The physical interpretation of perturbations of homogeneous, isotropic cosmological models in the early Universe, when the perturbation is larger than the particle horizon, is clarified by defining a complete set of gauge-invariant variables. The linearized perturbation equations written in these variables are simpler than the usual versions, and easily accommodate an arbitrary background equation of state, entropy perturbations, and anisotropic pressure perturbations. Particular attention is paid to how a scalar (density) perturbation might be generated by stress perturbations at very early times, when the non-gauge-invariant perturbation in the density itself is ill-defined. The amplitude of the fractional energy density perturbation at the particle horizon cannot be larger, in order of magnitude, than the maximum ratio of the stress perturbation to the background energy density at any earlier time, unless the perturbation is inherent in the initial singularity.

Gauge-Invariant Cosmological Perturbations

The cosmic connections between physics on the very largest and very smallest scales are reviewed with an emphasis on the symbiotic relation between elementary particle physics and cosmology. After a review of the early Universe as a cosmic accelerator, various cosmological and astrophysical constraints on models of particle physics are outlined. To illustrate this approach to particle physics via cosmology, reference is made to several areas of current research: baryon non-conservation and baryon asymmetry; free quarks, heavy hadrons and other exotic relics; primordial nucleosynthesis and neutrino masses. In the last few years we have witnessed the birth and growth to healthy adolescence of a new collaboration between astrophysicists and particle physicists. The most notable success of this cooperative effort has been to provide the framework for understanding, within the context of GUTs and the hot big-bang cosmology, the universal baryon asymmetry. The most exciting new predictions this effort has spawned are that exotic relics may exist in detectable abundances. In particular, we may live in a neutrino-dominated Universe. In the next few years, accummulating laboratory data (for example proton decay, neutrino masses and oscillations) coupled with theoritical work in particle physics and cosmology will ensure the growth to maturity of this joint effort.

Cosmology and particle physics

Galaxy imaging surveys provide us with information on both the galaxy distribution and their shapes. In this paper, we systematically investigate the sensitivity of galaxy shapes to new physics in the initial conditions. For this purpose, we decompose the galaxy shape function into spin components, and compute the contributions to each spin component from both intrinsic alignment and weak lensing. We then consider the angular-dependent primordial non-Gaussianity, which is generated by a non-zero integer spin particle when active during inflation, and show that a galaxy imaging survey essentially functions as a spin-sensitive detector of such particles in the early universe. We also perform a forecast of the PNG generated from a higher spin particle, considering a Rubin Observatory LSST-like galaxy survey.

Galaxy imaging surveys as spin-sensitive detector for cosmological colliders

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Updated neutrino mass constraints from galaxy clustering and CMB lensing-galaxy cross-correlation measurements

The shapes of galaxy N-point correlation functions can be used as standard rulers to constrain the distance-redshift relationship and thence the expansion rate of the Universe. The cosmological density fields traced by late-time galaxy formation are initially nearly Gaussian, and hence all the cosmological information can be extracted from their 2-Point Correlation Function (2PCF) or its Fourier-space analog the power spectrum. Subsequent nonlinear evolution under gravity, as well as halo and then galaxy formation, generate higher-order correlation functions. Since the mapping of the initial to the final density field is, on large scales, invertible, it is often claimed that the information content of the initial field's power spectrum is equal to that of all the higher-order functions of the final, nonlinear field. This claim implies that reconstruction of the initial density field from the nonlinear field renders analysis of higher-order correlation functions of the latter superfluous. We here show that this claim is false when the N-point functions are used as standard rulers. Constraints available from joint analysis of the galaxy power spectrum and bispectrum (Fourier-space analog of the 3-Point Correlation Function) can, in some cases, exceed those offered by the initial power spectrum even when the reconstruction is perfect. We provide a mathematical justification for this claim and also demonstrate it using a large suite of N-body simulations. In particular, we show that for the z = 0 real-space matter field in the limit of vanishing shot noise, taking modes up to k_max = 0.2 h/Mpc, using the bispectrum alone offers a factor of two reduction in the variance on the cosmic distance scale relative to that available from the power spectrum.

Information content of higher order galaxy correlation functions

We present the gauge-invariant formalism of cosmological weak lensing, accounting for all the relativistic effects due to the scalar, vector, and tensor perturbations at the linear order. While the light propagation is fully described by the geodesic equation, the relation of the photon wavevector to the physical quantities requires the specification of the frames, where they are defined. By constructing the local tetrad bases at the observer and the source positions, we clarify the relation of the weak lensing observables such as the convergence, the shear, and the rotation to the physical size and shape defined in the source rest-frame and the observed angle and redshift measured in the observer rest-frame. Compared to the standard lensing formalism, additional relativistic effects contribute to all the lensing observables. We explicitly verify the gauge-invariance of the lensing observables and compare our results to previous work. In particular, we demonstrate that even in the presence of the vector and tensor perturbations, the physical rotation of the lensing observables vanishes at the linear order, while the tetrad basis rotates along the light propagation compared to a FRW coordinate. Though the latter is often used as a probe of primordial gravitational waves, the rotation of the tetrad basis is indeed not a physical observable. We further clarify its relation to the E-B decomposition in weak lensing. Our formalism provides a transparent and comprehensive perspective of cosmological weak lensing.

Gauge-Invariant Formalism of Cosmological Weak Lensing

We present the galaxy power spectrum in general relativity. Using a novel approach, we derive the galaxy power spectrum taking into account all the relativistic effects in observations. In particular, we show independently of survey geometry that relativistic effects yield no divergent terms (proportional to $k^{-4}P_m(k)$ or $k^{-2}P_m(k)$ on all scales) that would mimic the signal of primordial non-Gaussianity. This cancellation of such divergent terms is indeed expected from the equivalence principle, meaning that any perturbation acting as a uniform gravity on the scale of the experiment cannot be measured. We find that the unphysical infrared divergence obtained in previous calculations occurred only due to not considering all general relativistic contributions consistently. Despite the absence of divergent terms, general relativistic effects represented by non-divergent terms alter the galaxy power spectrum at large scales (smaller than the horizon scale). In our numerical computation of the full galaxy power spectrum, we show the deviations from the standard redshift-space power spectrum due to these non-divergent corrections. We conclude that, as relativistic effects significantly alter the galaxy power spectrum at $k\lesssim k_{eq}$, they need to be taken into account in the analysis of large-scale data.

Galaxy power spectrum in general relativity

Gauge-Invariant Formalism of Cosmological Weak Lensing.

Cosmological weak lensing has been a highly successful and rapidly developing research field since the first detection of cosmic shear in 2000. However, it has recently been pointed out in Yoo et al. that the standard weak lensing formalism yields gauge-dependent results and, hence, does not meet the level of accuracy demanded by the next generation of weak lensing surveys. Here, we show that the Jacobi mapping formalism provides a solid alternative to the standard formalism, as it accurately describes all the relativistic effects contributing to the weak lensing observables. We calculate gauge-invariant expressions for the distortion in the luminosity distance, the cosmic shear components and the lensing rotation to linear order including scalar, vector and tensor perturbations. In particular, the Jacobi mapping formalism proves that the rotation is fully vanishing to linear order. Furthermore, the cosmic shear components contain an additional term in tensor modes which is absent in the results obtained with the standard formalism. Our work provides further support and confirmation of the gauge-invariant lensing formalism needed in the era of precision cosmology.

Jacobi mapping approach for a precise cosmological weak lensing formalism

Analytical computations in relativistic cosmology can be split into two sets: time evolution relating the initial conditions to the observer's light-cone and light propagation to obtain observables. Cosmological perturbation theory in the Friedmann–Lemaitre–Robertson–Walker (FLRW) coordinates constitutes an efficient tool for the former task, but the latter is dramatically simpler in light-cone-adapted coordinates that trivialize the light rays toward the observer world-line. Here we point out that time evolution and observable reconstruction can be combined into a single computation that relates directly initial conditions to observables. This is possible if one works uniquely in such light-cone coordinates, thus completely bypassing the FLRW 'middle-man' coordinates. We first present in detail these light-cone coordinates, extending and generalizing the presently available material in the literature, and construct a particularly convenient subset for cosmological perturbation theory. We then express the Einstein and energy–momentum conservation equations in these coordinates at the fully non-linear level. This is achieved through a careful 2 + 1 + 1 decomposition which leads to relatively compact expressions and provides good control over the geometrical interpretation of the involved quantities. Finally, we consider cosmological perturbation theory to linear order, paying attention to the remaining gauge symmetries and consistently obtaining gauge-invariant equations. Moreover, we show that it is possible to implement statistical homogeneity on stochastic fluctuations, despite the fact that the coordinate system privileges the observer world-line.

https://iopscience.iop.org/article/10.1088/1361-6382/abd681/pdf

Nastassia Grimm

Papers

Gauge-Invariant Formalism of Cosmological Weak Lensing

Galaxy power spectrum in general relativity

Gauge-Invariant Formalism of Cosmological Weak Lensing.

Jacobi mapping approach for a precise cosmological weak lensing formalism

Cutting out the cosmological middle man: general relativity in the light-cone coordinates