In a six-year program started in 2014 July, the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) will conduct novel cosmological observations using the BOSS spectrograph at Apache Point Observatory. These observations will be conducted simultaneously with the Time Domain Spectroscopic Survey (TDSS) designed for variability studies and the Spectroscopic Identification of eROSITA Sources (SPIDERS) program designed for studies of X-ray sources. In particular, eBOSS will measure with percent-level precision the distance-redshift relation with baryon acoustic oscillations (BAO) in the clustering of matter. eBOSS will use four different tracers of the underlying matter density field to vastly expand the volume covered by BOSS and map the large-scale-structures over the relatively unconstrained redshift range 0.6 0.6 sample of BOSS galaxies. With ~195,000 new emission line galaxy redshifts, we expect BAO measurements of d_A(z) to an accuracy of 3.1% and H(z) to 4.7% at an effective redshift of z = 0.87. A sample of more than 500,000 spectroscopically confirmed quasars will provide the first BAO distance measurements over the redshift range 0.9 2.1; these new data will enhance the precision of dA(z) and H(z) at z > 2.1 by a factor of 1.44 relative to BOSS. Furthermore, eBOSS will provide improved tests of General Relativity on cosmological scales through redshift-space distortion measurements, improved tests for non-Gaussianity in the primordial density field, and new constraints on the summed mass of all neutrino species. Here, we provide an overview of the cosmological goals, spectroscopic target sample, demonstration of spectral quality from early data, and projected cosmological constraints from eBOSS.

The SDSS-IV extended baryon oscillation spectroscopic survey: overview and early data

We present a full $\Lambda$CDM analysis of the BOSS DR12 dataset, including information from the power spectrum multipoles, the real-space power spectrum, the reconstructed power spectrum and the bispectrum monopole. This is the first analysis to feature a complete treatment of the galaxy bispectrum, including a consistent theoretical model and without large-scale cuts. Unlike previous works, the statistics are measured using window-free estimators: this greatly reduces computational costs by removing the need to window-convolve the theory model. Our pipeline is tested using a suite of high-resolution mocks and shown to be robust and precise, with systematic errors far below the statistical thresholds. Inclusion of the bispectrum yields consistent parameter constraints and shrinks the $\sigma_8$ posterior by $13\%$ to reach $<5\%$ precision; less conservative analysis choices would reduce the error-bars further. Our constraints are broadly consistent with Planck: in particular, we find $H_0 = 69.6^{+1.1}_{-1.3}\,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$, $\sigma_8 = 0.692^{+0.035}_{-0.041}$ and $n_s=0.870^{+0.067}_{-0.064}$, including a BBN prior on the baryon density. When $n_s$ is set by Planck, we find $H_0 = 68.31^{+0.83}_{-0.86}\,\mathrm{km}\,\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$ and $\sigma_8 = 0.722^{+0.032}_{-0.036}$. Our $S_8$ posterior, $0.751\pm0.039$, is consistent with weak lensing studies, but lower than Planck. Constraints on the higher-order bias parameters are significantly strengthened from the inclusion of the bispectrum, and we find no evidence for deviation from the dark matter halo bias relations. These results represent the most complete full-shape analysis of BOSS DR12 to-date, and the corresponding spectra will enable a variety of beyond-$\Lambda$CDM analyses, probing phenomena such as the neutrino mass and primordial non-Gaussianity. 

BOSS DR12 full-shape cosmology: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi><mml:mi>CDM</mml:mi></mml:mrow></mml:math> constraints from the large-scale galaxy power spectrum and bispectrum monopole

Massive spinning particles, if present during inflation, lead to a distinctive bispectrum of primordial perturbations, the shape and amplitude of which depend on the masses and spins of the extra particles. This signal, in turn, leaves an imprint in the statistical distribution of galaxies; in particular, as a non-vanishing galaxy bispectrum, which can be used to probe the masses and spins of these particles. In this paper, we present for the first time a new theoretical template for the bispectrum generated by massive spinning particles, valid for a general triangle configuration. We then proceed to perform a Fisher-matrix forecast to assess the potential of two next-generation spectroscopic galaxy surveys, EUCLID and DESI, to constrain the primordial non-Gaussianity sourced by these extra particles. We model the galaxy bispectrum using tree-level perturbation theory, accounting for redshift-space distortions and the Alcock-Paczynski effect, and forecast constraints on the primordial non-Gaussianity parameters marginalizing over all relevant biases and cosmological parameters. Our results suggest that these surveys would potentially be sensitive to any primordial non-Gaussianity with an amplitude larger than $f_{\rm NL}\approx 1$, for massive particles with spins 2, 3, and 4. Interestingly, if non-Gaussianities are present at that level, these surveys will be able to infer the masses of these spinning particles to within tens of percent. If detected, this would provide a very clear window into the particle content of our Universe during inflation.

Galaxy Bispectrum from Massive Spinning Particles

Galaxy bispectrum from massive spinning particles

We explore two methods of compressing the redshift-space galaxy power spectrum and bispectrum
with respect to a chosen set of cosmological parameters. Both methods involve reducing
the dimension of the original data vector (e.g. 1000 elements) to the number of cosmological
parameters considered (e.g. seven ) using the Karhunen–Lo`eve algorithm. In the first case,
we run MCMC sampling on the compressed data vector in order to recover the 1D and 2D
posterior distributions. The second option, approximately 2000 times faster, works by orthogonalizing
the parameter space through diagonalization of the Fisher information matrix before
the compression, obtaining the posterior distributions without the need of MCMC sampling.
Using these methods for future spectroscopic redshift surveys like DESI, Euclid, and PFS
would drastically reduce the number of simulations needed to compute accurate covariance
matrices with minimal loss of constraining power. We consider a redshift bin of a DESI-like
experiment. Using the power spectrum combined with the bispectrum as a data vector, both
compression methods on average recover the 68 per cent credible regions to within 0.7 per cent
and 2 per cent of those resulting from standard MCMC sampling, respectively. These confidence
intervals are also smaller than the ones obtained using only the power spectrum by
81 per cent, 80 per cent, and 82 per cent respectively, for the bias parameter b1, the growth rate
f, and the scalar amplitude parameter As.

pdf/maximal-compression-of-the-redshift-space-galaxy-power-4wd326cpdt.pdf

Maximal compression of the redshift-space galaxy power spectrum and bispectrum

Polyhedral geometry and combinatorics of an autocatalytic ecosystem

Prior research on evolutionary mechanisms during the origin of life has mainly assumed the existence of populations of discrete entities with information encoded in genetic polymers. Recent theoretical advances in autocatalytic chemical ecology establish a broader evolutionary framework that allows for adaptive complexification prior to the emergence of bounded individuals or genetic encoding. This framework establishes the formal equivalence of cells, ecosystems and certain localized chemical reaction systems as autocatalytic chemical ecosystems (ACEs): food-driven (open) systems that can grow due to the action of autocatalytic cycles (ACs). When ACEs are organized in meta-ecosystems, whether they be populations of cells or sets of chemically similar environmental patches, evolution, defined as change in AC frequency over time, can occur. In cases where ACs are enriched because they enhance ACE persistence or dispersal ability, evolution is adaptive and can build complexity. In particular, adaptive evolution can explain the emergence of self-bounded units (e.g. protocells) and genetic inheritance mechanisms. Recognizing the continuity between ecological and evolutionary change through the lens of autocatalytic chemical ecology suggests that the origin of life should be seen as a general and predictable outcome of driven chemical ecosystems rather than a phenomenon requiring specific, rare conditions. 

The ecology–evolution continuum and the origin of life

We first derive the Hamilton-Jacobi theory underlying continuous-time Markov processes, and then we use the construction to develop a variational algorithm for estimating escape (least improbable or first passage) paths for a generic stochastic chemical reaction network that exhibits multiple fixed points. The design of our algorithm is such that it is independent of the underlying dimensionality of the system, the discretization control parameters are updated toward the continuum limit, and there is an easy-to-calculate measure for the correctness of its solution. We consider several applications of the algorithm and verify them against computationally expensive means such as the shooting method and stochastic simulation. While we employ theoretical techniques from mathematical physics, numerical optimization and chemical reaction network theory, we hope that our work finds practical applications with an inter-disciplinary audience including chemists, biologists, optimal control theorists and game theorists.

Action functional gradient descent algorithm for estimating escape paths in stochastic chemical reaction networks.

Thermodynamic ranking of pathways in reaction networks

https://export.arxiv.org/pdf/2510.05383v2.pdf

Mathematical Analysis for a Class of Stochastic Copolymerization Processes

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