arXiv subjects

Zvonimir Vlah

Publications and source records attributed to Zvonimir Vlah.

At least 19 recordsLinked to original sources

arXiv2026

One-Loop Galaxy Bispectrum: Consistent Theory, Efficient Analysis with COBRA, and Implications for Cosmological Parameters

We present an efficient and accurate pipeline for the analysis of the redshift-space galaxy bispectrum multipoles at one-loop order in effective field theory (EFT). We provide a systematic theory derivation based on power counting, which features the first comprehensive treatment of stochastic EFT contributions -- these are found to significantly improve the match to data. Our computational pipeline utilizes the COBRA technique that expands the linear matter power spectrum over a basis of principal components based on a singular value decomposition, allowing the cosmology dependence to be captured to sub-permille accuracy with just eight templates. This transforms the problem of computing the one-loop EFT bispectrum to a simple tensor multiplication, reducing the computation time to around a second per cosmology with negligible loss of accuracy. Using these tools, we study the cosmological information in the bispectrum by analyzing PTChallenge simulations, whose gigantic volume provides the most powerful test of the one-loop EFT bispectrum so far. We find that the one-loop prediction provides an excellent match to the bispectrum data up to $k_{\rm max}=0.15\,h\mathrm{Mpc}^{-1}$, as evidenced by the precise recovery of the dark matter density $ω_\text{cdm}$, Hubble constant $H_0$, and mass fluctuation amplitude $σ_8$ parameters, and the amplitude of equilateral primordial non-Gaussianity (PNG) $f_{\rm NL}^{\rm equil}$. Combined with the power spectrum, the COBRA-based one-loop bispectrum monopole and quadrupole yield tighter constraints than the tree-level bispectrum monopole, with the posteriors on $ω_{\text{cdm}}$, $H_0$, and $σ_8$ shrinking by 44\%, 32\%, and 25\%, respectively. This suggests that the COBRA-based bispectrum analysis will be an important tool in the interpretation of data from ongoing redshift surveys such as DESI and Euclid.

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arXiv2026

Intrinsic Alignments in Redshift Space I: Symmetries

Galaxy shapes are unique tensor tracers of large-scale structure, providing a promising avenue to both enhance current cosmological programs and detect new physics beyond the scalar sector. We develop a general formalism to describe the full 3D structure of galaxy shapes and their statistics, including the breaking of isotropy by the line of sight and redshift space distortions. We constructively show that the redshift-space mapping generates a kinematic basis whose form factors are strictly polynomial in the line-of-sight angle $μ= \hat{k} \cdot \hat{n}$, and that parity selection rules restrict scalar-tensor and tensor-tensor correlators to 3 and 13 independent form factors, respectively, with the latter further reduced to 9 by exchange symmetry. We show that this polynomiality is preserved transforming into a total helicity basis denoted by total angular momentum $M$---sourced to be nonzero by powers of the line-of-sight $\hat{n}$---and that this is equivalent to the form factors having spin weights $(1 - μ^2)^{|M|/2}$ and described by associated Legendre polynomials $P^{|M|}_\ell$. We construct estimators for form factors in the normalized total-helicity basis that provide the optimal angular weighting to extract shape information, and connect the full tensor basis to projected shape statistics. To validate our formalism, we study the above tensor form factors within a toy model, showing that all allowed channels are generated even within simplified assumptions, and apply our estimators to halo shape statistics in N-body simulations wherein all channels up to total angular momentum $|M| \leq 2$ are detected. We anticipate that the methods developed here will have applications ranging from optimal extraction of intrinsic-alignments in hydrodynamical simulations to identifying new physics in tensor channels forbidden by selection rules in the standard model of cosmology.

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arXiv2026

Two-loop renormalization and running of galaxy bias

We systematically extend the framework of galaxy bias renormalization to two-loop order. For the minimal complete basis of 29 deterministic bias operators up to fifth order in the density field and at leading order in gradient expansion we explicitly work out one- and two-loop renormalization. The latter is provided in terms of double-hard limits of bias kernels, which we find to depend on only one function of the ratio of the loop momenta. After including stochasticity in terms of composite operator renormalization, we apply the framework to the two-loop power spectrum of biased tracers and provide a simple result suitable for numerical evaluation. In addition, we work out one- and two-loop renormalization group equations (RGE) for deterministic bias coefficients related to bias operators constructed from a smoothed density field, generalizing previous works. We identify a linear combination of bias operators with enhanced UV sensitivity, related to a positive eigenvalue of the RGE. Finally, we present an analogy with the RGE as used in quantum field theory, suggesting that a resummation of large logarithms as employed in the latter may also yield useful applications in the study of large-scale galaxy bias.

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arXiv2026

Galaxy bias renormalization: Two-loop Power Spectrum, One-loop Trispectrum and Bispectrum

We present a complete treatment of fifth-order renormalized galaxy bias at the one- and two-loop level in real space, including gradient corrections to deterministic bias operators at next-to-leading order. We then provide a complete computation of the two-loop power spectrum as well as the one-loop bispectrum and trispectrum of biased tracers, and demonstrate how to jointly model these statistics in a fully renormalized framework. These statistics also require stochastic renormalization of products of two, three or four operators at coincidence, which we include at leading order in gradients by means of an operator product expansion. We verify that all UV limits of loop integrals are absorbed by the counterterms we consider. Upon solving the resulting renormalization group equations, we find a pronounced scale-dependence of higher-gradient bias coefficients. Since our renormalization prescription is performed manifestly at the operator level, our results can also easily be extended to higher $N$-point functions, higher loop orders and field-level analyses.

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arXiv2026

Efficient computation of the galaxy angular bispectrum in redshift space

Efficient computation of the angular bispectrum is an essential part of modelling large-scale structure observations, but it still remains an extremely challenging task. In this work, we compute the tree-level, unequal-time angular bispectrum in both real and redshift space. By deriving full-sky results, we show that the bispectrum can be expressed as a sum of products of two angular power spectra, enabling the use of our recently developed flat-sky approximation to enhance computational efficiency significantly. This flat-sky formalism preserves key line-of-sight mode information while discarding extraneous full-sky contributions. We validate our approach by comparing it with direct full-sky integration, finding excellent agreement across a wide range of scales and redshifts for all bispectrum configurations. At redshift $z = 1$, we achieve sub-percent agreement (for multipoles $\ell \gtrsim 5$) between full-sky and flat-sky results for equilateral, squeezed, and folded configurations, using narrow Gaussian radial window functions ($σ_z = 0.01$) in both equal-time and unequal-time scenarios. On small scales, where direct full-sky integration becomes computationally prohibitive, our results align with the Limber approximation (where applicable), confirming the robustness and accuracy of our implementation. To facilitate future studies, we provide a \texttt{Python} implementation of our results, which is publicly available on \texttt{GitHub}.

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arXiv2026

Testing parity with composite-field spectra of BOSS and DESI luminous red galaxies

Detection of parity violation on cosmological scales would have profound implications for fundamental physics. Motivated in part by recent measurements of parity-odd four-point correlation functions in BOSS and DESI luminous red galaxy samples, which probe parity violation in the scalar sector, we present the first measurement of parity-odd kurto spectra in spectroscopic galaxy survey data. We analyse two composite-field spectra, $\mathcal{P}_{2\times2}$ (vector--pseudo-vector) and $\mathcal{P}_{3\times1}$ (scalar--pseudo-scalar). Compared with parity-odd four-point correlation function analyses, the kurto-spectrum formalism performs physically motivated compression on the trispectrum into a substantially lower-dimensional data vector, allowing direct estimation of covariance matrices from mock catalogues and reducing sensitivity to covariance-modelling systematics. Using null-hypothesis $χ^2$ tests and cross-patch consistency checks, we find no evidence for a cosmological parity-violating signal in either survey. We examine the impact of the adopted mock catalogues and find that the high-fidelity mocks provide a better match to the data of both surveys than the approximate mocks. The DESI DR1 measurements exhibit a scatter smaller than that of BOSS DR12 by about a factor of four, consistent with the improved statistical precision expected from the higher tracer number density. Future DESI data releases, with larger volume and number density, together with larger suites of high-fidelity mocks, can enable significantly sharper tests of parity violation using kurto spectra.

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arXiv2026

Parity in Composite-Field Galaxy Correlators

Detecting parity violation on cosmological scales would provide a striking clue to new physics. Large-scale structure offers the raw statistical power -- many three-dimensional modes -- to make such tests. However, for scalar observables, like galaxy clustering, the leading parity-sensitive observable is the trispectrum, whose high dimensionality makes the measurement and noise estimation challenging. We present two late-time parity-odd kurto spectra that compress the parity-odd scalar trispectrum into one-dimensional, power-spectrum-like observables. They are built by correlating (i) two appropriately weighted quadratic composite fields, or (ii) a linear and cubic composite field, constructed from dark matter (DM) or galaxy overdensity fields. We develop an FFTLog pipeline for efficient theoretical predictions of the two observables. We then validate the estimators for a specific parity-odd primordial template on perturbative DM field, and on DM and halo fields in full N-body \texttt{Quijote} simulations, with and without parity-odd initial conditions, in real and redshift space. For DM, the variance is dominated by the parity-even contribution -- i.e., the gravitationally induced parity-even trispectrum -- and is efficiently suppressed by phase-matched fiducial subtraction. For halos, discreteness-driven stochasticity dominates and is not appreciably reduced by subtraction; however, optimal weighting and halo-matter cross kurto spectra considerably mitigate this noise and enhance the signal. Using controlled down-sampling of the matter field, we empirically calibrate how the parity-even variance scales with number density and volume, and provide an illustrative forecast for the detectability of parity-odd kurto spectra in a Euclid-like spectroscopic galaxy survey.

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arXiv2026

Rapid cosmological inference with the two-loop matter power spectrum

We compute the two-loop effective field theory (EFT) power spectrum of dark matter density fluctuations in $Λ$CDM using the recently proposed COBRA method (Bakx. et al, 2025). With COBRA, we are able to evaluate the two-loop matter power spectrum in $\sim 1$ millisecond at $ \sim 0.1 \%$ precision on one CPU for arbitrary redshifts and on scales where perturbation theory applies. As an application, we use the nonlinear matter power spectrum from the Dark Sky simulation to assess the performance of the two-loop EFT power spectrum compared to the one-loop EFT power spectrum at $z=0$. We find that, for volumes typical for Stage IV galaxy surveys, $V = 25 \,(\text{Gpc}/h)^3$, the two-loop EFT can provide unbiased cosmological constraints on $Ω_m,H_0$ and $A_s$ using scales up to $k_\text{max}=0.26\, h/\text{Mpc}$, thereby outperforming the constraints from the one-loop EFT ($k_\text{max}=0.11\, h/\text{Mpc}$). The Figure of Merit on these three parameters increases by a factor $\sim 2.6$ and the one-dimensional marginalized constraints improve by $\sim35\%$ for $Ω_m$, $\sim20\%$ for $H_0$ and $\sim 15\%$ for $A_s$.

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arXiv2025

The Bispectrum of Intrinsic Alignments: II. Precision Comparison Against Dark Matter Simulations

We measure three-dimensional bispectra of halo intrinsic alignments (IA) and dark matter overdensities in real space from N-body simulations for halos of mass $10^{12}-10^{12.5} M_\odot /h$. We show that their multipoles with respect to the line of sight can be accurately described by a tree-level perturbation theory model on large scales ($k\lesssim 0.11\,h$/Mpc) at $z=0$. For these scales and in a simulation volume of 1 (Gpc/$h)^3$, we detect the bispectrum monopole $B_{δδE}^{00}$ at SNR $\sim 30$ and the two quadrupoles $B_{δδE}^{11}$ and $B_{δδE}^{20}$ at SNR $\sim 25$ and SNR $\sim 15$, respectively. We also report similar SNR for the lowest order multipoles of $B_{δEE}$ and $B_{EEE}$, although these are largely driven by stochastic contributions. We show that the first and second order EFT parameters are consistent with those obtained from fitting the IA power spectrum analysis at next-to-leading order, without requiring any priors to break degeneracies for the quadratic bias parameters. Moreover, the inclusion of higher multipole moments of $B_{δδE}$ greatly reduces the errors on second order bias parameters, by factors of 5 or more. The IA bispectrum thus provides an effective means of determining higher order shape bias parameters, thereby characterizing the scale dependence of the IA signal. We also detect parity-odd bispectra such as $B_{δδB}$ and $B_{δEB}$ at $\sim 10 σ$ significance or more for $k<0.15\,h$/Mpc and they are consistent with the parity-even sector. Furthermore, we check that the Gaussian covariance approximation works reasonably well on the scales we consider here. These results lay the groundwork for using the bispectrum of IA in cosmological analyses.

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arXiv2025

The Bispectrum of Intrinsic Alignments: Theory Modelling and Forecasts for Stage IV Galaxy Surveys

We present a complete treatment of the bispectrum of intrinsic alignments, both in three spatial dimensions and in projection in the flat-sky approximation. Since intrinsic alignment is a spin-2 observable, the bispectrum of intrinsic alignments contains a parity-even and a parity-odd part, the latter being nonzero even in the absence of parity violation. Moreover, all possible combinations of scalar, E- and B-mode bispectra are nonzero in the absence of parity violation. In analogy to the galaxy bispectrum in redshift space, we construct a complete set of multipoles for anisotropic bispectra of projected spin-2 fields. We then construct separable bispectrum estimators, both for parity-even and parity-odd bispectra, which can be computed by means of Fast Fourier Transforms (FFTs). We compare several different choices of angular weighting in terms of signal-to-noise ratios (SNR) for a Stage IV setup using luminous red galaxies (LRGs) from the Dark Energy Spectroscopic Instrument (DESI) with galaxy shapes measured by the Legacy Survey of Space and Time (LSST). Assuming an overlapping area of $\sim 4,000$ square degrees (yielding $\sim 1.3$ million LRGs) and including scales up to $k_\text{max} = 0.14\,h$/Mpc, we find that the position-position-E-mode bispectrum $B_{DDE}$ (which is parity-even) can be strongly detected at SNR $\sim 30$, while detecting parity-odd bispectra (such as $B_{DDB}$, SNR $\sim 5$) or bispectra with more than one shape field (such as $B_{DEE}$, SNR $\sim 5$) may also be possible.

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arXiv2025

Flat-sky Angular Power Spectra Revisited

We revisit the flat-sky approximation for evaluating the angular power spectra of projected random fields by retaining information about the correlations along the line of sight. With broad, overlapping radial window functions, these line-of-sight correlations are suppressed and are ignored in the Limber approximation. However, retaining the correlations is important for narrow window functions or unequal-time spectra but introduces significant computational difficulties due to the highly oscillatory nature of the integrands involved. We deal with the integral over line-of-sight wave-modes in the flat-sky approximation analytically, using the FFTlog expansion of the 3D power spectrum. This results in an efficient computational method, which is a substantial improvement compared to any full-sky approaches. We apply our results to galaxy clustering (with and without redshift-space distortions), CMB lensing and galaxy lensing observables. For clustering, we find excellent agreement with the full-sky results on large (percent-level agreement) and intermediate or small (subpercent agreement) scales, dramatically out-performing the Limber approximation for both wide and narrow window functions, and in equal- and unequal-time cases. In the case of lensing, we show on the full sky that the angular power spectrum of the convergence can be very well approximated by projecting the 3D Laplacian (rather than the correct angular Laplacian) of the gravitational potential, even on large scales. Combining this approximation with our flat-sky techniques provides an efficient and accurate evaluation of the CMB lensing angular power spectrum on all scales.

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arXiv2025

COBRA: Optimal Factorization of Cosmological Observables

We introduce COBRA (Cosmology with Optimally factorized Bases of Radial Approximants), a novel framework for rapid computation of large-scale structure observables. COBRA separates scale dependence from cosmological parameters in the linear matter power spectrum while also minimising the number of necessary basis terms $N_b$, thus enabling direct and efficient computation of derived and nonlinear observables. Moreover, the dependence on cosmological parameters is efficiently approximated using radial basis function interpolation. We apply our framework to decompose the linear matter power spectrum in the standard $Λ$CDM scenario, as well as by adding curvature, dynamical dark energy and massive neutrinos, covering all redshifts relevant for Stage IV surveys. With only a dozen basis terms $N_b$, COBRA reproduces exact Boltzmann solver calculations to $\sim 0.1\%$ precision, which improves further to $0.02\%$ in the pure $Λ$CDM scenario. Using our decomposition, we recast the one-loop redshift space galaxy power spectrum in a separable minimal-basis form, enabling $\sim 4000$ model evaluations per second at $0.02\%$ precision on a single thread. This constitutes a considerable improvement over previously existing methods (e.g., FFTLog) opening a window for efficient computations of higher loop and higher order correlators involving multiple powers of the linear matter power spectra. The resulting factorisation can also be utilised in clustering, weak lensing and CMB analyses. Our implementation will be made public upon publication.

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arXiv2025

Observed unequal-time power spectrum

The next generation of galaxy surveys will provide highly precise measurements of galaxy clustering, therefore requiring a corresponding accuracy. Current approaches, which rely on approximations and idealized assumptions, may fall short in capturing the level of detail required for high-precision observations. In order to increase the modeling accuracy, recently, unequal-time contributions to the galaxy power spectrum have been introduced in order to include the effects of radial correlations. We present a generalization of the formalism for the observed unequal-time power spectrum, that includes Doppler and local general relativistic corrections, plus local primordial non-Gaussianity. We find that unequal time corrections can potentially mimic an effective $f_{\mathrm{NL}}$ of order unity. We provide a first assessment of the significance of unequal-time corrections for future galaxy clustering experiments, estimating a Signal-to-Noise-Ratio of $\sim3$ for Stage IV-like surveys.

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arXiv2025

Projecting Unequal Time Fields and Correlators of Large Scale Structure

Many large scale structure surveys sort their observations into redshift bins and treat every tracer as being located at the mean redshift of its bin, a treatment which we refer to as the equal time approximation. Recently, a new method was developed which allows for the estimation and correction of errors introduced by this approximation, which we refer to as the unequal time correlator-level projection. For single tracer power spectra, corrections arise at second order and above in a series expansion, with first order terms surviving only in multi-tracer analyses. In this paper we develop a new method which we refer to as the unequal time field level projection. This formalism projects the fields individually onto the celestial sphere, displaced from individual reference times, before defining their correlators. This method introduces new, first order correction terms even in the case of single tracer power spectra. Specifically, new first order terms are introduced which apply to both cross-bin and single bin correlators. All of these new corrections originate with derivatives over combinations of a delta function, a cross-bin phase term, and the power spectrum itself and stem from the introduction of two unequal time Fourier transforms into the analysis. We analyse these corrections in the context of a linearly biased power spectrum divided between two redshift bins and find that they can lead to non-trivial corrections, particularly to cross-bin correlators. We also show that these terms can be replicated by appropriately extending the correlator-level analysis to include a second Fourier transform which allows for a full redshift bin integration.

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arXiv2024

The Bispectrum in Lagrangian Perturbation Theory

We study the bispectrum in Lagrangian perturbation theory. Extending past results for the power spectrum, we describe a method to efficiently compute the bispectrum in LPT, focusing on the Zeldovich approximation, in which contributions due to linear displacements are captured to all orders in a manifestly infrared (IR) safe way. We then isolate the effects of these linear displacements on oscillatory components of the power spectrum like baryon acoustic oscillations or inflationary primordial features and show that the Eulerian perturbation theory (EPT) prescription wherein their effects are resummed by a Gaussian damping of the oscillations arise as a saddle-point approximation of our calculation. These two methods of IR resummation are in excellent agreement at 1-loop in the bispectrum. At tree level, resummed EPT does less well to capture the nonlinear damping of the oscillations, and the LPT calculation does not require an artificial split of the power spectrum into smooth and oscillatory components, making the latter particularly useful for modeling exotic features. We finish by extending our analysis of IR resummation in LPT to N-point functions of arbitrary order.

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arXiv2023

On the asymptotic connection between full- and flat-sky angular correlators

We investigate the connection between the full- and flat-sky angular power spectra. First, we revisit this connection established on the geometric and physical grounds, namely that the angular correlations on the sphere and in the plane (flat-sky approximation) correspond to each other in the limiting case of small angles and a distant observer. To establish the formal conditions for this limit, we first resort to a simplified shape of the 3D power spectrum, which allows us to obtain analytic results for both the full- and flat-sky angular power spectra. Using a saddle-point approximation, we find that the flat-sky results are obtained in the limit when the comoving distance and wave modes $\ell$ approach infinity at the same rate. This allows us to obtain an analogous asymptotic expansion of the full-sky angular power spectrum for general 3D power spectrum shapes, including the LCDM Universe. In this way, we find a robust limit of correspondence between the full- and flat-sky results. These results also establish a mathematical relation, i.e., an asymptotic expansion of the ordinary hypergeometric function of a particular choice of arguments that physically corresponds to the flat-sky approximation of a distant observer. This asymptotic form of the ordinary hypergeometric function is obtained in two ways: relying on our saddle-point approximation and using some of the known properties of the hypergeometric function.

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arXiv2023

The observed power spectrum & frequency-angular power spectrum

The two-point summary statistics is one of the most commonly used tools in the study of cosmological structure. Starting from the theoretical power spectrum defined in the 3D volume and obtained via the process of ensemble averaging, we establish the construction of the observed 3D power spectrum, folding the unequal-time information around the average position into the wave modes along the line of sight. We show how these unequal-time cross-correlation effects give rise to scale-dependent corrections in the observable 3D power spectrum. We also introduce a new dimensionless observable, the frequency-angular power spectrum, which is a function of dimensionless and directly observable quantities corresponding to Fourier counterparts of angles and redshifts. While inheriting many useful characteristics of the canonical observed power spectrum, this newly introduced statistic does not depend on physical distances and is hence free of so-called Alcock-Paczynski effects. Such observable thus presents a clear advantage and simplification over the traditional power spectrum. Moreover, relying on linear theory calculations, we estimate that unequal-time corrections, while generally small, can amount to a few percent on large scales and high redshifts. Interestingly, such corrections depend on the bias of the tracers, the growth rate, but also their time derivatives, opening up the possibility of new tests of cosmological models. These radial mode effects also introduce anisotropies in the observed power spectrum, in addition to the ones arising from redshift-space distortions, generating non-vanishing odd multiples and imaginary contributions. Lastly, we investigate the effects of unequal-time corrections in resumming long displacements (IR-resummation) of the observed power spectrum.

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arXiv2023

Power spectrum in the cave

Forthcoming galaxy surveys will provide measurements of galaxy clustering with an unprecedented level of precision, that will require comparably good accuracy. Current models for galaxy correlations rely on approximations and idealizations that might be inadequate for ultra precise measurements. On the other hand, exact calculations have proven to be computationally too expensive to be efficiently implemented in real data analyses. We start a project to provide precise and accurate formalisms for galaxy correlations, and in this paper we investigate the 3D angular power spectrum including effects of unequal time correlations. We establish an explicit link between the full- and flat-sky spectra by performing an asymptotic expansion of the full-sky result around the equal time case. The limiting case coincides with the idealized spectrum that a meta-observer would measure if it had access to the entire 4D Universe. The leading term in the obtained flat-sky expansion is the only translationally invariant term in the plane perpendicular to the line of sight, while the higher-order terms account for the deviation from this invariance. We study the behavior of such corrections for a simplified universe where we can analytically solve the power spectrum and have full control of the equations, therefore being able to understand the exact nature of all the terms and the origin of the corrections. We highlight that the conclusions and the structure of the unequal time spectra are fully general and serve as lessons and guidance in understanding galaxy clustering in any cosmology. Finally, we show that our flat-sky unequal time expression matches the exact full-sky calculation remarkably better than commonly adopted approximations, even at the largest scales and for both shallow and deep redshift bins.

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