal SU(5) SUSY GUT, (ii) Missing Partner SU(5) SUSY GUT, and (iii) an orbifold SU(5) SUSY GUT. In each case we derive interesting conclusions about the possible patterns of the supersymmetric spectrum once the present limits on the proton lifetime are imposed, and vice versa, we obtain the predictions for the proton lifetime for specific viable choices of the SUSY spectrum.

A novel analytical formalism is proposed, linking the supersymmetric and GUT spectra in any GUT model in which the three gauge couplings unify. In each specific GUT model, one can then fully explore the interplay between the pattern of supersymmetry breaking and the prediction for the proton lifetime. As an illustration, this formalism is then applied to three concrete GUT models: (i) Minimal SU(5) SUSY GUT, (ii) Missing Partner SU(5) SUSY GUT, and (iii) an orbifold SU(5) SUSY GUT. In each case we derive interesting conclusions about the possible patterns of the supersymmetric spectrum once the present limits on the proton lifetime are imposed, and vice versa, we obtain the predictions for the proton lifetime for specific viable choices of the SUSY spectrum.

A scale-invariant universe can have a period of accelerated expansion at early times: inflation. We use a frame-invariant approach to calculate inflationary observables in a scale invariant theory of gravity involving two scalar fields - the spectral indices, the tensor to scalar ratio, the level of isocurvature modes and non-Gaussianity. We show that scale symmetry leads to an exact cancellation of isocurvature modes and that, in the scale-symmetry broken phase, this theory is well described by a single scalar field theory. We find the predictions of this theory strongly compatible with current observations.