Galileons as the Scalar Analogue of General Relativity

We establish a correspondence between general relativity with diffeomorphism invariance and scalar field theories with Galilean invariance: notions such as the Levi-Civita connection and the Riemann tensor have a Galilean counterpart. This suggests Galilean theories as the unique nontrivial alternative to gauge theories (including general relativity). Moreover, it is shown that the requirement of first-order Palatini formalism uniquely determines the Galileon models with second-order field equations, similar to the Lovelock gravity theories. Possible extensions are discussed.Comment: 6 pages, v2: Version appeared in Phys. Rev.

Higher Derivative Field Theories: Degeneracy Conditions and Classes

We provide a full analysis of ghost free higher derivative field theories with coupled degrees of freedom. Assuming the absence of gauge symmetries, we derive the degeneracy conditions in order to evade the Ostrogradsky ghosts, and analyze which (non)trivial classes of solutions this allows for. It is shown explicitly how Lorentz invariance avoids the propagation of "half" degrees of freedom. Moreover, for a large class of theories, we construct the field redefinitions and/or (extended) contact transformations that put the theory in a manifestly first order form. Finally, we identify which class of theories cannot be brought to first order form by such transformations.Comment: 26 pages, 1 figure. v2: minor changes, references added, matches version published in JHE

Exorcising the Ostrogradsky ghost in coupled systems

The Ostrogradsky theorem implies that higher-derivative terms of a single mechanical variable are either trivial or lead to additional, ghost-like degrees of freedom. In this letter we systematically investigate how the introduction of additional variables can remedy this situation. Employing a Lagrangian analysis, we identify conditions on the Lagrangian to ensure the existence of primary and secondary constraints that together imply the absence of Ostrogradsky ghosts. We also show the implications of these conditions for the structure of the equations of motion as well as possible redefinitions of the variables. We discuss applications to analogous higher-derivative field theories such as multi-Galileons and beyond Horndeski.Comment: 8 pages. v3: minor changes, matches version published in JHE

Spontaneously broken spacetime symmetries and the role of inessential Goldstones

In contrast to internal symmetries, there is no general proof that the coset construction for spontaneously broken spacetime symmetries leads to universal dynamics. One key difference lies in the role of Goldstone bosons, which for spacetime symmetries includes a subset which are inessential for the non- linear realisation and hence can be eliminated. In this paper we address two important issues that arise when eliminating inessential Goldstones.The first concerns the elimination itself, which is often performed by imposing socalledinverse Higgs constraints. Contrary to claims in the literature, there are a series of conditions on the structure constants which must be satisfied to employ the inverse Higgs phenomenon, and we discuss which parametrisation of the coset element is the most effective in this regard. We also consider generalisations of the standard inverse Higgs constraints, which can include integrating out inessential Goldstones at low energies, and prove that under certain assumptions these give rise to identical effective field theories for the essential Goldstones.Secondly, we consider mappings between non- linear realisations that differ both in the coset element and the algebra basis. While these can always be related to each other by a point transformation, remarkably, the inverse Higgs constraints are not necessarily mapped onto each other under this transformation. We discuss the physical implications of this non- mapping, with a particular emphasis on the coset space corresponding to the spontaneous breaking of the Anti-De Sitter isometries by a Minkowski probe brane.</p

Formal aspects of cosmological models: higher derivatives and non-linear realisations

The field of cosmology deals with the properties and evolution of the universe as a whole, and tries to answer questions such as 'What did the universe look like in the past?', 'How did it evolve into its current state?' and 'What will it look like in the future?'. In this thesis we investigated several formal aspects of cosmological models that are intended to describe the accelerated expansion of the very early universe (also called inflation) and that of the current universe. Firstly we have examined under which conditions one can avoid particular unwanted instabilities that often appear in models with so-called higher derivatives. Our findings led us to introduce a classification of models that are free of such instabilities. We have also investigated particular mathematical properties of so-called non-linear realisations of space-time symmetries. Such non-linear realisations occur naturally whenever space-time symmetries of a model get spontaneously broken. Lastly, based on particular broken space-time symmetries, we have introduced new inflationary models that can be tested in the near future with the newest generation of satellite experiments

No-go theorem for a gauge vector as a spacetime Goldstone mode

Scalars and fermions can arise as Goldstone modes of nonlinearly realized extensions of the Poincare group (with important implications for the soft limits of such theories): the Dirac-Born-Infeld scalar realizes a higher-dimensional Poincare symmetry, while the Volkov-Akulov fermion corresponds to super-Poincare. In this paper we classify extensions of the Poincare group which give rise to a vector Goldstone mode instead. Our main result is that there are no healthy (ghost free) interacting U(1) gauge theories that nonlinearly realize space-time symmetries beyond gauge transformations. This implies that the structure of e.g., Born-Infeld theory is not fixed by symmetry

In-depth transcriptomic analysis of human retina reveals molecular mechanisms underlying diabetic retinopathy

Diabetic Retinopathy (DR) is among the major global causes for vision loss. With the rise in diabetes prevalence, an increase in DR incidence is expected. Current understanding of both the molecular etiology and pathways involved in the initiation and progression of DR is limited. Via RNA-Sequencing, we analyzed mRNA and miRNA expression profiles of 80 human post-mortem retinal samples from 43 patients diagnosed with various stages of DR. We found differentially expressed transcripts to be predominantly associated with late stage DR and pathways such as hippo and gap junction signaling. A multivariate regression model identified transcripts with progressive changes throughout disease stages, which in turn displayed significant overlap with sphingolipid and cGMP-PKG signaling. Combined analysis of miRNA and mRNA expression further uncovered disease-relevant miRNA/mRNA associations as potential mechanisms of post-transcriptional regulation. Finally, integrating human retinal single cell RNA-Sequencing data revealed a continuous loss of retinal ganglion cells, and Müller cell mediated changes in histidine and β-alanine signaling. While previously considered primarily a vascular disease, attention in DR has shifted to additional mechanisms and cell-types. Our findings offer an unprecedented and unbiased insight into molecular pathways and cell-specific changes in the development of DR, and provide potential avenues for future therapeutic intervention

Multiparameter Investigation of a 46,XX/46,XY Tetragametic Chimeric Phenotypical Male Patient with Bilateral Scrotal Ovotestes and Ovulatory Activity

We report on an adult male initially presenting with gynecomastia and a painless scrotal mass without additional genital anomalies. Hyperpigmentation of the skin following the Blaschko's lines was identified. He underwent gonadectomy because of suspected cancer. Histological analyses revealed an ovotestis with ovulatory activity confirmed by immunohistochemistry with multiple markers. Karyotyping of cultured peripheral blood lymphocytes and a buccal smear revealed a 46,XX/46,XY chimeric constitution with different percentages. Multiple molecular analyses as well as blood typing implied a tetragametic origin. After the unilateral gonadectomy, the patient developed recurrent painful cystic swellings of the remaining gonad. Because of the wish to preserve hormonal activity as well as future fertility, the patient underwent surgical resection of a cystic gonadal area. The removed tissue showed ovulation-related features in addition to both testicular and ovarian tissue, diagnosed as an ovotestis. Testosterone therapy was initiated to suppress the persistently elevated gonadotropins and thereby suppress ovarian activity. During treatment, the recurrent pain complaints and cystic swellings ceased, although gonadotropin levels were not fully suppressed. Based on these observations, the importance of a detailed genetic and pathological diagnosis and the clinical dilemmas including the pros and cons of personalized treatment with gonadal preservative surgery are discussed