Lorentz Symmetry Violation in String-Inspired Effective Modified Gravity Theories

Abstract

We discuss situations under which Lorentz symmetry is violated in effective gravitational field theories that arise in the low-energy limit of strings. In particular, we discuss spontaneous violation of the symmetry by the ground state of the system. In the flat space-time limit, the effective theory of the broken Lorentz Symmetry acquires a form that belongs to the general framework of the so-called Standard Model Extension (SME) formalism. A brief review of this formalism is given before we proceed to describe a concrete example, where we discuss a Lorentz-symmetry-Violating (LV) string-inspired cosmological model. The model is a gravitational field theory coupled to matter, which contains torsion, arising from the fundamental degrees of freedom of the underlying string theory. The latter, under certain conditions which we shall specify, can acquire a LV condensate, and lead, via the appropriate equations of motion, to solutions that violate Lorentz and CPT (Charge-Parity-Time-Reversal) symmetry. The model is described by a specific form of an SME effective theory, with specific LV and CPT symmetry Violating coefficients, which depend on the microscopic parameters of the underlying string theory, and thus can be bounded by current-era phenomenology. Lorentz-and CPT Symmetries in Particle Physics and Cosmology and their potential violationIgnoring gravity, particle-physics theory and the respective phenomenology, as we understand them today, are based exclusively on Lorentz Symmetric formalisms. The Standard Model (SM) of Particle Physics, which is a mathematically consistent

Stringy running vacuum model and current tensions in cosmology

“…It would, however, be desirable to derive the various coefficients parametrising the RVM energy density also from alternative microscopic descriptions. One interesting possibility is the embedding of the RVM into microscopic string-inspired gravitational models with axions and gravitational anomalies in the early universe [42][43][44][45] (for reviews and comparison with other approaches to quantum gravity (QG) and string theory [46], specifically theories with torsion [47,48], see [49][50][51]). Both approaches, QFT in curved spacetime and string-inspired gravitational theories can be simultaneously applicable, in the sense that matter QFT corrections to the gravitational effective actions, arising from integrating out massive quantum fields, can also be implemented in string effective field theory constructions.…”

“…Such H 4 terms, which are dominant at early epochs, drives RVM inflation without the need for external inflaton fields [19,20]. In [42,44,50] we have discussed the possibility of forming a condensate of the gravitational anomaly, in case there is a macroscopic number of sources of GWs, with constructive interference. In [42,44] an O(1) proper density of defects (i.e.…”

“…over the proper cosmological volume) was assumed, which lead for consistency to large (compared to Planck scale) string mass scales M s ∼ 10 −3 M Pl . In [50], on the other hand, we have assumed proper macroscopic densities of sources of such GW in the expanding Universe, n * ≡ N (t) √ −g , which implies a total number of sources N = ´d4 x N (t) = ´d4 x √ −g n * . As discussed in that work, in such a case, the string scale M s is a free parameter, to be fixed phenomenologically, and can also serve as the Ultra-Violet (UV) cutoff of the string-inspired effective point-like field theory.…”