The Standard-Model Extension (SME) is the general phenomenological framework used to investigate Lorentz violation at the level of effective field theory. It has been used to obtain stringent experimental bounds on Lorentz violation in a wide range of tests. In the gravity sector of the SME, it is typically assumed that the spacetime symmetry breaking occurs spontaneously in order to avoid potential conflicts with the Bianchi identities. A post-Newtonian limit as well as mattergravity couplings in the SME have been developed and investigated based on this assumption. In this paper, the possibility of using the SME to also describe gravity theories with explicit spacetime symmetry breaking is investigated. It is found that in a wide range of cases, particularly when matter-gravity couplings are included, consistency with the Bianchi identities can be maintained, and therefore the SME can be used to search for signals of the symmetry breaking. Two examples with explicit breaking are considered. The first is ghost-free massive gravity with an effective metric that couples to matter. The second is Hořava gravity coupled with matter in an infrared limit. I. INTRODUCTIONGeneral relativity (GR) and the Standard Model (SM) of particle physics are well-tested theories that describe the fundamental forces of nature. However, GR is not a quantum theory, since it is not renormalizable, and it must be treated as an effective field theory at low energies. This as well as open questions about the nature of dark matter and dark energy have led to investigations of alternative gravity theories that modify GR, where the ultimate goal is to find a consistent quantum theory of gravity. In many scenarios, small violations of local Lorentz and diffeomorphism invariance can occur, which would provide important signatures of new physics [1].The phenomenological framework known as the Standard-Model Extension (SME) has been developed and used to search for signals of spacetime symmetry breaking in a wide range of experimental tests [2][3][4][5]. The Lorentz-and diffeomorphism-breaking operators that appear in the SME involve couplings with fixed background fields, usually referred to as SME coefficients. The results of experimental tests can be interpreted as bounds on the SME coefficients. Many different types of operators and SME coefficients have been classified and probed. These include both power-counting renormalizable and nonrenormalizable operators [6]. Gravity sectors in the SME can be defined using metric or vierbein descriptions in Riemann spacetime or more generally in Riemann-Cartan spacetime [3]. Relationships between Lorentz violation and torsion [7], nonmetricity [8], and Riemann-Finsler geometry [9] have been explored using the SME.In investigations involving gravity, a post-Newtonian limit of the SME has been developed [10] and mattergravity interactions have been incorporated [11]. These are used to examine a variety of experiments, including lunar laser ranging tests [12], atom interferometry [13], short-range gravita...

The strained heterocyclic alkyne, 3-oxacyclohexyne, was generated photochemically for the first time using a cyclopropanated phenanthrene precursor, and trapped by cyclopentadienones as Diels-Alder adducts. The precursor initially produced the putative 3-oxacyclopentylidenecarbene that subsequently rearranged to the cycloalkyne. Computational studies indicate that the carbene favors a singlet state, and the barrier for its ring expansion by a 1,2-shift of the carbon proximal to oxygen is lower in energy than the corresponding shift of the distal carbon.

Standard cosmological data analyses typically constrain simple phenomenological dark-energy parameters, for example the present-day value of the equation of state parameter, w 0, and its variation with scale factor, w a. However, results from such an analysis cannot easily indicate the presence of modified gravity. Even if general relativity does not hold, experimental data could still be fit sufficiently well by a phenomenological w 0 w aCDM, unmodified-gravity model. Hence, it would be very useful to know if there are generic signatures of modified gravity in standard analyses. Here we present, for the first time to our knowledge, a quantitative mapping showing how modified gravity models look when (mis)interpreted within the standard unmodified-gravity analysis. Scanning through a broad space of modified-gravity (Horndeski) models, and assuming a near-future survey consisting of CMB, BAO, and SNIa observations, we report values of the best-fit set of cosmological parameters including (w 0, w a) that would be inferred if modified gravity were at work. We find that modified gravity models that can masquerade as standard gravity lead to very specific biases in standard-parameter spaces. We also comment on implications for measurements of the amplitude of mass fluctuations described by the parameter S 8.