Angpow: a software for the fast computation of accurate tomographic power spectra

The statistical distribution of galaxies is a powerful probe to constrain cosmological models and gravity. In particular the matter power spectrum $P(k)$ brings information about the cosmological distance evolution and the galaxy clustering together. However the building of $P(k)$ from galaxy catalogues needs a cosmological model to convert angles on the sky and redshifts into distances, which leads to difficulties when comparing data with predicted $P(k)$ from other cosmological models, and for photometric surveys like LSST. The angular power spectrum $C_\ell(z_1,z_2)$ between two bins located at redshift $z_1$ and $z_2$ contains the same information than the matter power spectrum, is free from any cosmological assumption, but the prediction of $C_\ell(z_1,z_2)$ from $P(k)$ is a costly computation when performed exactly. The Angpow software aims at computing quickly and accurately the auto ($z_1=z_2$) and cross ($z_1 \neq z_2$) angular power spectra between redshift bins. We describe the developed algorithm, based on developments on the Chebyshev polynomial basis and on the Clenshaw-Curtis quadrature method. We validate the results with other codes, and benchmark the performance. Angpow is flexible and can handle any user defined power spectra, transfer functions, and redshift selection windows. The code is fast enough to be embedded inside programs exploring large cosmological parameter spaces through the $C_\ell(z_1,z_2)$ comparison with data. We emphasize that the Limber's approximation, often used to fasten the computation, gives wrong $C_\ell$ values for cross-correlations.Comment: Published in Astronomy & Astrophysic

A direct method to compute the galaxy count angular correlation function including redshift-space distortions

In the near future, cosmology will enter the wide and deep galaxy survey area allowing high-precision studies of the large scale structure of the universe in three dimensions. To test cosmological models and determine their parameters accurately, it is natural to confront data with exact theoretical expectations expressed in the observational parameter space (angles and redshift). The data-driven galaxy number count fluctuations on redshift shells, can be used to build correlation functions $C(\theta; z_1, z_2)$ on and between shells which can probe the baryonic acoustic oscillations, the distance-redshift distortions as well as gravitational lensing and other relativistic effects. Transforming the model to the data space usually requires the computation of the angular power spectrum $C_\ell(z_1, z_2)$ but this appears as an artificial and inefficient step plagued by apodization issues. In this article we show that it is not necessary and present a compact expression for $C(\theta; z_1, z_2)$ that includes directly the leading density and redshift space distortions terms from the full linear theory. It can be evaluated using a fast integration method based on Clenshaw-Curtis quadrature and Chebyshev polynomial series. This new method to compute the correlation functions without any Limber approximation, allows us to produce and discuss maps of the correlation function directly in the observable space and is a significant step towards disentangling the data from the tested models

\u3cem\u3ela finta pazza di Venexia\u3c/em\u3e: Masking, performance and identity in Seventeenth century Venice

This paper briefly explores the relationship between the theatricality of Venice and the expression of Venice in the theatre. I will do so by focusing on the wildly popular performances in 1641 of La Finta Pazza and the architecture of the Teatro Novissimo in which the opera was performed. The masking of identities, a central theme in the original story on which the opera is based, was given a particularly Venetian twist in the operatic retelling. Essential to the performance was the double entendre of the character Deidama who, feigning madness, performed both as a masked actor on the stage and as a Venetian in the audience. Giacomo Torelli’s set design further blurred distinctions between the world of the stage and the city of Venice. Concurrent to the production of La Finta Pazza was the unprecedented construction of new theatres and specifically the development of palchi, or theater boxes, in the Teatro Novissimo. Such boxes, rented out for the season and occupied by masked Patricians and foreigners, allowed conversation between the two groups that was forbidden by law. It is my wager that the nature of identity and participation shifts within a context that is simultaneously both theater and city

Architectural Lessons of Carlo Lodoli (1690-1761): Indole of Material and of Self

Carlo Lodoli (1690-1761) exists as a footnote in most major history books of modern architecture. He is typically noted for either his influence on the Venetian Neoclassical tradition or as an early prophet to some sort of functionalism. Though I would not argue his influence, I doubt his role in the development of a structurally determined functionalism. The issue of influence is always present as very little of his writings have survived and his built work amounts to a few windowsills. He did, however, teach architecture. I propose to explore the pedagogic potential of Lodoli’s lessons of architecture. Lodoli’s teaching approach was not necessarily professional in that he did not instruct his students in the methods of drawing or construction techniques. Rather, his approach was dialogical. The topics were sweeping, often ethical, and ranged from the nature of truth to the nature of materials. Existing scholarship pertaining to Lodoli most often focuses upon his students’ production of texts, projects, and projections. Andrea Memmo’s Elementi dell’Architettura Lodoliana (1786, 1833) and Francesco Algarotti’s Saggio sopra l’architettura (1756) are both specifically named by the respective authors as advancing Lodoli’s architectural theories. Often overlooked are the apologues, or fables, used by Lodoli in lessons to his students. The main source for these fables is the Apologhi Immaginati (1787). Others were included in Memmo’s Elementi. Apologues from both sources have been translated for the first time into English and can be found in Appendix I of the dissertation. I look specifically to these stories to understand and illustrate Lodoli’s approach to making, teaching and thinking. This is understood through Lodoli’s characterisation of the identity of materials and of the self. Within this dissertation I intend to flesh out the textual and architectural fabric surrounding the pedagogic activities of the Venetian Friar known as the Socrates of Architecture, Carlo Lodoli

Renormalization Group Improved Optimized Perturbation Theory: Revisiting the Mass Gap of the O(2N) Gross-Neveu Model

We introduce an extension of a variationally optimized perturbation method, by combining it with renormalization group properties in a straightforward (perturbative) form. This leads to a very transparent and efficient procedure, with a clear improvement of the non-perturbative results with respect to previous similar variational approaches. This is illustrated here by deriving optimized results for the mass gap of the O(2N) Gross-Neveu model, compared with the exactly know results for arbitrary N. At large N, the exact result is reproduced already at the very first order of the modified perturbation using this procedure. For arbitrary values of N, using the original perturbative information only known at two-loop order, we obtain a controllable percent accuracy or less, for any N value, as compared with the exactly known result for the mass gap from the thermodynamical Bethe Ansatz. The procedure is very general and can be extended straightforwardly to any renormalizable Lagrangian model, being systematically improvable provided that a knowledge of enough perturbative orders of the relevant quantities is available.Comment: 18 pages, 1 figure, v2: Eq. (4.5) corrected, comments adde

Constraining the Λ\LambdaCDM and Galileon models with recent cosmological data

The Galileon theory belongs to the class of modified gravity models that can explain the late-time accelerated expansion of the Universe. In previous works, cosmological constraints on the Galileon model were derived, both in the uncoupled case and with a disformal coupling of the Galileon field to matter. There, we showed that these models agree with the most recent cosmological data. In this work, we used updated cosmological data sets to derive new constraints on Galileon models, including the case of a constant conformal Galileon coupling to matter. We also explored the tracker solution of the uncoupled Galileon model. After updating our data sets, especially with the latest \textit{Planck} data and BAO measurements, we fitted the cosmological parameters of the $\Lambda$CDM and Galileon models. The same analysis framework as in our previous papers was used to derive cosmological constraints, using precise measurements of cosmological distances and of the cosmic structure growth rate. We showed that all tested Galileon models are as compatible with cosmological data as the $\Lambda$CDM model. This means that present cosmological data are not accurate enough to distinguish clearly between both theories. Among the different Galileon models, we found that a conformal coupling is not favoured, contrary to the disformal coupling which is preferred at the $2.3\sigma$ level over the uncoupled case. The tracker solution of the uncoupled Galileon model is also highly disfavoured due to large tensions with supernovae and \textit{Planck}+BAO data. However, outside of the tracker solution, the general uncoupled Galileon model, as well as the general disformally coupled Galileon model, remain the most promising Galileon scenarios to confront with future cosmological data. Finally, we also discuss constraints coming from Lunar Laser Ranging experiment and gravitational wave speed of propagation.Comment: 22 pages, 17 figures, published version in A&