Asymptotically Weyl-invariant gravity

Abstract

We propose a novel theory of gravity that by construction is renormalizable, evades Ostragadsky's no-go theorem, is locally scale-invariant in the high-energy limit, and equivalent to general relativity in the low-energy limit. The theory is defined by a pure f (R) = R n action in the Palatini formalism, where the dimensionless exponent n runs from a value of two in the high-energy limit to one in the low-energy limit. We show that the proposed model contains no obvious cosmological curvature singularities. The viability of the proposed model is qualitatively assessed using several key criteria. PACS numbers: 04.60.-m, 04.60.Bc IntroductionGeneral relativity is theoretically beautiful, experimentally successful, and defines our best current description of gravity. Its key equations follow almost inevitably from a single symmetry principle and yield predictions that agree with experiment over a vast range of distance scales [1].Yet, general relativity is almost certainly incomplete. One major problem is that it appears to be incompatible with quantum field theory at high energies. Although general relativity has been successfully formulated as an effective quantum field theory at low energies, new divergences appear at each order in the perturbative expansion, leading to a complete loss of predictivity at high energies. Gravity is said to be perturbatively non-renormalizable, a fact demonstrated by explicit calculation at the one-loop level including matter content [2], and at the two-loop level without matter [3]. This behaviour stems from the fact that the gravitational coupling introduces a length scale into the theory so that higher-order corrections in a perturbative expansion come with ever-increasing powers of the cut-off scale.Higher-order actions have been explored as a possible solution to this problem [4]. Explicit calculations show that Lagrangians quadratic in the curvature tensor are renormalizable [5]. However, quadratic theories of gravity are not hailed as the theory of quantum gravity because they are not typically unitary, often containing unphysical ghost modes [5]. Higher-order theories are also generally unstable, violating a powerful no-go theorem first proposed by Ostragadsky [6]. Ostrogradsky's theorem proves that there is a fatal linear instability in any Hamiltonian associated with Lagrangians which depend on two or more time derivatives. This result helps explain the otherwise mysterious fact that the fundamental laws of physics seem to include at most two time derivatives [7]. The only higher-order theories that are both stable and unitary are f (R) theories, in which the Lagrangian is a general function f of the Ricci scalar R [8].Since f (R) gravity is not a single theory but a potentially infinite set of theories, one for each particular function f (R), we must identify a principle capable of selecting a specific function f (R). We contend that this principle should be local scale invariance. One reason for this is that scale-invariant theories of gravity are gauge theories [9,10]. ...

New class of hybrid metric-Palatini scalar-tensor theories of gravity

“…This shows that there is a renewing interest and ongoing activity in applications of Palatini STT in astrophysics, which is enforced due to the recent developments in solving dark matter, dark energy and cosmic inflation problems (cf. [69]- [81] and [114]- [120]).…”

Cosmological constraints of Palatini f(ℛ) gravity

“…, where the exponent depends on the temperature and varies from n = 1 in the low-energy limit, and n = 2 at the early Universe, yields a scale-invariant description of gravity in high-energy limit, reduces to GR at later times, and evades Ostrogradsky instability [104].…”

Is Asymptotically Weyl-Invariant Gravity Viable?

“…In order to further evaluate the viability criteria set out in the introduction we must also test whether our theory contains scalar curvature singularities [18]. A local rescaling of the metric tensor by a conformal factor Ω 2 (x) is equivalent to the transformations [37,38,39]…”

“…In Ref. [18] we proposed the theory of asymptotically Weyl-invariant gravity (AWIG) within the Palatini formalism. By construction AWIG satisfies criteria (i)-(iv).…”